A user-friendly tool for incremental haemodialysis prescription

A user-friendly tool for incremental haemodialysis prescription ABSTRACT Background There is a recently heightened interest in incremental haemodialysis (IHD), the main advantage of which could likely be a better preservation of the residual kidney function of the patients. The implementation of IHD, however, is hindered by many factors, among them, the mathematical complexity of its prescription. The aim of our study was to design a user-friendly tool for IHD prescription, consisting of only a few rows of a common spreadsheet. Methods The keystone of our spreadsheet was the following fundamental concept: the dialysis dose to be prescribed in IHD depends only on the normalized urea clearance provided by the native kidneys (KRUn) of the patient for each frequency of treatment, according to the variable target model recently proposed by Casino and Basile (The variable target model: a paradigm shift in the incremental haemodialysis prescription. Nephrol Dial Transplant 2017; 32 182–190). The first step was to put in sequence a series of equations in order to calculate, firstly, KRUn and, then, the key parameters to be prescribed for an adequate IHD; the second step was to compare KRUn values obtained with our spreadsheet with KRUn values obtainable with the gold standard Solute-solver (Daugirdas JT et al., Solute-solver: a web-based tool for modeling urea kinetics for a broad range of hemodialysis schedules in multiple patients. Am J Kidney Dis 2009; 54 798–809) in a sample of 40 incident haemodialysis patients. Results Our spreadsheet provided excellent results. The differences with Solute-solver were clinically negligible. This was confirmed by the Bland–Altman plot built to analyse the agreement between KRUn values obtained with the two methods: the difference was 0.07 ± 0.05 mL/min/35 L. Conclusions Our spreadsheet is a user-friendly tool able to provide clinically acceptable results in IHD prescription. Two immediate consequences could derive: (i) a larger dissemination of IHD might occur; and (ii) our spreadsheet could represent a useful tool for an ineludibly needed full-fledged clinical trial, comparing IHD with standard thrice-weekly HD. dialysis adequacy, equilibrated Kt/V, haemodialysis, incremental haemodialysis, renal urea clearance INTRODUCTION There is a recently heightened interest in incremental haemodialysis (IHD) [1–3], the main advantage of which could likely be a better preservation of the residual kidney function (RKF) of patients [4]. Literature data suggest that in such a way IHD could improve not only the quality of life but also the survival of patients [5, 6]. The implementation of IHD, however, is hindered by many factors [7]. Among them, the most important, at least in our opinion, is the current overestimation of the dialysis needs in the presence of a substantial RKF, due to the erroneous assumption of the clinical equivalence between the urea dialyser clearance (Kd) and the urea clearance provided by the native kidneys (Kru) [7]. Another factor that could negatively impact on the dissemination of IHD is the mathematical complexity of its prescription. In fact, the current state of the art would require that haemodialysis (HD) prescription be done using the complex double pool (dp) urea kinetic model [8]. To this end, Daugirdas et al. published a very useful paper [9] endorsed by the last KDOQI clinical practice guidelines for HD adequacy [10]. The software, named ‘Solute-solver’, is freely available at www.ureakinetics.org; it is of great help for nephrologists who are skilled in information technology, but could represent a difficult task for less experienced clinicians. Being aware of these difficulties, we aimed at designing a user-friendly tool for IHD prescription, consisting of only a few rows of a common spreadsheet. We named it ‘SPEEDY’, by using the acronym of its whole definition: Spreadsheet for the Prescription of incrEmental haEmoDalYsis. Our hypothesis was that the equations written in the complex java script language of Solute-solver [9] could be translated into the more intuitive language of an electronic spreadsheet: it could provide less accurate but, anyway, clinically acceptable results. MATERIALS AND METHODS The keystone of SPEEDY was the following fundamental concept: the dialysis dose to be prescribed in IHD depends only on the normalized Kru (KRUn) of the patient for each frequency of treatment [7, 11], according to the variable target model recently proposed by Casino and Basile [7]. The first step was to put in sequence a series of equations in order to calculate, firstly, KRUn and the associated adequate equilibrated Kt/V (eKt/V) value and, then, the operative parameters, namely, the session length (Td) and/or the Kd required to attain the above eKt/V; the second and final step was to compare KRUn values obtained with SPEEDY with KRUn values obtainable with Solute-solver [9] in a sample of 40 incident HD patients. First step SPEEDY consists of five sections, corresponding to five sheets, namely, KRUn&eKt/V, Kd&Td, Kd&QB, KoA_vitro and PCRn (where QB is the blood flow rate; KoA_vitro the haemodialyzer mass transfer-area coefficient for urea; PCRn the normalized protein catabolic rate). The first sheet is the key one for IHD prescription, in that it calculates the eKt/V to be delivered when accounting for KRUn and dialysis schedule. To this end, a series of well-known equations, in most of cases identical to those used by Solute-solver [9], were put in a sequence aiming at calculating Kru and then the urea distribution volume (V) as dp V (Vdp), and finally the KRUn, to be used to establish the needed eKt/V. The general plan for such calculations is as follows: V can be computed by dividing Kt/V by [(Kd + Kru) × Td], which requires computing single pool (sp) Kt/V (spKt/V) and the knowledge of Td, Kd and Kru. The spKt/V can be computed by means of an equation built for non-thrice-weekly HD schedules [12]. The diffusive Kd (KDIF) can be estimated from KoA [13], which is usually known as an in vitro value, but should be converted into an in vivo value [9, 14]. To account for the convective component of Kd, not only in HD but also in haemodiafiltration (HDF), Daugirdas adopted the equations provided by Tattersall et al. [15] in the last version of Solute-solver (www.ureakinetics.org). SPEEDY uses the same equations. Such a V value, being derived from spKt/V, is a sp V (Vsp) and can be transformed into a Vdp by computing the Vsp/Vdp ratio according to Daugirdas and Smye [16]: the latter requires firstly computing eKt/V [17]. On the other hand, Kru can be computed from a timed urine collection, for instance, over the 24 h preceding the studied HD session, as allowed by a very recent formula by Daugirdas et al. [18, 19]. By multiplying Kru × 35 L/Vdp one gets KRUn [7, 11], which can be used to compute the eKt/V to be prescribed to attain the target with either the normalized total equivalent renal urea clearance (EKRUn), or the standard fractional urea clearance (stdKt/V) [11]. Here we describe the first sheet of SPEEDY (Figure 1): it consists of 39 rows: the first 15 rows are used as input, and each of the following 24 rows contains an equation that provides an output, to be used as an input for subsequent equations. For the sake of clarity, these equations, are written in the current form and listed in Table 1, whereas they are written in the spreadsheet language in Table 2. The latter form should be copied ‘as is’ in the cell of the same row in the column B of Sheet 1 (just overwriting the numbers of the example given in Figure 1). In this sheet, the input data for a kind of ‘reference patient’ (‘Patient 0’), with the appropriate measurement units, are shown in the cells B1–B15. By copying the 24 equations on the appropriate cells in column B, one gets 24 output values. We suggest saving the column B as a reference column and using an adjacent column (for instance D) to run a single patient, by typing the input data on the first 15 cells, and using the cells B16–B39 as a ‘template’, to be copied on the corresponding cells (D16–D39). Clearly, this could allow running many patients at the same time. Table 1 Equations (Eq.) used to compute the KRUn and the required eKt/V (Figure 1)   Equations  References  Eq. 1  Ultrafiltration rate: QF = (BW0 − BWT)/Td  [9]  Eq. 2  Dialyzer mass transfer-area coefficient for urea: KoA = KoA_vitro × 0.537 × [1 + 0.0549 × (QD − 500)/300]  [9]  Eq. 3  Blood water flow rate: QBW = 0.894 × QB + HDFPRE  [9], [15]  Eq. 4  Intermediate variable: EZ = EXP [KoA/QBW × (1 − QBW/QDDIF)]  [9], [13]  Eq. 5  Diffusive dialyser urea clearance: KDIF = QBW × (EZ − 1)/(EZ − QBW/QDDIF)  [8], [9], [13]  Eq. 6  Convective dialyser urea clearance: KCONV = (QBW − KDIF)/QBW × (QF + HDFPRE + HDFPOST)  [15]  Eq. 7  Dilution factor = 0.894 × QB/QBW  [15]  Eq. 8  Total (diffusive + convective) dialyser urea clearance: KTOT = (KDIF + KCONV) × Dilution factor  [15]  Eq. 9  Single pool (sp) Kt/V = −LN(R − 0.0174/PIDI × Td/60) + (4 − 3.5 × R) × (BW0 −BWT)/BWT  [12]  Eq. 10  Single pool urea distribution volume: Vsp = (Kd + Kru) × Td/spKt/V  [9], [16]  Eq. 11  eKt/V = spKt/V × [Td/(Td + 30.7)]  [9], [17]  Eq. 12  Intermediate variable: FDP1 = CT/EXP{LN(C0) – (eKt/V)/[(spKt/V)/LN(C0/CT)]}  [9], [16]  Eq. 13  Urea distribution volume ratio: Vratio = LN(FDP1 × C0/CT)/[FDP1 × Ln(C0/CT)]  [9], [16]  Eq. 14  Double pool urea distribution volume: Vdp = Vsp/V_ratio  [9], [16]  Eq. 15  Vdp/BWT: V/BWT = Vdp/BWT  [9]  Eq. 16  Time averaged C: TACSUNwater = C0 × [1.075 − (0.0038 × URR + 0.059)× UDUR/IDI]  [18]  Eq. 17  Renal urea clearance: Kru = (UUN × UO/1440)/TACSUNwater  [9], [18], [19]  Eq. 18  Normalized Kru: KRUn = Kru × 35/Vdp  [7], [11]  Eq. 19  eKt/V required on 1 HD/week with EKRUn: y = 0.1532x2–2.2250x + 7.9006  [11]  Eq. 20  eKt/V required on 2 HD/week with EKRUn: y = 0.0221x2–0.4979x + 2.24  [11]  Eq. 21  eKt/V required on 3 HD/week with EKRUn: y = 0.0068x2–0.2514x + 1.2979  [11]  Eq. 22  eKt/V required on 1 HD/week with stdKt/V: y = 0.1755x2–2.7563x + 10.999  [11]  Eq. 23  eKt/V required on 2 HD/week with stdKt/V: y = 0.0776x2–0.9091x + 3.157  [11]  Eq. 24  eKt/V required on 3 HD/week with stdKt/V: y = 0.0145x2–0.2549x + 1.2496  [11]    Equations  References  Eq. 1  Ultrafiltration rate: QF = (BW0 − BWT)/Td  [9]  Eq. 2  Dialyzer mass transfer-area coefficient for urea: KoA = KoA_vitro × 0.537 × [1 + 0.0549 × (QD − 500)/300]  [9]  Eq. 3  Blood water flow rate: QBW = 0.894 × QB + HDFPRE  [9], [15]  Eq. 4  Intermediate variable: EZ = EXP [KoA/QBW × (1 − QBW/QDDIF)]  [9], [13]  Eq. 5  Diffusive dialyser urea clearance: KDIF = QBW × (EZ − 1)/(EZ − QBW/QDDIF)  [8], [9], [13]  Eq. 6  Convective dialyser urea clearance: KCONV = (QBW − KDIF)/QBW × (QF + HDFPRE + HDFPOST)  [15]  Eq. 7  Dilution factor = 0.894 × QB/QBW  [15]  Eq. 8  Total (diffusive + convective) dialyser urea clearance: KTOT = (KDIF + KCONV) × Dilution factor  [15]  Eq. 9  Single pool (sp) Kt/V = −LN(R − 0.0174/PIDI × Td/60) + (4 − 3.5 × R) × (BW0 −BWT)/BWT  [12]  Eq. 10  Single pool urea distribution volume: Vsp = (Kd + Kru) × Td/spKt/V  [9], [16]  Eq. 11  eKt/V = spKt/V × [Td/(Td + 30.7)]  [9], [17]  Eq. 12  Intermediate variable: FDP1 = CT/EXP{LN(C0) – (eKt/V)/[(spKt/V)/LN(C0/CT)]}  [9], [16]  Eq. 13  Urea distribution volume ratio: Vratio = LN(FDP1 × C0/CT)/[FDP1 × Ln(C0/CT)]  [9], [16]  Eq. 14  Double pool urea distribution volume: Vdp = Vsp/V_ratio  [9], [16]  Eq. 15  Vdp/BWT: V/BWT = Vdp/BWT  [9]  Eq. 16  Time averaged C: TACSUNwater = C0 × [1.075 − (0.0038 × URR + 0.059)× UDUR/IDI]  [18]  Eq. 17  Renal urea clearance: Kru = (UUN × UO/1440)/TACSUNwater  [9], [18], [19]  Eq. 18  Normalized Kru: KRUn = Kru × 35/Vdp  [7], [11]  Eq. 19  eKt/V required on 1 HD/week with EKRUn: y = 0.1532x2–2.2250x + 7.9006  [11]  Eq. 20  eKt/V required on 2 HD/week with EKRUn: y = 0.0221x2–0.4979x + 2.24  [11]  Eq. 21  eKt/V required on 3 HD/week with EKRUn: y = 0.0068x2–0.2514x + 1.2979  [11]  Eq. 22  eKt/V required on 1 HD/week with stdKt/V: y = 0.1755x2–2.7563x + 10.999  [11]  Eq. 23  eKt/V required on 2 HD/week with stdKt/V: y = 0.0776x2–0.9091x + 3.157  [11]  Eq. 24  eKt/V required on 3 HD/week with stdKt/V: y = 0.0145x2–0.2549x + 1.2496  [11]  The key equations are written in bold. Table 1 Equations (Eq.) used to compute the KRUn and the required eKt/V (Figure 1)   Equations  References  Eq. 1  Ultrafiltration rate: QF = (BW0 − BWT)/Td  [9]  Eq. 2  Dialyzer mass transfer-area coefficient for urea: KoA = KoA_vitro × 0.537 × [1 + 0.0549 × (QD − 500)/300]  [9]  Eq. 3  Blood water flow rate: QBW = 0.894 × QB + HDFPRE  [9], [15]  Eq. 4  Intermediate variable: EZ = EXP [KoA/QBW × (1 − QBW/QDDIF)]  [9], [13]  Eq. 5  Diffusive dialyser urea clearance: KDIF = QBW × (EZ − 1)/(EZ − QBW/QDDIF)  [8], [9], [13]  Eq. 6  Convective dialyser urea clearance: KCONV = (QBW − KDIF)/QBW × (QF + HDFPRE + HDFPOST)  [15]  Eq. 7  Dilution factor = 0.894 × QB/QBW  [15]  Eq. 8  Total (diffusive + convective) dialyser urea clearance: KTOT = (KDIF + KCONV) × Dilution factor  [15]  Eq. 9  Single pool (sp) Kt/V = −LN(R − 0.0174/PIDI × Td/60) + (4 − 3.5 × R) × (BW0 −BWT)/BWT  [12]  Eq. 10  Single pool urea distribution volume: Vsp = (Kd + Kru) × Td/spKt/V  [9], [16]  Eq. 11  eKt/V = spKt/V × [Td/(Td + 30.7)]  [9], [17]  Eq. 12  Intermediate variable: FDP1 = CT/EXP{LN(C0) – (eKt/V)/[(spKt/V)/LN(C0/CT)]}  [9], [16]  Eq. 13  Urea distribution volume ratio: Vratio = LN(FDP1 × C0/CT)/[FDP1 × Ln(C0/CT)]  [9], [16]  Eq. 14  Double pool urea distribution volume: Vdp = Vsp/V_ratio  [9], [16]  Eq. 15  Vdp/BWT: V/BWT = Vdp/BWT  [9]  Eq. 16  Time averaged C: TACSUNwater = C0 × [1.075 − (0.0038 × URR + 0.059)× UDUR/IDI]  [18]  Eq. 17  Renal urea clearance: Kru = (UUN × UO/1440)/TACSUNwater  [9], [18], [19]  Eq. 18  Normalized Kru: KRUn = Kru × 35/Vdp  [7], [11]  Eq. 19  eKt/V required on 1 HD/week with EKRUn: y = 0.1532x2–2.2250x + 7.9006  [11]  Eq. 20  eKt/V required on 2 HD/week with EKRUn: y = 0.0221x2–0.4979x + 2.24  [11]  Eq. 21  eKt/V required on 3 HD/week with EKRUn: y = 0.0068x2–0.2514x + 1.2979  [11]  Eq. 22  eKt/V required on 1 HD/week with stdKt/V: y = 0.1755x2–2.7563x + 10.999  [11]  Eq. 23  eKt/V required on 2 HD/week with stdKt/V: y = 0.0776x2–0.9091x + 3.157  [11]  Eq. 24  eKt/V required on 3 HD/week with stdKt/V: y = 0.0145x2–0.2549x + 1.2496  [11]    Equations  References  Eq. 1  Ultrafiltration rate: QF = (BW0 − BWT)/Td  [9]  Eq. 2  Dialyzer mass transfer-area coefficient for urea: KoA = KoA_vitro × 0.537 × [1 + 0.0549 × (QD − 500)/300]  [9]  Eq. 3  Blood water flow rate: QBW = 0.894 × QB + HDFPRE  [9], [15]  Eq. 4  Intermediate variable: EZ = EXP [KoA/QBW × (1 − QBW/QDDIF)]  [9], [13]  Eq. 5  Diffusive dialyser urea clearance: KDIF = QBW × (EZ − 1)/(EZ − QBW/QDDIF)  [8], [9], [13]  Eq. 6  Convective dialyser urea clearance: KCONV = (QBW − KDIF)/QBW × (QF + HDFPRE + HDFPOST)  [15]  Eq. 7  Dilution factor = 0.894 × QB/QBW  [15]  Eq. 8  Total (diffusive + convective) dialyser urea clearance: KTOT = (KDIF + KCONV) × Dilution factor  [15]  Eq. 9  Single pool (sp) Kt/V = −LN(R − 0.0174/PIDI × Td/60) + (4 − 3.5 × R) × (BW0 −BWT)/BWT  [12]  Eq. 10  Single pool urea distribution volume: Vsp = (Kd + Kru) × Td/spKt/V  [9], [16]  Eq. 11  eKt/V = spKt/V × [Td/(Td + 30.7)]  [9], [17]  Eq. 12  Intermediate variable: FDP1 = CT/EXP{LN(C0) – (eKt/V)/[(spKt/V)/LN(C0/CT)]}  [9], [16]  Eq. 13  Urea distribution volume ratio: Vratio = LN(FDP1 × C0/CT)/[FDP1 × Ln(C0/CT)]  [9], [16]  Eq. 14  Double pool urea distribution volume: Vdp = Vsp/V_ratio  [9], [16]  Eq. 15  Vdp/BWT: V/BWT = Vdp/BWT  [9]  Eq. 16  Time averaged C: TACSUNwater = C0 × [1.075 − (0.0038 × URR + 0.059)× UDUR/IDI]  [18]  Eq. 17  Renal urea clearance: Kru = (UUN × UO/1440)/TACSUNwater  [9], [18], [19]  Eq. 18  Normalized Kru: KRUn = Kru × 35/Vdp  [7], [11]  Eq. 19  eKt/V required on 1 HD/week with EKRUn: y = 0.1532x2–2.2250x + 7.9006  [11]  Eq. 20  eKt/V required on 2 HD/week with EKRUn: y = 0.0221x2–0.4979x + 2.24  [11]  Eq. 21  eKt/V required on 3 HD/week with EKRUn: y = 0.0068x2–0.2514x + 1.2979  [11]  Eq. 22  eKt/V required on 1 HD/week with stdKt/V: y = 0.1755x2–2.7563x + 10.999  [11]  Eq. 23  eKt/V required on 2 HD/week with stdKt/V: y = 0.0776x2–0.9091x + 3.157  [11]  Eq. 24  eKt/V required on 3 HD/week with stdKt/V: y = 0.0145x2–0.2549x + 1.2496  [11]  The key equations are written in bold. Table 2 Formulae to be copied into the associated cells in column B of sheet 1 (Figure 1) B16  Eq.1  = (B3 − B4) × 1000/B5  B17  Eq. 2  = 0.537 × B11 × (1+ 0.0549 × (B9 − 500)/300)  B18  Eq. 3  = 0.894 × B6 + B7  B19  Eq. 4  = EXP(B17/B18 × (1 − B18/B9))  B20  Eq. 5  = B18 × (B19 − 1)/(B19 − B18/B9)  B21  Eq. 6  = (B18 − B20)/B18 × (B7+ B8 + B16)  B22  Eq. 7  = 0.894 × B6/B18  B23  Eq. 8  = (B20 + B21) × B22  B24  Eq. 9  = − LN(B13/B12 − 0.0174/B2 × B5/60) + (4 − 3.5 × B13/B12) × (B3 − B4)/B4  B25  Eq. 10  = (B23+B32) × B5/B24/1000  B26  Eq. 11  = B24 × (B5/(B5 + 30.7))  B27  Eq. 12  = B13/(EXP(LN(B12) − B26/(B24/LN(B12/B13))))  B28  Eq. 13  = LN(B27 × B12/B13)/(B27 × LN(B12/B13))  B29  Eq. 14  = B25/B28  B30  Eq. 15  = B29/B4  B31  Eq. 16  = B12 × (1.075 − (0.38 × (1 − B13/B12)+0.059) × 1440/(B2 × 1440 − B5))  B32  Eq. 17  = B14 × B15/B31/1440  B33  Eq. 18  = B32 × 35/B29  B34  Eq. 19  = 0.1532 × B332− 2.225 × B33 + 7.9006  B35  Eq. 20  = 0.0221 × B332− 0.4979 × B33 + 2.24  B36  Eq. 21  = 0.0068 × B332− 0.2514 × B33 + 1.2979  B37  Eq. 22  = 0.1755 × B332− 2.7563 × B33 + 10.999  B38  Eq. 23  = 0.0776 × B332− 0.9091 × B33 + 3.157  B39  Eq. 24  = 0.0145 × B332− 0.2549 × B33 + 1.2496  B16  Eq.1  = (B3 − B4) × 1000/B5  B17  Eq. 2  = 0.537 × B11 × (1+ 0.0549 × (B9 − 500)/300)  B18  Eq. 3  = 0.894 × B6 + B7  B19  Eq. 4  = EXP(B17/B18 × (1 − B18/B9))  B20  Eq. 5  = B18 × (B19 − 1)/(B19 − B18/B9)  B21  Eq. 6  = (B18 − B20)/B18 × (B7+ B8 + B16)  B22  Eq. 7  = 0.894 × B6/B18  B23  Eq. 8  = (B20 + B21) × B22  B24  Eq. 9  = − LN(B13/B12 − 0.0174/B2 × B5/60) + (4 − 3.5 × B13/B12) × (B3 − B4)/B4  B25  Eq. 10  = (B23+B32) × B5/B24/1000  B26  Eq. 11  = B24 × (B5/(B5 + 30.7))  B27  Eq. 12  = B13/(EXP(LN(B12) − B26/(B24/LN(B12/B13))))  B28  Eq. 13  = LN(B27 × B12/B13)/(B27 × LN(B12/B13))  B29  Eq. 14  = B25/B28  B30  Eq. 15  = B29/B4  B31  Eq. 16  = B12 × (1.075 − (0.38 × (1 − B13/B12)+0.059) × 1440/(B2 × 1440 − B5))  B32  Eq. 17  = B14 × B15/B31/1440  B33  Eq. 18  = B32 × 35/B29  B34  Eq. 19  = 0.1532 × B332− 2.225 × B33 + 7.9006  B35  Eq. 20  = 0.0221 × B332− 0.4979 × B33 + 2.24  B36  Eq. 21  = 0.0068 × B332− 0.2514 × B33 + 1.2979  B37  Eq. 22  = 0.1755 × B332− 2.7563 × B33 + 10.999  B38  Eq. 23  = 0.0776 × B332− 0.9091 × B33 + 3.157  B39  Eq. 24  = 0.0145 × B332− 0.2549 × B33 + 1.2496  The key formulae are written in bold. Table 2 Formulae to be copied into the associated cells in column B of sheet 1 (Figure 1) B16  Eq.1  = (B3 − B4) × 1000/B5  B17  Eq. 2  = 0.537 × B11 × (1+ 0.0549 × (B9 − 500)/300)  B18  Eq. 3  = 0.894 × B6 + B7  B19  Eq. 4  = EXP(B17/B18 × (1 − B18/B9))  B20  Eq. 5  = B18 × (B19 − 1)/(B19 − B18/B9)  B21  Eq. 6  = (B18 − B20)/B18 × (B7+ B8 + B16)  B22  Eq. 7  = 0.894 × B6/B18  B23  Eq. 8  = (B20 + B21) × B22  B24  Eq. 9  = − LN(B13/B12 − 0.0174/B2 × B5/60) + (4 − 3.5 × B13/B12) × (B3 − B4)/B4  B25  Eq. 10  = (B23+B32) × B5/B24/1000  B26  Eq. 11  = B24 × (B5/(B5 + 30.7))  B27  Eq. 12  = B13/(EXP(LN(B12) − B26/(B24/LN(B12/B13))))  B28  Eq. 13  = LN(B27 × B12/B13)/(B27 × LN(B12/B13))  B29  Eq. 14  = B25/B28  B30  Eq. 15  = B29/B4  B31  Eq. 16  = B12 × (1.075 − (0.38 × (1 − B13/B12)+0.059) × 1440/(B2 × 1440 − B5))  B32  Eq. 17  = B14 × B15/B31/1440  B33  Eq. 18  = B32 × 35/B29  B34  Eq. 19  = 0.1532 × B332− 2.225 × B33 + 7.9006  B35  Eq. 20  = 0.0221 × B332− 0.4979 × B33 + 2.24  B36  Eq. 21  = 0.0068 × B332− 0.2514 × B33 + 1.2979  B37  Eq. 22  = 0.1755 × B332− 2.7563 × B33 + 10.999  B38  Eq. 23  = 0.0776 × B332− 0.9091 × B33 + 3.157  B39  Eq. 24  = 0.0145 × B332− 0.2549 × B33 + 1.2496  B16  Eq.1  = (B3 − B4) × 1000/B5  B17  Eq. 2  = 0.537 × B11 × (1+ 0.0549 × (B9 − 500)/300)  B18  Eq. 3  = 0.894 × B6 + B7  B19  Eq. 4  = EXP(B17/B18 × (1 − B18/B9))  B20  Eq. 5  = B18 × (B19 − 1)/(B19 − B18/B9)  B21  Eq. 6  = (B18 − B20)/B18 × (B7+ B8 + B16)  B22  Eq. 7  = 0.894 × B6/B18  B23  Eq. 8  = (B20 + B21) × B22  B24  Eq. 9  = − LN(B13/B12 − 0.0174/B2 × B5/60) + (4 − 3.5 × B13/B12) × (B3 − B4)/B4  B25  Eq. 10  = (B23+B32) × B5/B24/1000  B26  Eq. 11  = B24 × (B5/(B5 + 30.7))  B27  Eq. 12  = B13/(EXP(LN(B12) − B26/(B24/LN(B12/B13))))  B28  Eq. 13  = LN(B27 × B12/B13)/(B27 × LN(B12/B13))  B29  Eq. 14  = B25/B28  B30  Eq. 15  = B29/B4  B31  Eq. 16  = B12 × (1.075 − (0.38 × (1 − B13/B12)+0.059) × 1440/(B2 × 1440 − B5))  B32  Eq. 17  = B14 × B15/B31/1440  B33  Eq. 18  = B32 × 35/B29  B34  Eq. 19  = 0.1532 × B332− 2.225 × B33 + 7.9006  B35  Eq. 20  = 0.0221 × B332− 0.4979 × B33 + 2.24  B36  Eq. 21  = 0.0068 × B332− 0.2514 × B33 + 1.2979  B37  Eq. 22  = 0.1755 × B332− 2.7563 × B33 + 10.999  B38  Eq. 23  = 0.0776 × B332− 0.9091 × B33 + 3.157  B39  Eq. 24  = 0.0145 × B332− 0.2549 × B33 + 1.2496  The key formulae are written in bold. FIGURE 1 View largeDownload slide Sheet 1 aims at computing, firstly, the normalized Kru (KRUn), and, then, the required eKt/V. The column B shows the input and output data for ‘Patient 0’, who is a kind of ‘reference patient’, allowing both an immediate check for the measurement units of the input data (cells B1–B15) as well as the magnitude of the expected output data (cells B16–B39). To run a single patient (e.g. Patient 1) one could type the input data on the cells D1–D15, and use the cells B16–B39 as a template to be copied on the cells D16–D39. As shown in the figure, by filling the input data set for additional patients one has simply to copy the template as needed. Of note, the key parameters, namely KRUn and eKt/V, are written in bold. A very important note is that in these calculations one can also use different units for urea concentration, such as mg/L or mmol/L, provided that the same units are used for blood (C0 and CT) and urine (UUN). FIGURE 1 View largeDownload slide Sheet 1 aims at computing, firstly, the normalized Kru (KRUn), and, then, the required eKt/V. The column B shows the input and output data for ‘Patient 0’, who is a kind of ‘reference patient’, allowing both an immediate check for the measurement units of the input data (cells B1–B15) as well as the magnitude of the expected output data (cells B16–B39). To run a single patient (e.g. Patient 1) one could type the input data on the cells D1–D15, and use the cells B16–B39 as a template to be copied on the cells D16–D39. As shown in the figure, by filling the input data set for additional patients one has simply to copy the template as needed. Of note, the key parameters, namely KRUn and eKt/V, are written in bold. A very important note is that in these calculations one can also use different units for urea concentration, such as mg/L or mmol/L, provided that the same units are used for blood (C0 and CT) and urine (UUN). As stated above, the final product of Sheet 1 is the eKt/V to be prescribed for a given patient, when accounting for her/his KRUn and dialysis schedule. The next sheet is named ‘Td&Kd’ and aims at calculating the values for both Td and Kd to be prescribed to attain the desired eKt/V (Figure 2). In short, if Td is fixed, the needed Kd (Kdn) could be computed as follows: Kdn = spKt/V × Vsp/Td [8]. This means that one has, firstly, to convert the required eKt/V into the associated spKt/V, and, then, estimate Vsp using the Daugirdas and Smye approach [16]. FIGURE 2 View largeDownload slide Quantitative calculation of Td and/or Kd needed to attain the required eKt/V. By copying the cells B6–B11 into the corresponding cells in column D–H, and using increasing Td values in the fifth row, one can approximate immediately the most suitable combination of the two parameters. FIGURE 2 View largeDownload slide Quantitative calculation of Td and/or Kd needed to attain the required eKt/V. By copying the cells B6–B11 into the corresponding cells in column D–H, and using increasing Td values in the fifth row, one can approximate immediately the most suitable combination of the two parameters. For the sake of clarity, the relevant equations are listed in Table 3, as written usually, and in Table 4, as written in the spreadsheet form. Again, we suggest saving the column B for the ‘Patient 0’ and using the active cells B6–B11 as a template. In order to select the most suitable values for both Td and Kd to be prescribed to a given patient, we suggest, firstly, typing the known values of Kru, Vdp and eKt/V required into cells D2, D3 and D4, respectively, and, then, copying these values into the corresponding cells in columns E–H. As shown in Figure 2, by using increasing values for Td, for instance, from 150 to 270 min (see cells D5–H5), and copying the cells B6–B11, the template, on the columns D–H, one can select the most suitable coupling of Td and Kd values. If needed, one could consider a time interval of 15 min or less. Once Kdn is known, it remains to compute the QB required as a function of dialyzer KoA and ultrafiltration. To this end, as shown in Figure 3, one can adapt just the same sheet used to compute KRUn, by only using the relevant lines, and using increasing values for QB (see cells D6−16), as done for Td in the previous sheet. Table 3 Equations (Eq.) used in Figure 2 to compute the Kd needed (Kdn) to attain the required eKt/V   Equations (Eq.)  References  Eq. 25  Single pool Kt/V: spKt/V = eKt/V × (Td + 30.7)/Td  [9], [17]  Eq. 26  Predicted Ct/C0: R = exp(−spKt/V/1.18)  [15]  Eq. 27  Intemediate variable: F = 1 – 0.44 × spKt/V/(Td/60)  [15]  Eq. 28  Volume ratio: V_ratio = Ln(F/R)/[F × Ln(1/R)]  [15]  Eq. 29  Single pool urea distribution volume: Vsp = Vdp × V_ratio  [15]  Eq.30  Needed Kd: Kdn = spKt/V × Vsp/Td × 1000 − Kru  [8]    Equations (Eq.)  References  Eq. 25  Single pool Kt/V: spKt/V = eKt/V × (Td + 30.7)/Td  [9], [17]  Eq. 26  Predicted Ct/C0: R = exp(−spKt/V/1.18)  [15]  Eq. 27  Intemediate variable: F = 1 – 0.44 × spKt/V/(Td/60)  [15]  Eq. 28  Volume ratio: V_ratio = Ln(F/R)/[F × Ln(1/R)]  [15]  Eq. 29  Single pool urea distribution volume: Vsp = Vdp × V_ratio  [15]  Eq.30  Needed Kd: Kdn = spKt/V × Vsp/Td × 1000 − Kru  [8]  Table 3 Equations (Eq.) used in Figure 2 to compute the Kd needed (Kdn) to attain the required eKt/V   Equations (Eq.)  References  Eq. 25  Single pool Kt/V: spKt/V = eKt/V × (Td + 30.7)/Td  [9], [17]  Eq. 26  Predicted Ct/C0: R = exp(−spKt/V/1.18)  [15]  Eq. 27  Intemediate variable: F = 1 – 0.44 × spKt/V/(Td/60)  [15]  Eq. 28  Volume ratio: V_ratio = Ln(F/R)/[F × Ln(1/R)]  [15]  Eq. 29  Single pool urea distribution volume: Vsp = Vdp × V_ratio  [15]  Eq.30  Needed Kd: Kdn = spKt/V × Vsp/Td × 1000 − Kru  [8]    Equations (Eq.)  References  Eq. 25  Single pool Kt/V: spKt/V = eKt/V × (Td + 30.7)/Td  [9], [17]  Eq. 26  Predicted Ct/C0: R = exp(−spKt/V/1.18)  [15]  Eq. 27  Intemediate variable: F = 1 – 0.44 × spKt/V/(Td/60)  [15]  Eq. 28  Volume ratio: V_ratio = Ln(F/R)/[F × Ln(1/R)]  [15]  Eq. 29  Single pool urea distribution volume: Vsp = Vdp × V_ratio  [15]  Eq.30  Needed Kd: Kdn = spKt/V × Vsp/Td × 1000 − Kru  [8]  Table 4 Formulae to be copied into the associated cells in column B of Sheet 2 (Figure 2) Cell  Equations  Spreadsheet formula  B6  Eq. 25  = B4 × (B5 + 30.7)/B5  B7  Eq. 26  = EXP(− B6/1.18)  B8  Eq. 27  = 1 − 0.44 × B6/(B5/60)  B9  Eq. 28  = LN(B8/B7)/(B8 × LN(1/B7))  B10  Eq. 29  = B3 × B9  B11  Eq. 30  = B6 × B10/B5 × 1000 − B2  Cell  Equations  Spreadsheet formula  B6  Eq. 25  = B4 × (B5 + 30.7)/B5  B7  Eq. 26  = EXP(− B6/1.18)  B8  Eq. 27  = 1 − 0.44 × B6/(B5/60)  B9  Eq. 28  = LN(B8/B7)/(B8 × LN(1/B7))  B10  Eq. 29  = B3 × B9  B11  Eq. 30  = B6 × B10/B5 × 1000 − B2  The key formulae are written in bold. Table 4 Formulae to be copied into the associated cells in column B of Sheet 2 (Figure 2) Cell  Equations  Spreadsheet formula  B6  Eq. 25  = B4 × (B5 + 30.7)/B5  B7  Eq. 26  = EXP(− B6/1.18)  B8  Eq. 27  = 1 − 0.44 × B6/(B5/60)  B9  Eq. 28  = LN(B8/B7)/(B8 × LN(1/B7))  B10  Eq. 29  = B3 × B9  B11  Eq. 30  = B6 × B10/B5 × 1000 − B2  Cell  Equations  Spreadsheet formula  B6  Eq. 25  = B4 × (B5 + 30.7)/B5  B7  Eq. 26  = EXP(− B6/1.18)  B8  Eq. 27  = 1 − 0.44 × B6/(B5/60)  B9  Eq. 28  = LN(B8/B7)/(B8 × LN(1/B7))  B10  Eq. 29  = B3 × B9  B11  Eq. 30  = B6 × B10/B5 × 1000 − B2  The key formulae are written in bold. FIGURE 3 View largeDownload slide Calculation of the QB to be prescribed to obtain the desired Kd. The same spreadsheet shown in Figure 1 is used, but the input is limited to the parameters required to compute Kd. FIGURE 3 View largeDownload slide Calculation of the QB to be prescribed to obtain the desired Kd. The same spreadsheet shown in Figure 1 is used, but the input is limited to the parameters required to compute Kd. For the sake of completeness, we have added two useful sheets to compute, respectively, the in vitro KoA [13] from the manufacturer’s data (Figure 4), and PCRn calculated according to Depner and Daugirdas equations [20], recently modified by Daugirdas [21] (Table 5 and Figure 5). Table 5 PCRn for thrice-weekly and twice-weekly HD schedules Thrice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [0.70 + 3.08/(Kt/V)] × Kru/V}   beginning of the week: PCRn  = C0/[36.3 + 5.48 Kt/V + 53.5/(Kt/V)] + 0.168   midweek: PCRn  = C0/[25.8 + 1.15 Kt/V + 56.4/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[16.3 + 4.30 Kt/V + 56.6/(Kt/V)] + 0.168  Twice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [1.15 + 4.56/(Kt/V)] × Kru/V}   beginning-of the week: PCRn  = C0/[48.0 + 5.14 Kt/V +79.0/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[33.0 + 3.60 Kt/V + 83.2/(Kt/V)] + 0.168  Thrice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [0.70 + 3.08/(Kt/V)] × Kru/V}   beginning of the week: PCRn  = C0/[36.3 + 5.48 Kt/V + 53.5/(Kt/V)] + 0.168   midweek: PCRn  = C0/[25.8 + 1.15 Kt/V + 56.4/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[16.3 + 4.30 Kt/V + 56.6/(Kt/V)] + 0.168  Twice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [1.15 + 4.56/(Kt/V)] × Kru/V}   beginning-of the week: PCRn  = C0/[48.0 + 5.14 Kt/V +79.0/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[33.0 + 3.60 Kt/V + 83.2/(Kt/V)] + 0.168  Table 5 PCRn for thrice-weekly and twice-weekly HD schedules Thrice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [0.70 + 3.08/(Kt/V)] × Kru/V}   beginning of the week: PCRn  = C0/[36.3 + 5.48 Kt/V + 53.5/(Kt/V)] + 0.168   midweek: PCRn  = C0/[25.8 + 1.15 Kt/V + 56.4/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[16.3 + 4.30 Kt/V + 56.6/(Kt/V)] + 0.168  Twice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [1.15 + 4.56/(Kt/V)] × Kru/V}   beginning-of the week: PCRn  = C0/[48.0 + 5.14 Kt/V +79.0/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[33.0 + 3.60 Kt/V + 83.2/(Kt/V)] + 0.168  Thrice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [0.70 + 3.08/(Kt/V)] × Kru/V}   beginning of the week: PCRn  = C0/[36.3 + 5.48 Kt/V + 53.5/(Kt/V)] + 0.168   midweek: PCRn  = C0/[25.8 + 1.15 Kt/V + 56.4/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[16.3 + 4.30 Kt/V + 56.6/(Kt/V)] + 0.168  Twice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [1.15 + 4.56/(Kt/V)] × Kru/V}   beginning-of the week: PCRn  = C0/[48.0 + 5.14 Kt/V +79.0/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[33.0 + 3.60 Kt/V + 83.2/(Kt/V)] + 0.168  FIGURE 4 View largeDownload slide Calculation of KoA in vitro by the manufacturer’s data. By using the reported in vitro KDIF value at the usual in vitro setting (for instance, QB = 300 mL/min and QD = 500 mL/min, QF = 0 mL/min), KoA_vitro can be easily computed by firstly splitting the Michaels equation [13] into two factors (i.e. F1 and F2) and then multiplying F1 × Ln(F2). FIGURE 4 View largeDownload slide Calculation of KoA in vitro by the manufacturer’s data. By using the reported in vitro KDIF value at the usual in vitro setting (for instance, QB = 300 mL/min and QD = 500 mL/min, QF = 0 mL/min), KoA_vitro can be easily computed by firstly splitting the Michaels equation [13] into two factors (i.e. F1 and F2) and then multiplying F1 × Ln(F2). FIGURE 5 View largeDownload slide Calculation of PCRn for thrice-weekly and twice-weekly HD schedules. The formulae introduced by Depner and Daugirdas [20] were typed on the cells B8–B15, for the Patient 0, to be used as template with one column per patient. Of note, the equations described by Depner and Daugirdas [20] were based on spKt/V values. However, our calculations are based on eKt/V and Vdp values, in agreement with very recent data by Daugirdas [21]. In contrast to the Sheet 1, here one has to use only concentrations of serum urea nitrogen in mg/dL. FIGURE 5 View largeDownload slide Calculation of PCRn for thrice-weekly and twice-weekly HD schedules. The formulae introduced by Depner and Daugirdas [20] were typed on the cells B8–B15, for the Patient 0, to be used as template with one column per patient. Of note, the equations described by Depner and Daugirdas [20] were based on spKt/V values. However, our calculations are based on eKt/V and Vdp values, in agreement with very recent data by Daugirdas [21]. In contrast to the Sheet 1, here one has to use only concentrations of serum urea nitrogen in mg/dL. Second step A randomly selected sample of 40 incident patients with measured RKF was extracted from the historical database of our unit [3]. We retrieved the data concerning one routine kinetic study performed within the first year of treatment. The main characteristics of the patients were: 20 males, age 68 ± 12 years, pre-dialysis body weight (BW0) 68.5 ± 12 kg, post-dialysis body weight (BWT) 66.8 ± 12 kg. Eighteen patients were on standard HD, 16 on pre-dilution HDF and 6 on post-dilution HDF, respectively; Td was 224 ± 13 min, in vitro KoA 1269 ± 170 mL/min. The data of these patients were used as input for both our spreadsheet and the Solute-solver [9]. Statistical analysis Data are given as mean ± standard deviation. The results were compared with the Student’s paired t-test (P < 0.05 was assumed as statistically significant). Bland–Altman plot analysed the agreement between KRUn values obtained with SPEEDY and Solute-solver [9]. RESULTS The key results provided by SPEEDY and Solute-solver [9] are given in Table 6. Briefly, the Kd values were almost identical, and all the differences between the paired parameters were minimal and clinically negligible (usually less than ±5% is acceptable), even if statistically significant. This was confirmed by the Bland–Altman plot built to analyse the agreement between KRUn values obtained with the two methods: the difference was 0.07 ± 0.05 mL/min/35 L (Figure 6). Table 6 The results obtained by means of Solute-solver [9] and SPEEDY are compared (n = 40)     Solute-solvera  SPEEDYa  Difference  Pb  Dialyzer urea clearance  Kd (mL/min)  199.0 ± 20.13  199.1 ± 20.12  − 0.04 ± 0.19  0.200  Single pool Kt/V  spKt/V  1.48 ± 0.24  1.46 ± 0.23  0.03 ± 0.02  0.000  Equilibrated Kt/V  eKt/V  1.31 ± 0.21  1.28 ± 0.21  0.02 ± 0.02  0.000  Single pool urea volume  Vsp (L)  30.64 ± 4.92  31.61 ± 5.00  − 0.97 ± 0.36  0.000  Double pool urea volume  Vdp (L)  30.01 ± 5.34  30.81 ± 5.37  0.80 ± 0.39  0.000  Renal urea clearance  Kru (mL/min)  2.47 ± 1.23  2.49 ± 1.26  − 0.02 ± 0.04  0.001  Normalized Kru  KRUn (mL/min/35 L)  2.98 ± 1.54  2.84 ± 1.41  0.15 ± 0.35  0.012      Solute-solvera  SPEEDYa  Difference  Pb  Dialyzer urea clearance  Kd (mL/min)  199.0 ± 20.13  199.1 ± 20.12  − 0.04 ± 0.19  0.200  Single pool Kt/V  spKt/V  1.48 ± 0.24  1.46 ± 0.23  0.03 ± 0.02  0.000  Equilibrated Kt/V  eKt/V  1.31 ± 0.21  1.28 ± 0.21  0.02 ± 0.02  0.000  Single pool urea volume  Vsp (L)  30.64 ± 4.92  31.61 ± 5.00  − 0.97 ± 0.36  0.000  Double pool urea volume  Vdp (L)  30.01 ± 5.34  30.81 ± 5.37  0.80 ± 0.39  0.000  Renal urea clearance  Kru (mL/min)  2.47 ± 1.23  2.49 ± 1.26  − 0.02 ± 0.04  0.001  Normalized Kru  KRUn (mL/min/35 L)  2.98 ± 1.54  2.84 ± 1.41  0.15 ± 0.35  0.012  a Means ± standard deviation. b Student’s paired t-test. Table 6 The results obtained by means of Solute-solver [9] and SPEEDY are compared (n = 40)     Solute-solvera  SPEEDYa  Difference  Pb  Dialyzer urea clearance  Kd (mL/min)  199.0 ± 20.13  199.1 ± 20.12  − 0.04 ± 0.19  0.200  Single pool Kt/V  spKt/V  1.48 ± 0.24  1.46 ± 0.23  0.03 ± 0.02  0.000  Equilibrated Kt/V  eKt/V  1.31 ± 0.21  1.28 ± 0.21  0.02 ± 0.02  0.000  Single pool urea volume  Vsp (L)  30.64 ± 4.92  31.61 ± 5.00  − 0.97 ± 0.36  0.000  Double pool urea volume  Vdp (L)  30.01 ± 5.34  30.81 ± 5.37  0.80 ± 0.39  0.000  Renal urea clearance  Kru (mL/min)  2.47 ± 1.23  2.49 ± 1.26  − 0.02 ± 0.04  0.001  Normalized Kru  KRUn (mL/min/35 L)  2.98 ± 1.54  2.84 ± 1.41  0.15 ± 0.35  0.012      Solute-solvera  SPEEDYa  Difference  Pb  Dialyzer urea clearance  Kd (mL/min)  199.0 ± 20.13  199.1 ± 20.12  − 0.04 ± 0.19  0.200  Single pool Kt/V  spKt/V  1.48 ± 0.24  1.46 ± 0.23  0.03 ± 0.02  0.000  Equilibrated Kt/V  eKt/V  1.31 ± 0.21  1.28 ± 0.21  0.02 ± 0.02  0.000  Single pool urea volume  Vsp (L)  30.64 ± 4.92  31.61 ± 5.00  − 0.97 ± 0.36  0.000  Double pool urea volume  Vdp (L)  30.01 ± 5.34  30.81 ± 5.37  0.80 ± 0.39  0.000  Renal urea clearance  Kru (mL/min)  2.47 ± 1.23  2.49 ± 1.26  − 0.02 ± 0.04  0.001  Normalized Kru  KRUn (mL/min/35 L)  2.98 ± 1.54  2.84 ± 1.41  0.15 ± 0.35  0.012  a Means ± standard deviation. b Student’s paired t-test. FIGURE 6 View largeDownload slide Bland–Altman plot showing the agreement between the KRUn values obtained with Solute-solver [9] and SPEEDY. FIGURE 6 View largeDownload slide Bland–Altman plot showing the agreement between the KRUn values obtained with Solute-solver [9] and SPEEDY. When commenting on some of the most relevant data shown in Figure 1, we would like to underline, with reference to Patient 0, the first key result, namely KRUn (shown in cell B33). In this example, KRUn = 2.4 mL/min/35 L. The following three rows (34–36) show the eKt/V required to get the dialysis adequacy on 1, 2 or 3 HD/week schedules, respectively, according to the relationship EKRUn = (12 – KRUn) [11]. In this example, one gets the following eKt/V values: 3.43, 1.17 and 0.73, meaning that with this KRUn the once-weekly schedule is not possible (eKt/V = 3.43), but the twice-weekly schedule is feasible with an eKt/V of 1.17. The thrice-weekly schedule could be done with a very low eKt/V of 0.73. The last three rows (37–39) show the eKt/V required to get stdKt/V(100%Kru) = 2.3 volumes/week, in agreement with the current KDOQI guidelines [10]. They are 5.37, 1.42 and 0.73, respectively. Similar to EKRUn, with stdKt/V the 1 HD/week schedule is not possible (eKt/V = 5.37); the 2 HD/week schedule is feasible with a slightly higher eKt/V (1.42); and the 3 HD/week schedule could be done with an eKt/V as low as 0.72. With regards to Figure 2, we would like to point out that, based on the proposed Td, one can immediately see the Kdn. For example, for Patient 1 a proposed Td of 240 min would require a Kdn of about 200 mL/min. Moreover, using the Sheet 3, one can realize that it could suffice using a dialyser with KoA of 800 mL/min and with a QB a little bit greater than 300 mL/min. A list of abbreviations is being provided as online Supplementary Material. DISCUSSION Recently, two new concepts have begun to emerge within the context of IHD: the first one is that, starting HD with an incremental approach seems to preserve RKF [4, 7]; the second is that, ‘the more the better’ principle may not be true anymore for HD patients with a substantial RKF: in fact, both a high dialysis dose and a high frequency of treatment could accelerate RKF decline [6, 7, 22]. These concepts are in contrast to the current clinical practice whereby patients are often started directly on the full 3 HD/week schedule, with the aim of providing an amount of dialysis as high as possible, to be sure that the minimum is being delivered. Such approach is favoured by at least two factors: (i) the current guidelines overestimate the need of dialysis in the presence of a substantial RKF [3, 7, 11]; and (ii) an accurate prescription of HD would require complex modelling [8, 9]. It has recently been pointed out that such an overestimation of the dialysis needs is due to the erroneous assumption of the clinical equivalence between Kru and Kd [7]. The mistake could be corrected, at least in part, by increasing the relative clinical weight of Kru. This has been done, independently, by Daugirdas et al. [23] and Casino and Basile [7]. The former authors changed the way of computing the stdKt/V, by adding Kru at a 100% strength; in this way Kru is no longer compressed, which translates into an increased relative clinical weight for Kru. With a different approach, Casino and Basile introduced the concept of a variable target for EKRUn, which also increases the relative clinical weight of Kru, because the target EKRU is set at very low levels when Kru is high and vice versa at a maximum level in anuria [7]. The latter authors, in order to ease the calculation of the adequate dialysis dose associated with the actual Kru, provided graphs with so-called ‘adequacy lines’, for 1, 2 and 3 HD sessions/week, for both EKRUn and stdKt/V [7, 11]. They also reported the fitting equations associated with the above adequacy lines that are the basis of IHD prescription [11]. At the present time, no available evidence favours either EKRUn or stdKt/V as a guide for IHD prescription. Actually, after the introduction of the variable target for EKRUn, the two equivalent clearances are more alike than we suspected and provide not particularly different results, at least as far as thrice-weekly and twice-weekly HD schedules are concerned [7, 11]. This is an important feature because, even if it is true that a trial on IHD is needed to confirm the hypothesis of a variable target for EKRUn with IHD, the current target for stdKt/V could be safely used to guide the twice-weekly HD schedule, using either the Solute-solver [9] or SPEEDY. The results presented in Table 6 and Figure 6 show that SPEEDY provides excellent results. This is due to the fact that the both SPEEDY and Solute-solver [9] compute some parameters using the same equations. Clearly, the two methods differ in many aspects. For instance, Solute-solver [9] uses iterations to compute urea generation rate, which, among other things, allows an accurate measurement of V. On the contrary, SPEEDY estimates Vsp by using a recent version of the classical Daugirdas equation that estimates the spKt/V for patients being dialysed with schedules different from the standard thrice-weekly schedule [12]. Then, SPEEDY converts Vsp into Vdp by, firstly, computing eKt/V with Tattersall et al. equation [17] and, then, using Daugirdas and Smye approach [16], just as the Solute-solver [9] does. The latter, however, uses such estimate of Vdp as a starting value for iterations aiming at providing a more accurate estimate of Vdp. Another difference is that Solute-solver [9] predicts the time-averaged urea concentration in serum water over the urine collection interval using iterations, whereas SPEEDY estimates it with another recent equation by Daugirdas et al. [18, 19]. Of note, the last six rows of Sheet 1 show the eKt/V required for 1, 2 and 3 HD/week schedules, based either on EKRUn or stdKt/V target, respectively. Obviously, too high or too low eKt/V values mean that the associated frequency of treatment is not possible. Having selected a realistic eKt/V value, one can fix Td, and estimate firstly Kd and then QB, as shown in Figures 2 and 3. In conclusion, SPEEDY is able to provide clinically acceptable results; thus, any interested reader/clinician could be encouraged to copy the few lines of the spreadsheet and get a personal tool for an easy and fast prescription of IHD. Two immediate consequences of the extensive utilization of SPEEDY could derive: (i) a larger dissemination of IHD might occur, potentially leading to advantages to patients, nephrologists, caregivers and financial resources; and (ii) SPEEDY could represent a useful tool to set an ineludibly needed full-fledged clinical trial, comparing IHD with standard thrice-weekly HD as far as some hard outcomes, such as survival and quality of life, are concerned [11]. SUPPLEMENTARY DATA Supplementary data are available at ndt online. CONFLICT OF INTEREST STATEMENT None declared. REFERENCES 1 Kalantar-Zadeh K, Casino FG. Let us give twice-weekly hemodialysis a chance: revisiting the taboo. Nephrol Dial Transplant  2014; 29: 1618– 1620 Google Scholar CrossRef Search ADS PubMed  2 Wong J, Vilar E, Davenport A et al.  . Incremental haemodialysis. Nephrol Dial Transplant  2015; 30: 1639– 1648 Google Scholar CrossRef Search ADS PubMed  3 Basile C, Casino FG, Kalantar-Zadeh K. Is incremental hemodialysis ready to return on the scene? From empiricism to kinetic modelling. J Nephrol  2017; 30: 521– 529 Google Scholar CrossRef Search ADS PubMed  4 Zhang M, Wang M, Li H et al.  . Association of initial twice-weekly hemodialysis treatment with preservation of residual kidney function in ESRD patients. Am J Nephrol  2014; 40: 140– 150 Google Scholar CrossRef Search ADS PubMed  5 Termorshuizen F, Dekker FW, van Manen JG et al.  . Relative contribution of residual renal function and different measures of adequacy to survival in hemodialysis patients: an analysis of the Netherlands Cooperative Study on the Adequacy of Dialysis (NECOSAD)-2. J Am Soc Nephrol  2004; 15: 1061– 1070 Google Scholar CrossRef Search ADS PubMed  6 Obi Y, Streja E, Rhee CM et al.  . Incremental hemodialysis, residual kidney function, and mortality risk in incident dialysis patients: a cohort study. Am J Kidney Dis  2016; 68: 256– 265 Google Scholar CrossRef Search ADS PubMed  7 Casino FG, Basile C. The variable target model: a paradigm shift in the incremental haemodialysis prescription. Nephrol Dial Transplant  2017; 32: 182– 190 Google Scholar CrossRef Search ADS PubMed  8 Depner TA. Prescribing Hemodialysis: A Guide to Urea Modeling . Boston, MA: Kluwer Academic Publishers, 1991 9 Daugirdas JT, Depner TA, Greene T et al.  . Solute-solver: a web-based tool for modeling urea kinetics for a broad range of hemodialysis schedules in multiple patients. Am J Kidney Dis  2009; 54: 798– 809 Google Scholar CrossRef Search ADS PubMed  10 National Kidney Foundation. KDOQI clinical practice guidelines for hemodialysis adequacy: 2015 update. Am J Kidney Dis  2015; 66: 884– 930 CrossRef Search ADS PubMed  11 Casino FG, Basile C. How to set the stage for a full-fledged clinical trial testing ‘incremental haemodialysis’. Nephrol Dial Transplant  2017; doi: https://doi.org/10.1093/ndt/gfx225 12 Daugirdas JT, Leypoldt KJ, Akonur A et al.  . The FHN Trial Group. Improved equation for estimating single-pool Kt/V at higher dialysis frequencies. Nephrol Dial Transplant  2013; 28: 2156– 2160 Google Scholar CrossRef Search ADS PubMed  13 Michaels AS. Operating parameters and performance criteria for hemodialyzers and other membrane-separation devices. Trans Am Soc Artif Intern Organs  1966; 12: 387– 392 Google Scholar PubMed  14 Depner TA, Greene T, Daugirdas JT et al.  . Dialyzer performance in the HEMO Study: in vivo K0A and true blood flow determined from a model of cross-dialyzer urea extraction. Asaio J  2004; 50: 85– 93 Google Scholar CrossRef Search ADS PubMed  15 Tattersall JE, Ward RA; EUDIAL group. Online haemodiafiltration: definition, dose quantification and safety revisited. Nephrol Dial Transplant  2013; 22: 542– 550 Google Scholar CrossRef Search ADS   16 Daugirdas JT, Smye SW. Effect of a two compartment distribution on apparent urea distribution volume. Kidney Int  1997; 51: 1270– 1723 Google Scholar CrossRef Search ADS PubMed  17 Tattersall JE, DeTakats D, Chamney P et al.  . The post-hemodialysis rebound: predicting and quantifying its effect on Kt/V. Kidney Int  1996; 50: 2094– 2102 Google Scholar CrossRef Search ADS PubMed  18 Daugirdas JT. Estimating time-averaged serum urea nitrogen concentration during various urine collection periods: a prediction equation for thrice weekly and biweekly dialysis schedules. Semin Dial  2016; 29: 507– 509 Google Scholar CrossRef Search ADS PubMed  19 Obi Y, Kalantar-Zadeh K, Streja E et al.  . Prediction equation for calculating residual kidney urea clearance using urine collections for different hemodialysis treatment frequencies and interdialytic intervals. Nephrol Dial Transplant  2018; 33: 530– 539 Google Scholar CrossRef Search ADS PubMed  20 Depner TA, Daugirdas JT. Equations for normalized protein catabolic rate based on two point modeling of hemodialysis urea kinetics. J Am Soc Nephrol  1996; 7: 780– 785 Google Scholar PubMed  21 Daugirdas JT. Errors in computing the normalized protein catabolic rate due to use of single-pool urea kinetic modeling or to omission of the residual kidney urea clearance. J Ren Nutr  2017; 27: 256– 259 Google Scholar CrossRef Search ADS PubMed  22 Daugirdas JT, Green T, Rocco MV et al.  . Effect of frequent hemodialysis on residual kidney function. Kidney Int  2013; 83: 949– 958 Google Scholar CrossRef Search ADS PubMed  23 Daugirdas JT, Depner TA, Greene T et al.  .; Frequent Hemodialysis Network Trial Group. Standard Kt/V(urea): a method of calculation that includes effects of fluid removal and residual kidney clearance. Kidney Int  2010; 77: 637– 644 Google Scholar CrossRef Search ADS PubMed  © The Author(s) 2018. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nephrology Dialysis Transplantation Oxford University Press

A user-friendly tool for incremental haemodialysis prescription

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Oxford University Press
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© The Author(s) 2018. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.
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0931-0509
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1460-2385
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10.1093/ndt/gfx343
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Abstract

ABSTRACT Background There is a recently heightened interest in incremental haemodialysis (IHD), the main advantage of which could likely be a better preservation of the residual kidney function of the patients. The implementation of IHD, however, is hindered by many factors, among them, the mathematical complexity of its prescription. The aim of our study was to design a user-friendly tool for IHD prescription, consisting of only a few rows of a common spreadsheet. Methods The keystone of our spreadsheet was the following fundamental concept: the dialysis dose to be prescribed in IHD depends only on the normalized urea clearance provided by the native kidneys (KRUn) of the patient for each frequency of treatment, according to the variable target model recently proposed by Casino and Basile (The variable target model: a paradigm shift in the incremental haemodialysis prescription. Nephrol Dial Transplant 2017; 32 182–190). The first step was to put in sequence a series of equations in order to calculate, firstly, KRUn and, then, the key parameters to be prescribed for an adequate IHD; the second step was to compare KRUn values obtained with our spreadsheet with KRUn values obtainable with the gold standard Solute-solver (Daugirdas JT et al., Solute-solver: a web-based tool for modeling urea kinetics for a broad range of hemodialysis schedules in multiple patients. Am J Kidney Dis 2009; 54 798–809) in a sample of 40 incident haemodialysis patients. Results Our spreadsheet provided excellent results. The differences with Solute-solver were clinically negligible. This was confirmed by the Bland–Altman plot built to analyse the agreement between KRUn values obtained with the two methods: the difference was 0.07 ± 0.05 mL/min/35 L. Conclusions Our spreadsheet is a user-friendly tool able to provide clinically acceptable results in IHD prescription. Two immediate consequences could derive: (i) a larger dissemination of IHD might occur; and (ii) our spreadsheet could represent a useful tool for an ineludibly needed full-fledged clinical trial, comparing IHD with standard thrice-weekly HD. dialysis adequacy, equilibrated Kt/V, haemodialysis, incremental haemodialysis, renal urea clearance INTRODUCTION There is a recently heightened interest in incremental haemodialysis (IHD) [1–3], the main advantage of which could likely be a better preservation of the residual kidney function (RKF) of patients [4]. Literature data suggest that in such a way IHD could improve not only the quality of life but also the survival of patients [5, 6]. The implementation of IHD, however, is hindered by many factors [7]. Among them, the most important, at least in our opinion, is the current overestimation of the dialysis needs in the presence of a substantial RKF, due to the erroneous assumption of the clinical equivalence between the urea dialyser clearance (Kd) and the urea clearance provided by the native kidneys (Kru) [7]. Another factor that could negatively impact on the dissemination of IHD is the mathematical complexity of its prescription. In fact, the current state of the art would require that haemodialysis (HD) prescription be done using the complex double pool (dp) urea kinetic model [8]. To this end, Daugirdas et al. published a very useful paper [9] endorsed by the last KDOQI clinical practice guidelines for HD adequacy [10]. The software, named ‘Solute-solver’, is freely available at www.ureakinetics.org; it is of great help for nephrologists who are skilled in information technology, but could represent a difficult task for less experienced clinicians. Being aware of these difficulties, we aimed at designing a user-friendly tool for IHD prescription, consisting of only a few rows of a common spreadsheet. We named it ‘SPEEDY’, by using the acronym of its whole definition: Spreadsheet for the Prescription of incrEmental haEmoDalYsis. Our hypothesis was that the equations written in the complex java script language of Solute-solver [9] could be translated into the more intuitive language of an electronic spreadsheet: it could provide less accurate but, anyway, clinically acceptable results. MATERIALS AND METHODS The keystone of SPEEDY was the following fundamental concept: the dialysis dose to be prescribed in IHD depends only on the normalized Kru (KRUn) of the patient for each frequency of treatment [7, 11], according to the variable target model recently proposed by Casino and Basile [7]. The first step was to put in sequence a series of equations in order to calculate, firstly, KRUn and the associated adequate equilibrated Kt/V (eKt/V) value and, then, the operative parameters, namely, the session length (Td) and/or the Kd required to attain the above eKt/V; the second and final step was to compare KRUn values obtained with SPEEDY with KRUn values obtainable with Solute-solver [9] in a sample of 40 incident HD patients. First step SPEEDY consists of five sections, corresponding to five sheets, namely, KRUn&eKt/V, Kd&Td, Kd&QB, KoA_vitro and PCRn (where QB is the blood flow rate; KoA_vitro the haemodialyzer mass transfer-area coefficient for urea; PCRn the normalized protein catabolic rate). The first sheet is the key one for IHD prescription, in that it calculates the eKt/V to be delivered when accounting for KRUn and dialysis schedule. To this end, a series of well-known equations, in most of cases identical to those used by Solute-solver [9], were put in a sequence aiming at calculating Kru and then the urea distribution volume (V) as dp V (Vdp), and finally the KRUn, to be used to establish the needed eKt/V. The general plan for such calculations is as follows: V can be computed by dividing Kt/V by [(Kd + Kru) × Td], which requires computing single pool (sp) Kt/V (spKt/V) and the knowledge of Td, Kd and Kru. The spKt/V can be computed by means of an equation built for non-thrice-weekly HD schedules [12]. The diffusive Kd (KDIF) can be estimated from KoA [13], which is usually known as an in vitro value, but should be converted into an in vivo value [9, 14]. To account for the convective component of Kd, not only in HD but also in haemodiafiltration (HDF), Daugirdas adopted the equations provided by Tattersall et al. [15] in the last version of Solute-solver (www.ureakinetics.org). SPEEDY uses the same equations. Such a V value, being derived from spKt/V, is a sp V (Vsp) and can be transformed into a Vdp by computing the Vsp/Vdp ratio according to Daugirdas and Smye [16]: the latter requires firstly computing eKt/V [17]. On the other hand, Kru can be computed from a timed urine collection, for instance, over the 24 h preceding the studied HD session, as allowed by a very recent formula by Daugirdas et al. [18, 19]. By multiplying Kru × 35 L/Vdp one gets KRUn [7, 11], which can be used to compute the eKt/V to be prescribed to attain the target with either the normalized total equivalent renal urea clearance (EKRUn), or the standard fractional urea clearance (stdKt/V) [11]. Here we describe the first sheet of SPEEDY (Figure 1): it consists of 39 rows: the first 15 rows are used as input, and each of the following 24 rows contains an equation that provides an output, to be used as an input for subsequent equations. For the sake of clarity, these equations, are written in the current form and listed in Table 1, whereas they are written in the spreadsheet language in Table 2. The latter form should be copied ‘as is’ in the cell of the same row in the column B of Sheet 1 (just overwriting the numbers of the example given in Figure 1). In this sheet, the input data for a kind of ‘reference patient’ (‘Patient 0’), with the appropriate measurement units, are shown in the cells B1–B15. By copying the 24 equations on the appropriate cells in column B, one gets 24 output values. We suggest saving the column B as a reference column and using an adjacent column (for instance D) to run a single patient, by typing the input data on the first 15 cells, and using the cells B16–B39 as a ‘template’, to be copied on the corresponding cells (D16–D39). Clearly, this could allow running many patients at the same time. Table 1 Equations (Eq.) used to compute the KRUn and the required eKt/V (Figure 1)   Equations  References  Eq. 1  Ultrafiltration rate: QF = (BW0 − BWT)/Td  [9]  Eq. 2  Dialyzer mass transfer-area coefficient for urea: KoA = KoA_vitro × 0.537 × [1 + 0.0549 × (QD − 500)/300]  [9]  Eq. 3  Blood water flow rate: QBW = 0.894 × QB + HDFPRE  [9], [15]  Eq. 4  Intermediate variable: EZ = EXP [KoA/QBW × (1 − QBW/QDDIF)]  [9], [13]  Eq. 5  Diffusive dialyser urea clearance: KDIF = QBW × (EZ − 1)/(EZ − QBW/QDDIF)  [8], [9], [13]  Eq. 6  Convective dialyser urea clearance: KCONV = (QBW − KDIF)/QBW × (QF + HDFPRE + HDFPOST)  [15]  Eq. 7  Dilution factor = 0.894 × QB/QBW  [15]  Eq. 8  Total (diffusive + convective) dialyser urea clearance: KTOT = (KDIF + KCONV) × Dilution factor  [15]  Eq. 9  Single pool (sp) Kt/V = −LN(R − 0.0174/PIDI × Td/60) + (4 − 3.5 × R) × (BW0 −BWT)/BWT  [12]  Eq. 10  Single pool urea distribution volume: Vsp = (Kd + Kru) × Td/spKt/V  [9], [16]  Eq. 11  eKt/V = spKt/V × [Td/(Td + 30.7)]  [9], [17]  Eq. 12  Intermediate variable: FDP1 = CT/EXP{LN(C0) – (eKt/V)/[(spKt/V)/LN(C0/CT)]}  [9], [16]  Eq. 13  Urea distribution volume ratio: Vratio = LN(FDP1 × C0/CT)/[FDP1 × Ln(C0/CT)]  [9], [16]  Eq. 14  Double pool urea distribution volume: Vdp = Vsp/V_ratio  [9], [16]  Eq. 15  Vdp/BWT: V/BWT = Vdp/BWT  [9]  Eq. 16  Time averaged C: TACSUNwater = C0 × [1.075 − (0.0038 × URR + 0.059)× UDUR/IDI]  [18]  Eq. 17  Renal urea clearance: Kru = (UUN × UO/1440)/TACSUNwater  [9], [18], [19]  Eq. 18  Normalized Kru: KRUn = Kru × 35/Vdp  [7], [11]  Eq. 19  eKt/V required on 1 HD/week with EKRUn: y = 0.1532x2–2.2250x + 7.9006  [11]  Eq. 20  eKt/V required on 2 HD/week with EKRUn: y = 0.0221x2–0.4979x + 2.24  [11]  Eq. 21  eKt/V required on 3 HD/week with EKRUn: y = 0.0068x2–0.2514x + 1.2979  [11]  Eq. 22  eKt/V required on 1 HD/week with stdKt/V: y = 0.1755x2–2.7563x + 10.999  [11]  Eq. 23  eKt/V required on 2 HD/week with stdKt/V: y = 0.0776x2–0.9091x + 3.157  [11]  Eq. 24  eKt/V required on 3 HD/week with stdKt/V: y = 0.0145x2–0.2549x + 1.2496  [11]    Equations  References  Eq. 1  Ultrafiltration rate: QF = (BW0 − BWT)/Td  [9]  Eq. 2  Dialyzer mass transfer-area coefficient for urea: KoA = KoA_vitro × 0.537 × [1 + 0.0549 × (QD − 500)/300]  [9]  Eq. 3  Blood water flow rate: QBW = 0.894 × QB + HDFPRE  [9], [15]  Eq. 4  Intermediate variable: EZ = EXP [KoA/QBW × (1 − QBW/QDDIF)]  [9], [13]  Eq. 5  Diffusive dialyser urea clearance: KDIF = QBW × (EZ − 1)/(EZ − QBW/QDDIF)  [8], [9], [13]  Eq. 6  Convective dialyser urea clearance: KCONV = (QBW − KDIF)/QBW × (QF + HDFPRE + HDFPOST)  [15]  Eq. 7  Dilution factor = 0.894 × QB/QBW  [15]  Eq. 8  Total (diffusive + convective) dialyser urea clearance: KTOT = (KDIF + KCONV) × Dilution factor  [15]  Eq. 9  Single pool (sp) Kt/V = −LN(R − 0.0174/PIDI × Td/60) + (4 − 3.5 × R) × (BW0 −BWT)/BWT  [12]  Eq. 10  Single pool urea distribution volume: Vsp = (Kd + Kru) × Td/spKt/V  [9], [16]  Eq. 11  eKt/V = spKt/V × [Td/(Td + 30.7)]  [9], [17]  Eq. 12  Intermediate variable: FDP1 = CT/EXP{LN(C0) – (eKt/V)/[(spKt/V)/LN(C0/CT)]}  [9], [16]  Eq. 13  Urea distribution volume ratio: Vratio = LN(FDP1 × C0/CT)/[FDP1 × Ln(C0/CT)]  [9], [16]  Eq. 14  Double pool urea distribution volume: Vdp = Vsp/V_ratio  [9], [16]  Eq. 15  Vdp/BWT: V/BWT = Vdp/BWT  [9]  Eq. 16  Time averaged C: TACSUNwater = C0 × [1.075 − (0.0038 × URR + 0.059)× UDUR/IDI]  [18]  Eq. 17  Renal urea clearance: Kru = (UUN × UO/1440)/TACSUNwater  [9], [18], [19]  Eq. 18  Normalized Kru: KRUn = Kru × 35/Vdp  [7], [11]  Eq. 19  eKt/V required on 1 HD/week with EKRUn: y = 0.1532x2–2.2250x + 7.9006  [11]  Eq. 20  eKt/V required on 2 HD/week with EKRUn: y = 0.0221x2–0.4979x + 2.24  [11]  Eq. 21  eKt/V required on 3 HD/week with EKRUn: y = 0.0068x2–0.2514x + 1.2979  [11]  Eq. 22  eKt/V required on 1 HD/week with stdKt/V: y = 0.1755x2–2.7563x + 10.999  [11]  Eq. 23  eKt/V required on 2 HD/week with stdKt/V: y = 0.0776x2–0.9091x + 3.157  [11]  Eq. 24  eKt/V required on 3 HD/week with stdKt/V: y = 0.0145x2–0.2549x + 1.2496  [11]  The key equations are written in bold. Table 1 Equations (Eq.) used to compute the KRUn and the required eKt/V (Figure 1)   Equations  References  Eq. 1  Ultrafiltration rate: QF = (BW0 − BWT)/Td  [9]  Eq. 2  Dialyzer mass transfer-area coefficient for urea: KoA = KoA_vitro × 0.537 × [1 + 0.0549 × (QD − 500)/300]  [9]  Eq. 3  Blood water flow rate: QBW = 0.894 × QB + HDFPRE  [9], [15]  Eq. 4  Intermediate variable: EZ = EXP [KoA/QBW × (1 − QBW/QDDIF)]  [9], [13]  Eq. 5  Diffusive dialyser urea clearance: KDIF = QBW × (EZ − 1)/(EZ − QBW/QDDIF)  [8], [9], [13]  Eq. 6  Convective dialyser urea clearance: KCONV = (QBW − KDIF)/QBW × (QF + HDFPRE + HDFPOST)  [15]  Eq. 7  Dilution factor = 0.894 × QB/QBW  [15]  Eq. 8  Total (diffusive + convective) dialyser urea clearance: KTOT = (KDIF + KCONV) × Dilution factor  [15]  Eq. 9  Single pool (sp) Kt/V = −LN(R − 0.0174/PIDI × Td/60) + (4 − 3.5 × R) × (BW0 −BWT)/BWT  [12]  Eq. 10  Single pool urea distribution volume: Vsp = (Kd + Kru) × Td/spKt/V  [9], [16]  Eq. 11  eKt/V = spKt/V × [Td/(Td + 30.7)]  [9], [17]  Eq. 12  Intermediate variable: FDP1 = CT/EXP{LN(C0) – (eKt/V)/[(spKt/V)/LN(C0/CT)]}  [9], [16]  Eq. 13  Urea distribution volume ratio: Vratio = LN(FDP1 × C0/CT)/[FDP1 × Ln(C0/CT)]  [9], [16]  Eq. 14  Double pool urea distribution volume: Vdp = Vsp/V_ratio  [9], [16]  Eq. 15  Vdp/BWT: V/BWT = Vdp/BWT  [9]  Eq. 16  Time averaged C: TACSUNwater = C0 × [1.075 − (0.0038 × URR + 0.059)× UDUR/IDI]  [18]  Eq. 17  Renal urea clearance: Kru = (UUN × UO/1440)/TACSUNwater  [9], [18], [19]  Eq. 18  Normalized Kru: KRUn = Kru × 35/Vdp  [7], [11]  Eq. 19  eKt/V required on 1 HD/week with EKRUn: y = 0.1532x2–2.2250x + 7.9006  [11]  Eq. 20  eKt/V required on 2 HD/week with EKRUn: y = 0.0221x2–0.4979x + 2.24  [11]  Eq. 21  eKt/V required on 3 HD/week with EKRUn: y = 0.0068x2–0.2514x + 1.2979  [11]  Eq. 22  eKt/V required on 1 HD/week with stdKt/V: y = 0.1755x2–2.7563x + 10.999  [11]  Eq. 23  eKt/V required on 2 HD/week with stdKt/V: y = 0.0776x2–0.9091x + 3.157  [11]  Eq. 24  eKt/V required on 3 HD/week with stdKt/V: y = 0.0145x2–0.2549x + 1.2496  [11]    Equations  References  Eq. 1  Ultrafiltration rate: QF = (BW0 − BWT)/Td  [9]  Eq. 2  Dialyzer mass transfer-area coefficient for urea: KoA = KoA_vitro × 0.537 × [1 + 0.0549 × (QD − 500)/300]  [9]  Eq. 3  Blood water flow rate: QBW = 0.894 × QB + HDFPRE  [9], [15]  Eq. 4  Intermediate variable: EZ = EXP [KoA/QBW × (1 − QBW/QDDIF)]  [9], [13]  Eq. 5  Diffusive dialyser urea clearance: KDIF = QBW × (EZ − 1)/(EZ − QBW/QDDIF)  [8], [9], [13]  Eq. 6  Convective dialyser urea clearance: KCONV = (QBW − KDIF)/QBW × (QF + HDFPRE + HDFPOST)  [15]  Eq. 7  Dilution factor = 0.894 × QB/QBW  [15]  Eq. 8  Total (diffusive + convective) dialyser urea clearance: KTOT = (KDIF + KCONV) × Dilution factor  [15]  Eq. 9  Single pool (sp) Kt/V = −LN(R − 0.0174/PIDI × Td/60) + (4 − 3.5 × R) × (BW0 −BWT)/BWT  [12]  Eq. 10  Single pool urea distribution volume: Vsp = (Kd + Kru) × Td/spKt/V  [9], [16]  Eq. 11  eKt/V = spKt/V × [Td/(Td + 30.7)]  [9], [17]  Eq. 12  Intermediate variable: FDP1 = CT/EXP{LN(C0) – (eKt/V)/[(spKt/V)/LN(C0/CT)]}  [9], [16]  Eq. 13  Urea distribution volume ratio: Vratio = LN(FDP1 × C0/CT)/[FDP1 × Ln(C0/CT)]  [9], [16]  Eq. 14  Double pool urea distribution volume: Vdp = Vsp/V_ratio  [9], [16]  Eq. 15  Vdp/BWT: V/BWT = Vdp/BWT  [9]  Eq. 16  Time averaged C: TACSUNwater = C0 × [1.075 − (0.0038 × URR + 0.059)× UDUR/IDI]  [18]  Eq. 17  Renal urea clearance: Kru = (UUN × UO/1440)/TACSUNwater  [9], [18], [19]  Eq. 18  Normalized Kru: KRUn = Kru × 35/Vdp  [7], [11]  Eq. 19  eKt/V required on 1 HD/week with EKRUn: y = 0.1532x2–2.2250x + 7.9006  [11]  Eq. 20  eKt/V required on 2 HD/week with EKRUn: y = 0.0221x2–0.4979x + 2.24  [11]  Eq. 21  eKt/V required on 3 HD/week with EKRUn: y = 0.0068x2–0.2514x + 1.2979  [11]  Eq. 22  eKt/V required on 1 HD/week with stdKt/V: y = 0.1755x2–2.7563x + 10.999  [11]  Eq. 23  eKt/V required on 2 HD/week with stdKt/V: y = 0.0776x2–0.9091x + 3.157  [11]  Eq. 24  eKt/V required on 3 HD/week with stdKt/V: y = 0.0145x2–0.2549x + 1.2496  [11]  The key equations are written in bold. Table 2 Formulae to be copied into the associated cells in column B of sheet 1 (Figure 1) B16  Eq.1  = (B3 − B4) × 1000/B5  B17  Eq. 2  = 0.537 × B11 × (1+ 0.0549 × (B9 − 500)/300)  B18  Eq. 3  = 0.894 × B6 + B7  B19  Eq. 4  = EXP(B17/B18 × (1 − B18/B9))  B20  Eq. 5  = B18 × (B19 − 1)/(B19 − B18/B9)  B21  Eq. 6  = (B18 − B20)/B18 × (B7+ B8 + B16)  B22  Eq. 7  = 0.894 × B6/B18  B23  Eq. 8  = (B20 + B21) × B22  B24  Eq. 9  = − LN(B13/B12 − 0.0174/B2 × B5/60) + (4 − 3.5 × B13/B12) × (B3 − B4)/B4  B25  Eq. 10  = (B23+B32) × B5/B24/1000  B26  Eq. 11  = B24 × (B5/(B5 + 30.7))  B27  Eq. 12  = B13/(EXP(LN(B12) − B26/(B24/LN(B12/B13))))  B28  Eq. 13  = LN(B27 × B12/B13)/(B27 × LN(B12/B13))  B29  Eq. 14  = B25/B28  B30  Eq. 15  = B29/B4  B31  Eq. 16  = B12 × (1.075 − (0.38 × (1 − B13/B12)+0.059) × 1440/(B2 × 1440 − B5))  B32  Eq. 17  = B14 × B15/B31/1440  B33  Eq. 18  = B32 × 35/B29  B34  Eq. 19  = 0.1532 × B332− 2.225 × B33 + 7.9006  B35  Eq. 20  = 0.0221 × B332− 0.4979 × B33 + 2.24  B36  Eq. 21  = 0.0068 × B332− 0.2514 × B33 + 1.2979  B37  Eq. 22  = 0.1755 × B332− 2.7563 × B33 + 10.999  B38  Eq. 23  = 0.0776 × B332− 0.9091 × B33 + 3.157  B39  Eq. 24  = 0.0145 × B332− 0.2549 × B33 + 1.2496  B16  Eq.1  = (B3 − B4) × 1000/B5  B17  Eq. 2  = 0.537 × B11 × (1+ 0.0549 × (B9 − 500)/300)  B18  Eq. 3  = 0.894 × B6 + B7  B19  Eq. 4  = EXP(B17/B18 × (1 − B18/B9))  B20  Eq. 5  = B18 × (B19 − 1)/(B19 − B18/B9)  B21  Eq. 6  = (B18 − B20)/B18 × (B7+ B8 + B16)  B22  Eq. 7  = 0.894 × B6/B18  B23  Eq. 8  = (B20 + B21) × B22  B24  Eq. 9  = − LN(B13/B12 − 0.0174/B2 × B5/60) + (4 − 3.5 × B13/B12) × (B3 − B4)/B4  B25  Eq. 10  = (B23+B32) × B5/B24/1000  B26  Eq. 11  = B24 × (B5/(B5 + 30.7))  B27  Eq. 12  = B13/(EXP(LN(B12) − B26/(B24/LN(B12/B13))))  B28  Eq. 13  = LN(B27 × B12/B13)/(B27 × LN(B12/B13))  B29  Eq. 14  = B25/B28  B30  Eq. 15  = B29/B4  B31  Eq. 16  = B12 × (1.075 − (0.38 × (1 − B13/B12)+0.059) × 1440/(B2 × 1440 − B5))  B32  Eq. 17  = B14 × B15/B31/1440  B33  Eq. 18  = B32 × 35/B29  B34  Eq. 19  = 0.1532 × B332− 2.225 × B33 + 7.9006  B35  Eq. 20  = 0.0221 × B332− 0.4979 × B33 + 2.24  B36  Eq. 21  = 0.0068 × B332− 0.2514 × B33 + 1.2979  B37  Eq. 22  = 0.1755 × B332− 2.7563 × B33 + 10.999  B38  Eq. 23  = 0.0776 × B332− 0.9091 × B33 + 3.157  B39  Eq. 24  = 0.0145 × B332− 0.2549 × B33 + 1.2496  The key formulae are written in bold. Table 2 Formulae to be copied into the associated cells in column B of sheet 1 (Figure 1) B16  Eq.1  = (B3 − B4) × 1000/B5  B17  Eq. 2  = 0.537 × B11 × (1+ 0.0549 × (B9 − 500)/300)  B18  Eq. 3  = 0.894 × B6 + B7  B19  Eq. 4  = EXP(B17/B18 × (1 − B18/B9))  B20  Eq. 5  = B18 × (B19 − 1)/(B19 − B18/B9)  B21  Eq. 6  = (B18 − B20)/B18 × (B7+ B8 + B16)  B22  Eq. 7  = 0.894 × B6/B18  B23  Eq. 8  = (B20 + B21) × B22  B24  Eq. 9  = − LN(B13/B12 − 0.0174/B2 × B5/60) + (4 − 3.5 × B13/B12) × (B3 − B4)/B4  B25  Eq. 10  = (B23+B32) × B5/B24/1000  B26  Eq. 11  = B24 × (B5/(B5 + 30.7))  B27  Eq. 12  = B13/(EXP(LN(B12) − B26/(B24/LN(B12/B13))))  B28  Eq. 13  = LN(B27 × B12/B13)/(B27 × LN(B12/B13))  B29  Eq. 14  = B25/B28  B30  Eq. 15  = B29/B4  B31  Eq. 16  = B12 × (1.075 − (0.38 × (1 − B13/B12)+0.059) × 1440/(B2 × 1440 − B5))  B32  Eq. 17  = B14 × B15/B31/1440  B33  Eq. 18  = B32 × 35/B29  B34  Eq. 19  = 0.1532 × B332− 2.225 × B33 + 7.9006  B35  Eq. 20  = 0.0221 × B332− 0.4979 × B33 + 2.24  B36  Eq. 21  = 0.0068 × B332− 0.2514 × B33 + 1.2979  B37  Eq. 22  = 0.1755 × B332− 2.7563 × B33 + 10.999  B38  Eq. 23  = 0.0776 × B332− 0.9091 × B33 + 3.157  B39  Eq. 24  = 0.0145 × B332− 0.2549 × B33 + 1.2496  B16  Eq.1  = (B3 − B4) × 1000/B5  B17  Eq. 2  = 0.537 × B11 × (1+ 0.0549 × (B9 − 500)/300)  B18  Eq. 3  = 0.894 × B6 + B7  B19  Eq. 4  = EXP(B17/B18 × (1 − B18/B9))  B20  Eq. 5  = B18 × (B19 − 1)/(B19 − B18/B9)  B21  Eq. 6  = (B18 − B20)/B18 × (B7+ B8 + B16)  B22  Eq. 7  = 0.894 × B6/B18  B23  Eq. 8  = (B20 + B21) × B22  B24  Eq. 9  = − LN(B13/B12 − 0.0174/B2 × B5/60) + (4 − 3.5 × B13/B12) × (B3 − B4)/B4  B25  Eq. 10  = (B23+B32) × B5/B24/1000  B26  Eq. 11  = B24 × (B5/(B5 + 30.7))  B27  Eq. 12  = B13/(EXP(LN(B12) − B26/(B24/LN(B12/B13))))  B28  Eq. 13  = LN(B27 × B12/B13)/(B27 × LN(B12/B13))  B29  Eq. 14  = B25/B28  B30  Eq. 15  = B29/B4  B31  Eq. 16  = B12 × (1.075 − (0.38 × (1 − B13/B12)+0.059) × 1440/(B2 × 1440 − B5))  B32  Eq. 17  = B14 × B15/B31/1440  B33  Eq. 18  = B32 × 35/B29  B34  Eq. 19  = 0.1532 × B332− 2.225 × B33 + 7.9006  B35  Eq. 20  = 0.0221 × B332− 0.4979 × B33 + 2.24  B36  Eq. 21  = 0.0068 × B332− 0.2514 × B33 + 1.2979  B37  Eq. 22  = 0.1755 × B332− 2.7563 × B33 + 10.999  B38  Eq. 23  = 0.0776 × B332− 0.9091 × B33 + 3.157  B39  Eq. 24  = 0.0145 × B332− 0.2549 × B33 + 1.2496  The key formulae are written in bold. FIGURE 1 View largeDownload slide Sheet 1 aims at computing, firstly, the normalized Kru (KRUn), and, then, the required eKt/V. The column B shows the input and output data for ‘Patient 0’, who is a kind of ‘reference patient’, allowing both an immediate check for the measurement units of the input data (cells B1–B15) as well as the magnitude of the expected output data (cells B16–B39). To run a single patient (e.g. Patient 1) one could type the input data on the cells D1–D15, and use the cells B16–B39 as a template to be copied on the cells D16–D39. As shown in the figure, by filling the input data set for additional patients one has simply to copy the template as needed. Of note, the key parameters, namely KRUn and eKt/V, are written in bold. A very important note is that in these calculations one can also use different units for urea concentration, such as mg/L or mmol/L, provided that the same units are used for blood (C0 and CT) and urine (UUN). FIGURE 1 View largeDownload slide Sheet 1 aims at computing, firstly, the normalized Kru (KRUn), and, then, the required eKt/V. The column B shows the input and output data for ‘Patient 0’, who is a kind of ‘reference patient’, allowing both an immediate check for the measurement units of the input data (cells B1–B15) as well as the magnitude of the expected output data (cells B16–B39). To run a single patient (e.g. Patient 1) one could type the input data on the cells D1–D15, and use the cells B16–B39 as a template to be copied on the cells D16–D39. As shown in the figure, by filling the input data set for additional patients one has simply to copy the template as needed. Of note, the key parameters, namely KRUn and eKt/V, are written in bold. A very important note is that in these calculations one can also use different units for urea concentration, such as mg/L or mmol/L, provided that the same units are used for blood (C0 and CT) and urine (UUN). As stated above, the final product of Sheet 1 is the eKt/V to be prescribed for a given patient, when accounting for her/his KRUn and dialysis schedule. The next sheet is named ‘Td&Kd’ and aims at calculating the values for both Td and Kd to be prescribed to attain the desired eKt/V (Figure 2). In short, if Td is fixed, the needed Kd (Kdn) could be computed as follows: Kdn = spKt/V × Vsp/Td [8]. This means that one has, firstly, to convert the required eKt/V into the associated spKt/V, and, then, estimate Vsp using the Daugirdas and Smye approach [16]. FIGURE 2 View largeDownload slide Quantitative calculation of Td and/or Kd needed to attain the required eKt/V. By copying the cells B6–B11 into the corresponding cells in column D–H, and using increasing Td values in the fifth row, one can approximate immediately the most suitable combination of the two parameters. FIGURE 2 View largeDownload slide Quantitative calculation of Td and/or Kd needed to attain the required eKt/V. By copying the cells B6–B11 into the corresponding cells in column D–H, and using increasing Td values in the fifth row, one can approximate immediately the most suitable combination of the two parameters. For the sake of clarity, the relevant equations are listed in Table 3, as written usually, and in Table 4, as written in the spreadsheet form. Again, we suggest saving the column B for the ‘Patient 0’ and using the active cells B6–B11 as a template. In order to select the most suitable values for both Td and Kd to be prescribed to a given patient, we suggest, firstly, typing the known values of Kru, Vdp and eKt/V required into cells D2, D3 and D4, respectively, and, then, copying these values into the corresponding cells in columns E–H. As shown in Figure 2, by using increasing values for Td, for instance, from 150 to 270 min (see cells D5–H5), and copying the cells B6–B11, the template, on the columns D–H, one can select the most suitable coupling of Td and Kd values. If needed, one could consider a time interval of 15 min or less. Once Kdn is known, it remains to compute the QB required as a function of dialyzer KoA and ultrafiltration. To this end, as shown in Figure 3, one can adapt just the same sheet used to compute KRUn, by only using the relevant lines, and using increasing values for QB (see cells D6−16), as done for Td in the previous sheet. Table 3 Equations (Eq.) used in Figure 2 to compute the Kd needed (Kdn) to attain the required eKt/V   Equations (Eq.)  References  Eq. 25  Single pool Kt/V: spKt/V = eKt/V × (Td + 30.7)/Td  [9], [17]  Eq. 26  Predicted Ct/C0: R = exp(−spKt/V/1.18)  [15]  Eq. 27  Intemediate variable: F = 1 – 0.44 × spKt/V/(Td/60)  [15]  Eq. 28  Volume ratio: V_ratio = Ln(F/R)/[F × Ln(1/R)]  [15]  Eq. 29  Single pool urea distribution volume: Vsp = Vdp × V_ratio  [15]  Eq.30  Needed Kd: Kdn = spKt/V × Vsp/Td × 1000 − Kru  [8]    Equations (Eq.)  References  Eq. 25  Single pool Kt/V: spKt/V = eKt/V × (Td + 30.7)/Td  [9], [17]  Eq. 26  Predicted Ct/C0: R = exp(−spKt/V/1.18)  [15]  Eq. 27  Intemediate variable: F = 1 – 0.44 × spKt/V/(Td/60)  [15]  Eq. 28  Volume ratio: V_ratio = Ln(F/R)/[F × Ln(1/R)]  [15]  Eq. 29  Single pool urea distribution volume: Vsp = Vdp × V_ratio  [15]  Eq.30  Needed Kd: Kdn = spKt/V × Vsp/Td × 1000 − Kru  [8]  Table 3 Equations (Eq.) used in Figure 2 to compute the Kd needed (Kdn) to attain the required eKt/V   Equations (Eq.)  References  Eq. 25  Single pool Kt/V: spKt/V = eKt/V × (Td + 30.7)/Td  [9], [17]  Eq. 26  Predicted Ct/C0: R = exp(−spKt/V/1.18)  [15]  Eq. 27  Intemediate variable: F = 1 – 0.44 × spKt/V/(Td/60)  [15]  Eq. 28  Volume ratio: V_ratio = Ln(F/R)/[F × Ln(1/R)]  [15]  Eq. 29  Single pool urea distribution volume: Vsp = Vdp × V_ratio  [15]  Eq.30  Needed Kd: Kdn = spKt/V × Vsp/Td × 1000 − Kru  [8]    Equations (Eq.)  References  Eq. 25  Single pool Kt/V: spKt/V = eKt/V × (Td + 30.7)/Td  [9], [17]  Eq. 26  Predicted Ct/C0: R = exp(−spKt/V/1.18)  [15]  Eq. 27  Intemediate variable: F = 1 – 0.44 × spKt/V/(Td/60)  [15]  Eq. 28  Volume ratio: V_ratio = Ln(F/R)/[F × Ln(1/R)]  [15]  Eq. 29  Single pool urea distribution volume: Vsp = Vdp × V_ratio  [15]  Eq.30  Needed Kd: Kdn = spKt/V × Vsp/Td × 1000 − Kru  [8]  Table 4 Formulae to be copied into the associated cells in column B of Sheet 2 (Figure 2) Cell  Equations  Spreadsheet formula  B6  Eq. 25  = B4 × (B5 + 30.7)/B5  B7  Eq. 26  = EXP(− B6/1.18)  B8  Eq. 27  = 1 − 0.44 × B6/(B5/60)  B9  Eq. 28  = LN(B8/B7)/(B8 × LN(1/B7))  B10  Eq. 29  = B3 × B9  B11  Eq. 30  = B6 × B10/B5 × 1000 − B2  Cell  Equations  Spreadsheet formula  B6  Eq. 25  = B4 × (B5 + 30.7)/B5  B7  Eq. 26  = EXP(− B6/1.18)  B8  Eq. 27  = 1 − 0.44 × B6/(B5/60)  B9  Eq. 28  = LN(B8/B7)/(B8 × LN(1/B7))  B10  Eq. 29  = B3 × B9  B11  Eq. 30  = B6 × B10/B5 × 1000 − B2  The key formulae are written in bold. Table 4 Formulae to be copied into the associated cells in column B of Sheet 2 (Figure 2) Cell  Equations  Spreadsheet formula  B6  Eq. 25  = B4 × (B5 + 30.7)/B5  B7  Eq. 26  = EXP(− B6/1.18)  B8  Eq. 27  = 1 − 0.44 × B6/(B5/60)  B9  Eq. 28  = LN(B8/B7)/(B8 × LN(1/B7))  B10  Eq. 29  = B3 × B9  B11  Eq. 30  = B6 × B10/B5 × 1000 − B2  Cell  Equations  Spreadsheet formula  B6  Eq. 25  = B4 × (B5 + 30.7)/B5  B7  Eq. 26  = EXP(− B6/1.18)  B8  Eq. 27  = 1 − 0.44 × B6/(B5/60)  B9  Eq. 28  = LN(B8/B7)/(B8 × LN(1/B7))  B10  Eq. 29  = B3 × B9  B11  Eq. 30  = B6 × B10/B5 × 1000 − B2  The key formulae are written in bold. FIGURE 3 View largeDownload slide Calculation of the QB to be prescribed to obtain the desired Kd. The same spreadsheet shown in Figure 1 is used, but the input is limited to the parameters required to compute Kd. FIGURE 3 View largeDownload slide Calculation of the QB to be prescribed to obtain the desired Kd. The same spreadsheet shown in Figure 1 is used, but the input is limited to the parameters required to compute Kd. For the sake of completeness, we have added two useful sheets to compute, respectively, the in vitro KoA [13] from the manufacturer’s data (Figure 4), and PCRn calculated according to Depner and Daugirdas equations [20], recently modified by Daugirdas [21] (Table 5 and Figure 5). Table 5 PCRn for thrice-weekly and twice-weekly HD schedules Thrice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [0.70 + 3.08/(Kt/V)] × Kru/V}   beginning of the week: PCRn  = C0/[36.3 + 5.48 Kt/V + 53.5/(Kt/V)] + 0.168   midweek: PCRn  = C0/[25.8 + 1.15 Kt/V + 56.4/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[16.3 + 4.30 Kt/V + 56.6/(Kt/V)] + 0.168  Twice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [1.15 + 4.56/(Kt/V)] × Kru/V}   beginning-of the week: PCRn  = C0/[48.0 + 5.14 Kt/V +79.0/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[33.0 + 3.60 Kt/V + 83.2/(Kt/V)] + 0.168  Thrice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [0.70 + 3.08/(Kt/V)] × Kru/V}   beginning of the week: PCRn  = C0/[36.3 + 5.48 Kt/V + 53.5/(Kt/V)] + 0.168   midweek: PCRn  = C0/[25.8 + 1.15 Kt/V + 56.4/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[16.3 + 4.30 Kt/V + 56.6/(Kt/V)] + 0.168  Twice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [1.15 + 4.56/(Kt/V)] × Kru/V}   beginning-of the week: PCRn  = C0/[48.0 + 5.14 Kt/V +79.0/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[33.0 + 3.60 Kt/V + 83.2/(Kt/V)] + 0.168  Table 5 PCRn for thrice-weekly and twice-weekly HD schedules Thrice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [0.70 + 3.08/(Kt/V)] × Kru/V}   beginning of the week: PCRn  = C0/[36.3 + 5.48 Kt/V + 53.5/(Kt/V)] + 0.168   midweek: PCRn  = C0/[25.8 + 1.15 Kt/V + 56.4/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[16.3 + 4.30 Kt/V + 56.6/(Kt/V)] + 0.168  Twice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [1.15 + 4.56/(Kt/V)] × Kru/V}   beginning-of the week: PCRn  = C0/[48.0 + 5.14 Kt/V +79.0/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[33.0 + 3.60 Kt/V + 83.2/(Kt/V)] + 0.168  Thrice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [0.70 + 3.08/(Kt/V)] × Kru/V}   beginning of the week: PCRn  = C0/[36.3 + 5.48 Kt/V + 53.5/(Kt/V)] + 0.168   midweek: PCRn  = C0/[25.8 + 1.15 Kt/V + 56.4/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[16.3 + 4.30 Kt/V + 56.6/(Kt/V)] + 0.168  Twice-weekly HD     adjusted C0 (C′0), when Kru >0  = C0 {1 + [1.15 + 4.56/(Kt/V)] × Kru/V}   beginning-of the week: PCRn  = C0/[48.0 + 5.14 Kt/V +79.0/(Kt/V)] + 0.168   end of the week: PCRn  = C0/[33.0 + 3.60 Kt/V + 83.2/(Kt/V)] + 0.168  FIGURE 4 View largeDownload slide Calculation of KoA in vitro by the manufacturer’s data. By using the reported in vitro KDIF value at the usual in vitro setting (for instance, QB = 300 mL/min and QD = 500 mL/min, QF = 0 mL/min), KoA_vitro can be easily computed by firstly splitting the Michaels equation [13] into two factors (i.e. F1 and F2) and then multiplying F1 × Ln(F2). FIGURE 4 View largeDownload slide Calculation of KoA in vitro by the manufacturer’s data. By using the reported in vitro KDIF value at the usual in vitro setting (for instance, QB = 300 mL/min and QD = 500 mL/min, QF = 0 mL/min), KoA_vitro can be easily computed by firstly splitting the Michaels equation [13] into two factors (i.e. F1 and F2) and then multiplying F1 × Ln(F2). FIGURE 5 View largeDownload slide Calculation of PCRn for thrice-weekly and twice-weekly HD schedules. The formulae introduced by Depner and Daugirdas [20] were typed on the cells B8–B15, for the Patient 0, to be used as template with one column per patient. Of note, the equations described by Depner and Daugirdas [20] were based on spKt/V values. However, our calculations are based on eKt/V and Vdp values, in agreement with very recent data by Daugirdas [21]. In contrast to the Sheet 1, here one has to use only concentrations of serum urea nitrogen in mg/dL. FIGURE 5 View largeDownload slide Calculation of PCRn for thrice-weekly and twice-weekly HD schedules. The formulae introduced by Depner and Daugirdas [20] were typed on the cells B8–B15, for the Patient 0, to be used as template with one column per patient. Of note, the equations described by Depner and Daugirdas [20] were based on spKt/V values. However, our calculations are based on eKt/V and Vdp values, in agreement with very recent data by Daugirdas [21]. In contrast to the Sheet 1, here one has to use only concentrations of serum urea nitrogen in mg/dL. Second step A randomly selected sample of 40 incident patients with measured RKF was extracted from the historical database of our unit [3]. We retrieved the data concerning one routine kinetic study performed within the first year of treatment. The main characteristics of the patients were: 20 males, age 68 ± 12 years, pre-dialysis body weight (BW0) 68.5 ± 12 kg, post-dialysis body weight (BWT) 66.8 ± 12 kg. Eighteen patients were on standard HD, 16 on pre-dilution HDF and 6 on post-dilution HDF, respectively; Td was 224 ± 13 min, in vitro KoA 1269 ± 170 mL/min. The data of these patients were used as input for both our spreadsheet and the Solute-solver [9]. Statistical analysis Data are given as mean ± standard deviation. The results were compared with the Student’s paired t-test (P < 0.05 was assumed as statistically significant). Bland–Altman plot analysed the agreement between KRUn values obtained with SPEEDY and Solute-solver [9]. RESULTS The key results provided by SPEEDY and Solute-solver [9] are given in Table 6. Briefly, the Kd values were almost identical, and all the differences between the paired parameters were minimal and clinically negligible (usually less than ±5% is acceptable), even if statistically significant. This was confirmed by the Bland–Altman plot built to analyse the agreement between KRUn values obtained with the two methods: the difference was 0.07 ± 0.05 mL/min/35 L (Figure 6). Table 6 The results obtained by means of Solute-solver [9] and SPEEDY are compared (n = 40)     Solute-solvera  SPEEDYa  Difference  Pb  Dialyzer urea clearance  Kd (mL/min)  199.0 ± 20.13  199.1 ± 20.12  − 0.04 ± 0.19  0.200  Single pool Kt/V  spKt/V  1.48 ± 0.24  1.46 ± 0.23  0.03 ± 0.02  0.000  Equilibrated Kt/V  eKt/V  1.31 ± 0.21  1.28 ± 0.21  0.02 ± 0.02  0.000  Single pool urea volume  Vsp (L)  30.64 ± 4.92  31.61 ± 5.00  − 0.97 ± 0.36  0.000  Double pool urea volume  Vdp (L)  30.01 ± 5.34  30.81 ± 5.37  0.80 ± 0.39  0.000  Renal urea clearance  Kru (mL/min)  2.47 ± 1.23  2.49 ± 1.26  − 0.02 ± 0.04  0.001  Normalized Kru  KRUn (mL/min/35 L)  2.98 ± 1.54  2.84 ± 1.41  0.15 ± 0.35  0.012      Solute-solvera  SPEEDYa  Difference  Pb  Dialyzer urea clearance  Kd (mL/min)  199.0 ± 20.13  199.1 ± 20.12  − 0.04 ± 0.19  0.200  Single pool Kt/V  spKt/V  1.48 ± 0.24  1.46 ± 0.23  0.03 ± 0.02  0.000  Equilibrated Kt/V  eKt/V  1.31 ± 0.21  1.28 ± 0.21  0.02 ± 0.02  0.000  Single pool urea volume  Vsp (L)  30.64 ± 4.92  31.61 ± 5.00  − 0.97 ± 0.36  0.000  Double pool urea volume  Vdp (L)  30.01 ± 5.34  30.81 ± 5.37  0.80 ± 0.39  0.000  Renal urea clearance  Kru (mL/min)  2.47 ± 1.23  2.49 ± 1.26  − 0.02 ± 0.04  0.001  Normalized Kru  KRUn (mL/min/35 L)  2.98 ± 1.54  2.84 ± 1.41  0.15 ± 0.35  0.012  a Means ± standard deviation. b Student’s paired t-test. Table 6 The results obtained by means of Solute-solver [9] and SPEEDY are compared (n = 40)     Solute-solvera  SPEEDYa  Difference  Pb  Dialyzer urea clearance  Kd (mL/min)  199.0 ± 20.13  199.1 ± 20.12  − 0.04 ± 0.19  0.200  Single pool Kt/V  spKt/V  1.48 ± 0.24  1.46 ± 0.23  0.03 ± 0.02  0.000  Equilibrated Kt/V  eKt/V  1.31 ± 0.21  1.28 ± 0.21  0.02 ± 0.02  0.000  Single pool urea volume  Vsp (L)  30.64 ± 4.92  31.61 ± 5.00  − 0.97 ± 0.36  0.000  Double pool urea volume  Vdp (L)  30.01 ± 5.34  30.81 ± 5.37  0.80 ± 0.39  0.000  Renal urea clearance  Kru (mL/min)  2.47 ± 1.23  2.49 ± 1.26  − 0.02 ± 0.04  0.001  Normalized Kru  KRUn (mL/min/35 L)  2.98 ± 1.54  2.84 ± 1.41  0.15 ± 0.35  0.012      Solute-solvera  SPEEDYa  Difference  Pb  Dialyzer urea clearance  Kd (mL/min)  199.0 ± 20.13  199.1 ± 20.12  − 0.04 ± 0.19  0.200  Single pool Kt/V  spKt/V  1.48 ± 0.24  1.46 ± 0.23  0.03 ± 0.02  0.000  Equilibrated Kt/V  eKt/V  1.31 ± 0.21  1.28 ± 0.21  0.02 ± 0.02  0.000  Single pool urea volume  Vsp (L)  30.64 ± 4.92  31.61 ± 5.00  − 0.97 ± 0.36  0.000  Double pool urea volume  Vdp (L)  30.01 ± 5.34  30.81 ± 5.37  0.80 ± 0.39  0.000  Renal urea clearance  Kru (mL/min)  2.47 ± 1.23  2.49 ± 1.26  − 0.02 ± 0.04  0.001  Normalized Kru  KRUn (mL/min/35 L)  2.98 ± 1.54  2.84 ± 1.41  0.15 ± 0.35  0.012  a Means ± standard deviation. b Student’s paired t-test. FIGURE 6 View largeDownload slide Bland–Altman plot showing the agreement between the KRUn values obtained with Solute-solver [9] and SPEEDY. FIGURE 6 View largeDownload slide Bland–Altman plot showing the agreement between the KRUn values obtained with Solute-solver [9] and SPEEDY. When commenting on some of the most relevant data shown in Figure 1, we would like to underline, with reference to Patient 0, the first key result, namely KRUn (shown in cell B33). In this example, KRUn = 2.4 mL/min/35 L. The following three rows (34–36) show the eKt/V required to get the dialysis adequacy on 1, 2 or 3 HD/week schedules, respectively, according to the relationship EKRUn = (12 – KRUn) [11]. In this example, one gets the following eKt/V values: 3.43, 1.17 and 0.73, meaning that with this KRUn the once-weekly schedule is not possible (eKt/V = 3.43), but the twice-weekly schedule is feasible with an eKt/V of 1.17. The thrice-weekly schedule could be done with a very low eKt/V of 0.73. The last three rows (37–39) show the eKt/V required to get stdKt/V(100%Kru) = 2.3 volumes/week, in agreement with the current KDOQI guidelines [10]. They are 5.37, 1.42 and 0.73, respectively. Similar to EKRUn, with stdKt/V the 1 HD/week schedule is not possible (eKt/V = 5.37); the 2 HD/week schedule is feasible with a slightly higher eKt/V (1.42); and the 3 HD/week schedule could be done with an eKt/V as low as 0.72. With regards to Figure 2, we would like to point out that, based on the proposed Td, one can immediately see the Kdn. For example, for Patient 1 a proposed Td of 240 min would require a Kdn of about 200 mL/min. Moreover, using the Sheet 3, one can realize that it could suffice using a dialyser with KoA of 800 mL/min and with a QB a little bit greater than 300 mL/min. A list of abbreviations is being provided as online Supplementary Material. DISCUSSION Recently, two new concepts have begun to emerge within the context of IHD: the first one is that, starting HD with an incremental approach seems to preserve RKF [4, 7]; the second is that, ‘the more the better’ principle may not be true anymore for HD patients with a substantial RKF: in fact, both a high dialysis dose and a high frequency of treatment could accelerate RKF decline [6, 7, 22]. These concepts are in contrast to the current clinical practice whereby patients are often started directly on the full 3 HD/week schedule, with the aim of providing an amount of dialysis as high as possible, to be sure that the minimum is being delivered. Such approach is favoured by at least two factors: (i) the current guidelines overestimate the need of dialysis in the presence of a substantial RKF [3, 7, 11]; and (ii) an accurate prescription of HD would require complex modelling [8, 9]. It has recently been pointed out that such an overestimation of the dialysis needs is due to the erroneous assumption of the clinical equivalence between Kru and Kd [7]. The mistake could be corrected, at least in part, by increasing the relative clinical weight of Kru. This has been done, independently, by Daugirdas et al. [23] and Casino and Basile [7]. The former authors changed the way of computing the stdKt/V, by adding Kru at a 100% strength; in this way Kru is no longer compressed, which translates into an increased relative clinical weight for Kru. With a different approach, Casino and Basile introduced the concept of a variable target for EKRUn, which also increases the relative clinical weight of Kru, because the target EKRU is set at very low levels when Kru is high and vice versa at a maximum level in anuria [7]. The latter authors, in order to ease the calculation of the adequate dialysis dose associated with the actual Kru, provided graphs with so-called ‘adequacy lines’, for 1, 2 and 3 HD sessions/week, for both EKRUn and stdKt/V [7, 11]. They also reported the fitting equations associated with the above adequacy lines that are the basis of IHD prescription [11]. At the present time, no available evidence favours either EKRUn or stdKt/V as a guide for IHD prescription. Actually, after the introduction of the variable target for EKRUn, the two equivalent clearances are more alike than we suspected and provide not particularly different results, at least as far as thrice-weekly and twice-weekly HD schedules are concerned [7, 11]. This is an important feature because, even if it is true that a trial on IHD is needed to confirm the hypothesis of a variable target for EKRUn with IHD, the current target for stdKt/V could be safely used to guide the twice-weekly HD schedule, using either the Solute-solver [9] or SPEEDY. The results presented in Table 6 and Figure 6 show that SPEEDY provides excellent results. This is due to the fact that the both SPEEDY and Solute-solver [9] compute some parameters using the same equations. Clearly, the two methods differ in many aspects. For instance, Solute-solver [9] uses iterations to compute urea generation rate, which, among other things, allows an accurate measurement of V. On the contrary, SPEEDY estimates Vsp by using a recent version of the classical Daugirdas equation that estimates the spKt/V for patients being dialysed with schedules different from the standard thrice-weekly schedule [12]. Then, SPEEDY converts Vsp into Vdp by, firstly, computing eKt/V with Tattersall et al. equation [17] and, then, using Daugirdas and Smye approach [16], just as the Solute-solver [9] does. The latter, however, uses such estimate of Vdp as a starting value for iterations aiming at providing a more accurate estimate of Vdp. Another difference is that Solute-solver [9] predicts the time-averaged urea concentration in serum water over the urine collection interval using iterations, whereas SPEEDY estimates it with another recent equation by Daugirdas et al. [18, 19]. Of note, the last six rows of Sheet 1 show the eKt/V required for 1, 2 and 3 HD/week schedules, based either on EKRUn or stdKt/V target, respectively. Obviously, too high or too low eKt/V values mean that the associated frequency of treatment is not possible. Having selected a realistic eKt/V value, one can fix Td, and estimate firstly Kd and then QB, as shown in Figures 2 and 3. In conclusion, SPEEDY is able to provide clinically acceptable results; thus, any interested reader/clinician could be encouraged to copy the few lines of the spreadsheet and get a personal tool for an easy and fast prescription of IHD. Two immediate consequences of the extensive utilization of SPEEDY could derive: (i) a larger dissemination of IHD might occur, potentially leading to advantages to patients, nephrologists, caregivers and financial resources; and (ii) SPEEDY could represent a useful tool to set an ineludibly needed full-fledged clinical trial, comparing IHD with standard thrice-weekly HD as far as some hard outcomes, such as survival and quality of life, are concerned [11]. SUPPLEMENTARY DATA Supplementary data are available at ndt online. CONFLICT OF INTEREST STATEMENT None declared. REFERENCES 1 Kalantar-Zadeh K, Casino FG. Let us give twice-weekly hemodialysis a chance: revisiting the taboo. Nephrol Dial Transplant  2014; 29: 1618– 1620 Google Scholar CrossRef Search ADS PubMed  2 Wong J, Vilar E, Davenport A et al.  . Incremental haemodialysis. Nephrol Dial Transplant  2015; 30: 1639– 1648 Google Scholar CrossRef Search ADS PubMed  3 Basile C, Casino FG, Kalantar-Zadeh K. Is incremental hemodialysis ready to return on the scene? From empiricism to kinetic modelling. J Nephrol  2017; 30: 521– 529 Google Scholar CrossRef Search ADS PubMed  4 Zhang M, Wang M, Li H et al.  . Association of initial twice-weekly hemodialysis treatment with preservation of residual kidney function in ESRD patients. Am J Nephrol  2014; 40: 140– 150 Google Scholar CrossRef Search ADS PubMed  5 Termorshuizen F, Dekker FW, van Manen JG et al.  . Relative contribution of residual renal function and different measures of adequacy to survival in hemodialysis patients: an analysis of the Netherlands Cooperative Study on the Adequacy of Dialysis (NECOSAD)-2. J Am Soc Nephrol  2004; 15: 1061– 1070 Google Scholar CrossRef Search ADS PubMed  6 Obi Y, Streja E, Rhee CM et al.  . Incremental hemodialysis, residual kidney function, and mortality risk in incident dialysis patients: a cohort study. Am J Kidney Dis  2016; 68: 256– 265 Google Scholar CrossRef Search ADS PubMed  7 Casino FG, Basile C. The variable target model: a paradigm shift in the incremental haemodialysis prescription. Nephrol Dial Transplant  2017; 32: 182– 190 Google Scholar CrossRef Search ADS PubMed  8 Depner TA. Prescribing Hemodialysis: A Guide to Urea Modeling . Boston, MA: Kluwer Academic Publishers, 1991 9 Daugirdas JT, Depner TA, Greene T et al.  . Solute-solver: a web-based tool for modeling urea kinetics for a broad range of hemodialysis schedules in multiple patients. Am J Kidney Dis  2009; 54: 798– 809 Google Scholar CrossRef Search ADS PubMed  10 National Kidney Foundation. KDOQI clinical practice guidelines for hemodialysis adequacy: 2015 update. Am J Kidney Dis  2015; 66: 884– 930 CrossRef Search ADS PubMed  11 Casino FG, Basile C. How to set the stage for a full-fledged clinical trial testing ‘incremental haemodialysis’. Nephrol Dial Transplant  2017; doi: https://doi.org/10.1093/ndt/gfx225 12 Daugirdas JT, Leypoldt KJ, Akonur A et al.  . The FHN Trial Group. Improved equation for estimating single-pool Kt/V at higher dialysis frequencies. Nephrol Dial Transplant  2013; 28: 2156– 2160 Google Scholar CrossRef Search ADS PubMed  13 Michaels AS. Operating parameters and performance criteria for hemodialyzers and other membrane-separation devices. Trans Am Soc Artif Intern Organs  1966; 12: 387– 392 Google Scholar PubMed  14 Depner TA, Greene T, Daugirdas JT et al.  . Dialyzer performance in the HEMO Study: in vivo K0A and true blood flow determined from a model of cross-dialyzer urea extraction. Asaio J  2004; 50: 85– 93 Google Scholar CrossRef Search ADS PubMed  15 Tattersall JE, Ward RA; EUDIAL group. Online haemodiafiltration: definition, dose quantification and safety revisited. Nephrol Dial Transplant  2013; 22: 542– 550 Google Scholar CrossRef Search ADS   16 Daugirdas JT, Smye SW. Effect of a two compartment distribution on apparent urea distribution volume. Kidney Int  1997; 51: 1270– 1723 Google Scholar CrossRef Search ADS PubMed  17 Tattersall JE, DeTakats D, Chamney P et al.  . The post-hemodialysis rebound: predicting and quantifying its effect on Kt/V. Kidney Int  1996; 50: 2094– 2102 Google Scholar CrossRef Search ADS PubMed  18 Daugirdas JT. Estimating time-averaged serum urea nitrogen concentration during various urine collection periods: a prediction equation for thrice weekly and biweekly dialysis schedules. Semin Dial  2016; 29: 507– 509 Google Scholar CrossRef Search ADS PubMed  19 Obi Y, Kalantar-Zadeh K, Streja E et al.  . Prediction equation for calculating residual kidney urea clearance using urine collections for different hemodialysis treatment frequencies and interdialytic intervals. Nephrol Dial Transplant  2018; 33: 530– 539 Google Scholar CrossRef Search ADS PubMed  20 Depner TA, Daugirdas JT. Equations for normalized protein catabolic rate based on two point modeling of hemodialysis urea kinetics. J Am Soc Nephrol  1996; 7: 780– 785 Google Scholar PubMed  21 Daugirdas JT. Errors in computing the normalized protein catabolic rate due to use of single-pool urea kinetic modeling or to omission of the residual kidney urea clearance. J Ren Nutr  2017; 27: 256– 259 Google Scholar CrossRef Search ADS PubMed  22 Daugirdas JT, Green T, Rocco MV et al.  . Effect of frequent hemodialysis on residual kidney function. Kidney Int  2013; 83: 949– 958 Google Scholar CrossRef Search ADS PubMed  23 Daugirdas JT, Depner TA, Greene T et al.  .; Frequent Hemodialysis Network Trial Group. Standard Kt/V(urea): a method of calculation that includes effects of fluid removal and residual kidney clearance. Kidney Int  2010; 77: 637– 644 Google Scholar CrossRef Search ADS PubMed  © The Author(s) 2018. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

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Nephrology Dialysis TransplantationOxford University Press

Published: Jan 5, 2018

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