Ferri, Raffaele; Silvani, Alessandro; Rundo, Francesco; Zucconi, Marco; Aricò, Debora; Bruni, Oliviero; Ferini-Strambi, Luigi; Manconi, Mauro

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SLEEP
, Volume 41 (3) – Mar 1, 2018

9 pages

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- Sleep Research Society
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- 10.1093/sleep/zsy008
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Abstract Study Objectives To define statistically the upper limit of the intermovement interval (IMI, the time interval between the onset of consecutive movements) of periodic leg movements during sleep (PLMS). Methods We computed the IMI distribution of a large sample (n = 141) of patients with restless legs syndrome (RLS) and analyzed it with two independent approaches, based on fitting either empirical functions or normal and exponential functions to the data. Results The two fitting approaches consistently pointed to an upper limit of the PLMS IMI in the range between 50 and 60 s. Decreasing the upper limit of PLMS IMI from 90 to 60 s evidently decreased the PLMS index in patients with RLS and control participants; nevertheless, the PLMS index remained significantly higher in RLS vs. control participants. Shifting the upper limit of PLMS IMI to 60 s did not significantly modify the effectiveness of discrimination of PLMS between controls and patients with RLS. Conclusion These results seem to indicate that a conservative, yet data-driven upper limit for IMI contributing to the PLMS in patients with RLS might be 60 s instead of 90 s, as recommended by the present guidelines. periodic leg movements during sleep, PLMS, restless legs syndrome, intermovement interval Statement of Significance Periodic leg movements during sleep (PLMS) occur at quasiregular intermovement intervals (IMIs) that, for many years, have been indicated to be between 5 and 90 s. Recently, scoring standards have been revised to increase the lower limit of PLMS IMI from 5 to 10 s. Here, we provide evidence that a more appropriate and data-driven upper limit for PLMS IMI might be 60 s instead of 90 s. The 60 s cutoff would also make the definition of PLMS more coherent with other correlated periodic sleep phenomena, such as those included in the cyclic alternating pattern and may be taken into account in future revisions of the PLMS scoring standards. Introduction Periodic leg movements during sleep (PLMS) have received particular attention since their polysomnographic discovery by the group led by Professor Lugaresi in Bologna (Italy) [1, 2] because of their occurrence at quasiregular intermovement intervals (IMIs, the time intervals between the onset of consecutive leg movements) that, for many years, have been indicated to be between 5 and 90 s [3–6]. However, in the last decade and following the seminal work by Ferri et al. [7], the use of data-driven statistical approaches [8–10] has indicated that the lower limit for PLMS IMI is 10 s, rather than 5 s. Consequently, the last World Association of Sleep Medicine (WASM) 2016 standards for recording and scoring leg movements in polysomnograms [11] have adopted a different IMI range to define PLMS, from 10 to 90 s. This change was based on a consistent amount of evidence on the existence of a different category of leg movements characterized by IMI < 10 s that can be clearly appreciated in the total IMI distribution as a separate peak, preceding that of PLMS [7, 9]. These short-IMI leg movements during sleep (SILMS) interfere with and disrupt the regular occurrence of PLMS [12], are characterized by an essentially nonperiodic time structure [13], and are accompanied by heart rate modifications that last longer than those accompanying PLMS [14]. Some [7, 15] but not all [16] statistical analyses of the IMI distribution have demonstrated that both PLMS and SILMS may be modeled with log-normal functions. The 10 s limit, separating SILMS from PLMS, was obtained by considering the crossing point of two fitted log-normal functions [7, 8], which was then a successful approach to discriminate the two IMI ranges. While the lower limit of the PLMS IMI range has been analyzed in detail, the upper limit of 90 s has never been challenged and was considered to be valid by Ferri et al. in 2006 [7] only because a statistical difference between the IMI distributions of control participants and patients with restless legs syndrome (RLS) was found exactly up to this value. However, this appears to be too weak a support for a validation of the 90 s upper limit and prompted us to plan a study to evaluate statistically the upper limit of the PLMS IMI range. For this purpose, we analyzed the IMI distribution of a large sample of 141 patients with RLS. In order to provide stronger support to data-driven inferences on the upper limit of the PLMS IMI, we employed two independent approaches based on the fitting of functions to the observed data, within a distribution mixture analysis. The first approach was essentially assumption-free and consisted of fitting empirical functions to the SILMS and PLMS peaks of the IMI distribution. The second approach was based on the assumption that the distribution of the IMI corresponding to SILMS and PLMS may be fitted by a sum of normal (Gaussian) functions, whereas the distribution of the IMI above the upper PLMS limit may be fitted by a single negative exponential function. Normal and exponential functions were selected for this approach because they are analytically convenient and lend themselves to potentially useful mechanistic interpretations in terms of the sum of independent processes (normal functions) and of the time between events that occur continuously and independently (negative exponential function). Methods Participants We performed a novel analysis of the IMI distribution of a retrospectively recruited set of 141 patients with RLS (61 males and 80 females) with age 53.9 ± 15.43 years (mean ± SD) and IRLS Severity Scale [17] score 25.3 ± 5.13, and of 68 normal controls (28 males and 40 females) with age 49.6 ± 17.92 years, who participated in studies previously published by our groups [7, 8, 18–27]. The diagnosis of RLS was made according to the International RLS Study Group [28, 29] by means of a semistructured clinical interview and a careful exclusion of RLS mimics. Routine blood tests, neurological examination, electromyography, and electroneurography of the lower limbs were also normal. The sleep respiratory pattern of each patient was assessed and participants with apnea/hypopnea index >5 were not included. None of the patients was taking drugs or substances known to be able to modify sleep leg movements (dopamine agonists or other drugs for RLS and antidepressants, in particular). The original studies were approved by the local ethics committees and allowed additional analyses on deidentified data collected previously. All participants had provided informed consent before entering the study. Recordings A polysomnographic full night recording, after an adaptation night, was obtained for each patient. The recording included electroencephalogram (EEG, with at least three channels: one frontal, one central, and one occipital, referred to the contralateral earlobe); electrooculogram (two channels); electromyogram (EMG) of the submentalis muscle and of both tibialis anterior muscles; and electrocardiogram (one derivation). The EMG signals were band-pass filtered at 10−100 Hz, with a notch filter at 50 Hz. At the beginning of each recording session, the amplitude of the EMG signal from the two tibialis anterior muscles was checked to be below 2 µV at rest. All recordings lasted at least for 6 hr. Sleep stages were visually scored on 30 s epochs [30] and all leg movements during sleep were detected following standard criteria [6, 11]. In particular, leg movement onset was defined when the EMG increased > 8 μV above baseline levels [6, 11]. All IMIs, defined as time intervals between the onset of successive leg movements during sleep [6, 11], were counted from each recording, in each participant, for 2 s classes (0.5 s < IMI ≤ 2 s, 2 s <IMI ≤4 s, 4 s < IMI ≤6 s, . . ., 148 s < IMI ≤ 150 s). The IMI counts for each 2 s class were then summed over all participants with RLS to obtain the RLS IMI distribution employed for the subsequent two curve fitting approaches 1 and 2. Data-driven approach 1: fitting peaks of the RLS IMI distribution with empirical functions An iterative nonlinear least-squares fitting (nonlinear regression) was used to find the function fPLMS(IMI) that best fitted the main PLMS peak of the observed RLS IMI distribution at IMI values ranging from 10 to 150 s. The function was selected from a list of several functions, including the most common and known in statistics, such as normal, log-normal, gamma, chi-square, and exponential (http://www.xuru.org). To evaluate the degree of fit of the functions to the observed RLS IMI distribution, loss functions (LFs) [31] were computed as the mean squared difference between the observed RLS IMI distribution and the fitted function for each 2 s class, divided by the variance of the observed RLS IMI distribution. With this definition of LF, LF = 0 indicates a perfect fit, i.e. a perfect mathematical description, whereas LF = 1 corresponds to fitting the observed RLS IMI distribution with a constant value equal to the arithmetic average of the values of the different 2 s classes, i.e. a poor mathematical description. The function whose fit provided the smallest LF value was retained. This was akin to finding the optimal mathematical description of the main PLMS peak of the IMI distribution in this dataset. After this first step, a similar fitting was done based on the analysis of residuals for the observed RLS IMI distribution in the IMI range from 2 to 10 s, which corresponded to the SILMS peak of the RLS IMI distribution. In essence, we searched for the optimal mathematical description also of the SILMS peak of the IMI distribution in this dataset. This yielded an empirical function fSILMS(IMI), whose new fitted values for IMI < 10 s were appended to those resulting from the function fPLMS(IMI) for IMI ≥ 10 s. In other words, the optimal mathematical description of the PLMS peak, for IMI values between 10 and 150 s, was appended to the optimal mathematical description of the SILMS peak, for IMI values < 10 s. The total LF value corresponding to the appended function and the new residuals in the IMI range of 0–150 s were then calculated. In step 3, a third function f3(IMI) was fitted to the residuals in the IMI range of 40–150 s, which was determined empirically based on visual inspection, and the corresponding values added to those obtained in the same range by the function fPLMS(IMI), so as to obtain the final function fTOT1(IMI). In other words, we searched to describe mathematically the portion of the IMI distribution between 40 and 150 s, which was not adequately explained by the description of the PLMS peak, and then we merged the original description of the PLMS peak with this complementary, additional description. The total LF value was eventually recalculated based on fTOT1(IMI) and the final residuals were plotted. With respect to the specific purpose of this study, we obtained with this approach two estimates of the upper limit of the PLMS. The more conservative estimate corresponded to the value of IMI at the crossing point between fPLMS(IMI) and f3(IMI). Above this IMI value, the optimal mathematical description of the PLMS peak performed worse than its complementary additional description on this dataset. The less conservative estimate corresponded to the value of IMI at which fPLMS(IMI) reached fitted values very close to 0, operationally defined as a cumulative percentage of 99.7% of the fitted values. This corresponded to the highest IMI value explained by the optimal mathematical description of the PLMS peak. Data-driven approach 2: fitting the RLS IMI distribution with normal and exponential functions In this approach, the first step consisted of fitting (“fit” function, Matlab, MathWorks, Natick, MA) the RLS IMI distribution with a function fnorm(IMI,ν) that consisted of the sum of ν normal (Gaussian) functions, fnorm(IMI,ν)=∑μ=1υαμe−(IMI−βμγμ)2 We started with a single normal function (ν = 1), then progressively increased ν until the LF (defined as for approach 1, see above) did not further decrease, or until the fitting yielded negative (nonsense) amplitude (α) parameters, whichever came first. This corresponded to finding the optimal mathematical description of the whole IMI distribution in this dataset, assuming that the distribution resulted from one or more large groups of independent neurophysiological processes. We then proceeded to the second step, fitting the values of the RLS IMI distribution higher than a cutoff value χ with an exponential function fexp(IMI, χ). The values of fexp(IMI, χ) for IMI ≥ χ were appended to the values of fnorm(IMI, ν) for IMI < χ, so as to obtain the final (appended) function fTOT2(IMI, ν, χ), fTOT2(IMI,V,χ)={fnorm(IMI,ν)=∑μ=1ναμ.e−(IMI−βμγμ),IMI<χfexp(χ)=δ.eε.IMI,IMI≥χ The value of χ was determined iteratively by repeating the procedure for each value of IMI, and selecting the value of χ that minimized the LF of fTOT2(IMI,ν,χ). With respect to the specific purpose of this study, we estimated the upper limit of the PLMS IMI at the value of IMI = χ. Above this IMI value, the IMI distribution in this dataset was better explained in terms of the time between events that occur continuously and independently than in terms of one or more large groups of independent processes. Effects of changing the definition of the upper limit of the PLMS IMI on the discrimination between participants with RLS and controls We analyzed the difference between participants with RLS and control participants in the PLMS index (number of PLMS per hour sleep time), the periodicity index (ratio between the number of PLMS and the total number of leg movements during sleep), and the index of “isolated” leg movements during sleep (number of leg movements with IMI higher than the upper limit of the PLMS + leg movements with IMI from 10 s to the PLMS upper limit in series shorter than 4, per hour sleep time). We computed these indexes employing either the standard definition of the upper limit of the PLMS IMI at 90 s, as per the current guidelines [4, 11], or the definition resulting from the analyses performed in the present study, and compared them between RLS and control participants (Mann–Whitney tests with significance at p < 0.05; SPSS software, IBM, Armonk, NY, USA). The effectiveness of these indexes to discriminate RLS from control participants with the 90 s vs. the newly obtained upper limit of PLMS IMI was quantified and compared with an analysis of receiver operating characteristic (ROC) functions (EasyRoc free web tool v. 1.3; http://www.biosoft.hacettepe.edu.tr/easyROC/). The optimal ROC cutoffs were estimated as the index values that minimized the absolute difference between sensitivity and specificity. Results Data-driven approach 1: fitting peaks of the RLS IMI distribution with empirical functions The results of the fitting of peaks of the RLS IMI distribution with empirical functions (data-driven approach 1) are shown in Figure 1. The fit to the main PLMS peak of the RLS IMI distribution (Figure 1, grey bars) for IMI ranging from 10 to 150 s, which provided the smallest LF (0.110), was obtained with the following empirical function (Figure 1A, red line): Figure 1. View largeDownload slide Fitting peaks of the IMI distribution of participants with RLS employing empirical functions. The grey bars show the distribution of IMI computed on 141 patients with RLS. The equations of the functions shown in the figure panels are reported in the results section (approach 1). PLMS and SILMS = periodic and short-interval leg movements during sleep, respectively. (c) shows that fPLMS(IMI) crossed f3(IMI) at IMI = 50 s and reached count values very close to 0 at IMI = 60 s. Figure 1. View largeDownload slide Fitting peaks of the IMI distribution of participants with RLS employing empirical functions. The grey bars show the distribution of IMI computed on 141 patients with RLS. The equations of the functions shown in the figure panels are reported in the results section (approach 1). PLMS and SILMS = periodic and short-interval leg movements during sleep, respectively. (c) shows that fPLMS(IMI) crossed f3(IMI) at IMI = 50 s and reached count values very close to 0 at IMI = 60 s. fPLMS(IMI)=a⋅eb⋅IMI⋅IMIc,IMI≥10s with the parameter coefficients reported in Table 1. After this first step, based on the analysis of residuals (Figure 1A, black line), a similar fitting was done for the observed RLS IMI distribution in the IMI range of 2–10 s, yielding a second empirical function, Table 1. Parameter coefficients of empirical functions fitting the IMI distribution of participants with RLS Functions fPLMS(IMI) IMI ≥ 10 s fSILMS(IMI) IMI < 10 s f3(IMI) IMI ⊆ [40–150]s Parameter Coefficient Parameter Coefficient Parameter Coefficient a 0.109 d 1045.710 l 88.683 b −0.244 g 1.5 m 0.5 c 5.029 h −7873.442 n −19.935 i 19106.646 o 0.689 j 0.5 p 0.077 k −13736.356 q 19.935 r −0.5 Functions fPLMS(IMI) IMI ≥ 10 s fSILMS(IMI) IMI < 10 s f3(IMI) IMI ⊆ [40–150]s Parameter Coefficient Parameter Coefficient Parameter Coefficient a 0.109 d 1045.710 l 88.683 b −0.244 g 1.5 m 0.5 c 5.029 h −7873.442 n −19.935 i 19106.646 o 0.689 j 0.5 p 0.077 k −13736.356 q 19.935 r −0.5 The coefficients of function parameters refer to equations reported in the results section concerning empirical functions. PLMS and SILMS = periodic and short-interval leg movements during sleep, respectively. IMI = intermovement interval. View Large fSILMS(IMI)=d⋅IMIg+h⋅IMI+i⋅IMIj+k,IMI<10s with the parameter coefficients reported in Table 1. The new fitted values (Figure 1B, green line) of the function fSILMS(IMI) for IMI < 10 s were appended to those of the function fPLMS(IMI) for IMI ≥ 10 s, so as to recalculate the total LF value (0.023) and the new residuals (Figure 1B, black line). In step 3, the residuals in the IMI range of 40–150 s, which was determined empirically based on visual inspection, were fitted with a third empirical function, f3(IMI)=l⋅(m⋅IMI+n)o⋅ep⋅(q+r⋅IMI),IMI⊆[40s−150s] with the parameter coefficients reported in Table 1. The values of f3(IMI) (Figure 1C, blue line) were then added to those of fPLMS(IMI) in the same IMI range of 40–150 s to yield the final function, fTOT1(IMI)={fSILMS(IMI),IMI<10sfPLMS(IMI),IMI⊆[10s-40s[fPLMS(IMI)+f3(IMI),IMI⊆[40s−150s] After this last step, the LF associated with fTOT1(IMI) was reduced to a very low value (0.006); consequently, the plot of the residuals (Figure 1C, black line) showed only very small deviations from zero. With respect to the specific purpose of this study, it was possible to note that fPLMS(IMI) crossed f3(IMI) at IMI = 50 s, with a cumulative percentage of 98.4% of the fitted IMI counts, and reached values very close to 0 (a cumulative percentage of 99.7% of the fitted counts) at IMI = 60 s. In summary, this approach yielded, by construction, a unique mathematical description for the counts of IMI < 10 s (SILMS), and two different and complementary descriptions for the counts of IMI ≥ 10 s. One of these two descriptions worked better for the counts of the shorter IMI ≥ 10 s, whereas the other worked better for the counts of the longer IMI ≥ 10 s. The boundary between the IMI values, whose counts each of these two descriptions explained better, was estimated at IMI = 50 s or IMI = 60 s, depending on the more or less conservative computational approach. Data-driven approach 2: fitting the IMI distribution with normal and exponential functions Fitting the RLS IMI distribution with 1 normal function or with the sum of 2 or 3 normal functions [i.e. with fnorm(IMI, 1), fnorm(IMI, 2), and fnorm(IMI, 3), respectively] yielded progressively decreasing the values of LF of 0.0563, 0.0166, and 0.0074. All the coefficients of these function parameters were positive. The values of these coefficients and their confidence intervals are reported in Supplementary Table S1 (ν = 1), Supplementary Table S2 (ν = 2), and in Table 2 (ν = 3). Fitting the RLS IMI distribution with the sum of four normal functions [i.e. with fnorm(IMI,4)] further decreased the LF to 0.0067, but yielded negative, nonsense coefficient values of the function parameters α2, β2, and β3 (Supplementary Table S3). On this basis, the value of ν was set to 3 for the subsequent analyses. We then moved on to the second step of this approach, fitting the values of the RLS IMI distribution higher than a cutoff value χ with an exponential function fexp(IMI, χ), and appending the values of fexp(IMI, χ) for IMI ≥ χ to the values of fnorm(IMI, 3) for IMI < χ, so as to obtain the final (appended) function fTOT2(IMI, 3, χ). The minimal value of the LF (0.0051) was obtained for χ = 54 s (Figure 2A). The results of fitting the RLS IMI distribution with the final appended function fTOT2(IMI, 3, 54 s) are shown in Figure 2B. Table 2. Parameter coefficients of normal functions and exponential function fitting the IMI distribution of participants with RLS Function 95% Confidence interval Parameter Coefficient Lower bound Upper bound fnorm(IMI, 3) α1 2547 2223 2871 β1 21.5 20.9 22.1 γ1 10.66 9.49 11.84 α2 512 311 713 β2 32.1 9.5 54.6 γ2 41.11 26.16 56.05 α3 955 735 1174 β3 4.7 4.2 5.1 γ3 1.85 0.61 3.08 fexp(IMI, 54 s) δ 1119 990 1248 ε −0.02478 −0.02632 −0.02324 Function 95% Confidence interval Parameter Coefficient Lower bound Upper bound fnorm(IMI, 3) α1 2547 2223 2871 β1 21.5 20.9 22.1 γ1 10.66 9.49 11.84 α2 512 311 713 β2 32.1 9.5 54.6 γ2 41.11 26.16 56.05 α3 955 735 1174 β3 4.7 4.2 5.1 γ3 1.85 0.61 3.08 fexp(IMI, 54 s) δ 1119 990 1248 ε −0.02478 −0.02632 −0.02324 Function parameters refer to equations reported in the methods section concerning the sum of three normal functions [fnorm(IMI, 3)] for IMI < 54 s and one exponential function for IMI ≥ 54 s [fexp(IMI, 54 s)]. IMI = intermovement interval. View Large Figure 2. View largeDownload slide Fitting the IMI distribution of participants with RLS employing normal and exponential functions. (A) shows the changes in the LF of fTOT2(IMI, 3, χ) as a function of χ (cf. methods for details). Values of the LF higher than 0.008 have been omitted for clarity of representation. The minimum value of the LF corresponded to χ = 54 s. (B) shows the results of fitting the IMI distribution with the final appended function fTOT2(IMI, 3, 54 s) (cf. methods for details). The grey bars show the distribution of IMI computed on 141 patients with RLS. The three component normal functions that are summed in function fnorm(IMI, 3) are also shown. Figure 2. View largeDownload slide Fitting the IMI distribution of participants with RLS employing normal and exponential functions. (A) shows the changes in the LF of fTOT2(IMI, 3, χ) as a function of χ (cf. methods for details). Values of the LF higher than 0.008 have been omitted for clarity of representation. The minimum value of the LF corresponded to χ = 54 s. (B) shows the results of fitting the IMI distribution with the final appended function fTOT2(IMI, 3, 54 s) (cf. methods for details). The grey bars show the distribution of IMI computed on 141 patients with RLS. The three component normal functions that are summed in function fnorm(IMI, 3) are also shown. In summary, this approach yielded, by construction, two different mathematical descriptions for the counts of IMI with relatively short and long values within the full IMI interval (0.5–150 s). The boundary between the IMI values, whose counts each of these two descriptions explained, was found at IMI = 54 s. Effects of changing the definition of the upper limit of the PLMS IMI on the discrimination between participants with RLS and controls Decreasing the upper limit of PLMS IMI from 90 to 60 s evidently decreased the PLMS index (Figure 3A) and the periodicity index (Figure 3D) and increased the “isolated” leg movement index (Figure 3G) in patients with RLS and control participants. Nevertheless, these indexes remained significantly higher in RLS vs. control participants either with the 90 s or with the 60 s IMI upper limit (Mann–Whitney tests, p < 0.001). The ROC functions discriminating RLS vs. control participants based on these indexes are shown in Figure 3, B, E, and H and quantified in Table 3. As expected, the PLMS index, the periodicity index, and, to a lower extent, the “isolated” leg movement index successfully discriminated RLS vs. control participants with the standard 90 s upper limit of PLMS IMI. Shifting the upper limit of PLMS IMI to 60 s did not significantly modify the effectiveness of discrimination (PLMS index: p = 0.902; periodicity index: p = 0.866; “isolated” leg movement index: p = 0.139), but decreased the optimal ROC cutoffs of the PLMS index (from 11.6 to 8.3 events/hr) and the periodicity index and increased the optimal ROC cutoff of the “isolated” leg movement index (Table 3). Table 3. Effects of changing the definition of the upper limit of the PLMS IMI on the discrimination between participants with RLS and controls Index Upper limit of PLMS IMI ROC AUC (SE) Optimal cutoff (Sensibility = Specificity) Sensibility and specificity at cutoff PLMS/hr 90 s 0.93 (0.02) 11.6 0.87 60 s 0.93 (0.02) 8.3 0.87 Periodicity index 90 s 0.92 (0.02) 0.45 0.85 60 s 0.91 (0.02) 0.35 0.82 ILMS/hr 90 s 0.65 (0.04) 8.7 0.60 60 s 0.73 (0.04) 10.5 0.66 Index Upper limit of PLMS IMI ROC AUC (SE) Optimal cutoff (Sensibility = Specificity) Sensibility and specificity at cutoff PLMS/hr 90 s 0.93 (0.02) 11.6 0.87 60 s 0.93 (0.02) 8.3 0.87 Periodicity index 90 s 0.92 (0.02) 0.45 0.85 60 s 0.91 (0.02) 0.35 0.82 ILMS/hr 90 s 0.65 (0.04) 8.7 0.60 60 s 0.73 (0.04) 10.5 0.66 The data refer to the discrimination between 141 participants with restless legs syndrome and 68 normal control participants based on the analysis of receiver operating characteristic (ROC) functions. Each ROC AUC was significantly different from 0.5 (p < 0.001). Differences in ROC AUC between the 90 and the 60 s upper limit of PLMS IMI were not statistically significant. PLMS = periodic leg movements during sleep; periodicity index = ratio between the number of PLMS and the total number of leg movements during sleep; ILMS = “isolated” leg movements during sleep with intermovement interval (IMI) higher than the upper limit of PLMS IMI + leg movements with IMI from 10 s to the PLMS upper limit in series shorter than 4; AUC = area under the curve; SE = standard error of the AUC. View Large Figure 3. View largeDownload slide Effects of changing the definition of the upper limit of the PLMS IMI on the discrimination between participants with RLS and controls. (A) shows box plots of the index of PLMS per hour sleep time in 141 participants with RLS and 68 normal control participants (CTRL), computed employing either the 90 s (red) or the 60 s (blue) upper limit of PLMS IMI. Open circles indicate outliers. *p < 0.05 vs. CTRL, Mann–Whitney test. (B) shows ROC functions to discriminate RLS vs. control participants based on the PLMS index. (C) shows the optimal PLMS index cutoffs (arrows) that minimize the absolute difference between sensitivity (continuous lines) and specificity (dotted lines) of the ROC functions. (D)–(F) and (G)–(I) show the same information as in (A)–(C), concerning the periodicity index (PI = number of PLMS divided by total number of leg movements during sleep) and the index of “isolated” leg movements during sleep (ILMS = IMI > upper PLMS limit + leg movements with IMI from 10 s to the PLMS upper limit in series shorter than 4), respectively. Figure 3. View largeDownload slide Effects of changing the definition of the upper limit of the PLMS IMI on the discrimination between participants with RLS and controls. (A) shows box plots of the index of PLMS per hour sleep time in 141 participants with RLS and 68 normal control participants (CTRL), computed employing either the 90 s (red) or the 60 s (blue) upper limit of PLMS IMI. Open circles indicate outliers. *p < 0.05 vs. CTRL, Mann–Whitney test. (B) shows ROC functions to discriminate RLS vs. control participants based on the PLMS index. (C) shows the optimal PLMS index cutoffs (arrows) that minimize the absolute difference between sensitivity (continuous lines) and specificity (dotted lines) of the ROC functions. (D)–(F) and (G)–(I) show the same information as in (A)–(C), concerning the periodicity index (PI = number of PLMS divided by total number of leg movements during sleep) and the index of “isolated” leg movements during sleep (ILMS = IMI > upper PLMS limit + leg movements with IMI from 10 s to the PLMS upper limit in series shorter than 4), respectively. Discussion The statistical analysis of the IMI distribution in a large sample of individuals with RLS allowed us to obtain a substantial amount of data upon which to base our curve fitting, especially in the IMI range ≥10 s, in which PLMS occur. With our distribution mixture analysis based on empirical functions (approach 1), we could fit to the RLS IMI distribution an additional curve, f3(IMI), with respect to two others [fSILMS(IMI) and fPLMS(IMI)], which were similar to those already used in earlier studies [7] for IMI < 10 s and for IMI 10–90 s, respectively. The curve f3(IMI) accounted for the residuals obtained after the fitting of the first two curves within the IMI range 40–150 s. As explained in the results, fPLMS(IMI) crossed f3(IMI) at IMI = 50 s and reached values very close to 0 at IMI = 60 s. These results indicate that the optimal mathematical description that we found for the PLMS peak of the IMI distribution in our dataset was not sufficient to explain properly the full IMI distribution in the IMI range of 40–150 s and needed to be complemented by an additional, separate description for this purpose. The optimal mathematical description of the PLMS peak “covered” IMI values up to 60 s, but it performed worse than its complementary additional description already above the IMI value of 50 s. With an independent approach (approach 2) based on fitting standard normal and exponential functions to the RLS IMI distribution, we reached a strikingly similar estimate of χ = 54 s for the cutoff between the IMI counts that were fitted by the sum of 3 normal functions and the IMI counts that were fitted by a single negative exponential function. These results indicate that above the IMI value of 54 s, the IMI distribution in our dataset was better explained in terms of time between events that occur continuously and independently, than in terms of one or more large groups of independent processes. The successful use of a negative exponential function in this approach raises the hypothesis that leg movements with IMI ≥ 54 s occur independently as a random, no-memory process (i.e. a random process in which the future is independent of the past) in participants with RLS. On the other hand, of the three normal functions employed to properly fit leg movements with IMI < 54 s in participants with RLS, one function peaked at IMI = 21 s (β1 parameter, Table 2) and another (β3 parameter, Table 2) peaked at IMI = 5 s. These functions broadly correspond to those already used in earlier studies [7] and to the fPLMS(IMI) and fSILMS(IMI) functions, respectively, obtained with approach 1. The need for a third normal function to properly fit the distribution of IMI < 54 s in participants with RLS was somewhat unexpected. The peak of this third function was centered at IMI = 32 s (β2 parameter, Table 2), with a rather wide 95% confidence interval ranging from 10 to 55 s. This may reflect variability of the PLMS periodicity among participants with RLS, or other periodic sleep phenomena such as those included in the so-called cyclic alternating pattern (CAP) [32]. CAP is formed by EEG events that can last up to 60 s and has been shown to have a time distribution very similar to that of PLMS [32, 33]. It is also possible that this peak reflects the presence of leg movements associated with undetected mild respiratory events, without the characteristics of clear obstructive sleep apnea (respiratory-related arousals or upper-airway resistance events), with a range of IMI length similar to that of respiratory-related leg movements (20–60 s) [34]. Taken together, both our independent approaches seem to indicate that the curves fitting best the RLS IMI distribution in the range of PLMS explain the observed data only up to 50–60 s, and that another phenomenon, possibly a no-memory random process, might be at the basis of the leg movements with IMI > 60 s. This was also evident in the earlier study by Ferri et al. [7] but was not investigated further. These results, obtained using an observational approach, are also in overall agreement with those obtained with an interventional pharmacological challenge, which showed a significant response to dopamine-agonists only for leg movements during sleep with IMI 15–42 s, suggesting a dopaminergic neurobiological substrate only for this IMI category, corresponding to PLMS [24]. The findings of this analysis, thus, seem to indicate that a more appropriate and data-driven upper limit for IMI contributing to the PLMS count might be 60 s instead of 90 s. This change in upper limit does not affect the ability of the PLMS index, the periodicity index, and even the “isolated” leg movement index to discriminate between participants with RLS and control participants, although it implies changes in the optimal PLMS index cutoffs (Figure 3). Nonetheless, if applied, it would make the definition of PLMS more coherent with other strictly correlated periodic sleep phenomena such as those included in CAP, which is formed by EEG events that can last up to 60 s [32]. On the other hand, the change in the upper limit of PLMS IMI increases the estimated number of “isolated” leg movements with IMI above the upper limit of PLMS (Figure 3G). Separating leg movements with long IMI from PLMS has a pathophysiological meaning because it has already been demonstrated that “isolated” leg movements with IMI > 90 s are accompanied by heart rate and spectral EEG changes more evident than those accompanying PLMS [35]. Moreover, the application of a better definition of the different categories of leg movements during sleep might affect the epidemiological studies trying to correlate leg movement activity during sleep with cerebrovascular and cardiovascular pathology. One main point of strength of the present study is that it was based on a large group of well-phenotyped, unmedicated RLS patients and controls. By the same token, the main limitation of the study was that curve fitting characterized the overall IMI distribution derived from all patients with RLS, as opposed to the IMI distribution of individual patients. Another limitation of the study is that since blood tests did not invariably include ferritin levels, these levels were not taken into account either as exclusion criteria or in the subsequent data analysis. To the best of our knowledge, however, there are no definite data in the literature that might indicate a different time structure of PLMS in patients with RLS with or without low ferritin levels. The two independent data-driven approaches employed in the present study yielded consistent results and had different strengths and limitations that tended to compensate each other. In particular, the main point of strength of the data-driven approach based on empirical functions was that it was essentially assumption-free, whereas its limitation was that the parameters of the ad hoc, empirical functions generally lacked an intuitive counterpart. Conversely, the limitation of the approach based on standard functions was that it assumed that data could be fitted with normal and exponential functions, whereas its main point of strength was that model parameters were intuitively related to the count (α, δ) and IMI value (β) at the curve peaks, the “bell” curve widths (γ), and the reciprocal of the time constant of count decay (ε). In conclusion, this study seems to indicate that the PLMS phenomenon involves leg movements with IMI up to 60 s, rather than up to 90 s as recommended by both the current sets of standard criteria, if allowance is made for the fact that the expression “period length” is used instead of IMI in AASM standards [4, 11]. However, the number of leg movements involved in this difference is relatively small and does not affect the ability of the PLMS index to discriminate between participants with RLS and control participants. Therefore, changing the rules at this time does not appear to be an urgent matter. This possibility should be taken into account in future amendments of the scoring standards. Supplementary Material Supplementary material is available at SLEEP online. Funding This study (Drs. Ferri, Aricò, and Rundo) was partially supported by a grant of the Italian Ministry of Health (“Ricerca Corrente”). Dr. Manconi was supported by the Swiss National Science Foundation (Grant No. 320030_144007). Conflict of interest statement. None declared. Work Performed: Department of Neurology I.C., Sleep Research Center, Oasi Research Institute - IRCCS, Troina, Italy References 1. Lugaresi Eet al. Rilievi poligrafici sui fenomeni motori nella sindrome delle gambe senza riposo. Riv Neurol . 1965; 35: 550– 561. Google Scholar PubMed 2. Lugaresi Eet al. Particularités cliniques et polygraphiques du syndrome d’impatience des membres inferieurs. Rev Neurol (Paris) . 1965; 113: 545– 555. 3. American Sleep Disorders Association. Recording and scoring leg movements. The Atlas Task Force. 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SLEEP – Oxford University Press

**Published: ** Mar 1, 2018

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