TY - JOUR
AU - Wang,, Henry
AB - Abstract OBJECTIVE Skeletal stress fracture of the lower limbs remains a significant problem for the military. The objective of this study was to develop a subject-specific 3D reconstruction of the tibia using only a few CT images for the prediction of peak stresses and locations. METHODS Full bilateral tibial CT scans were recorded for 63 healthy college male participants. A 3D finite element (FE) model of the tibia for each subject was generated from standard CT cross-section data (i.e., 4%, 14%, 38%, and 66% of the tibial length) via a transformation matrix. The final reconstructed FE models were used to calculate peak stress and location on the tibia due to a simulated walking load (3,700 N), and compared to the raw models. RESULTS The density-weighted, spatially-normalized errors between the raw and reconstructed CT models were small. The mean percent difference between the raw and reconstructed models for peak stress (0.62%) and location (−0.88%) was negligible. CONCLUSIONS Subject-specific tibia models can provide even great insights into the mechanisms of stress fracture injury, which are common in military and athletic settings. Rapid development of 3D tibia models allows for the future work of determining peak stress-related injury correlates to stress fracture outcomes. INTRODUCTION Skeletal stress injury (SSI) of the lower limbs remains a significant problem for the military due to the long recovery time, high associated financial cost, and poor prognosis. A wealth of military research has been conducted to investigate phenotypic risk factors for SSI.1–3 This research has demonstrated that bone morphology, i.e., specific combinations of density and bone shape, predispose recruits and soldiers to injury when combined with a rigorous physical activity regimen.4–6 Analysis of peripheral Quantitative Computed Tomography (pQCT) at various regions of the tibia can be used to estimate bone morphology. In particular, our group developed the Bone Alignment and Measurement Package (BAMPack) specifically for discerning subtle changes in bone pQCT during longitudinal studies of military recruits of the course of basic combat training.7 Through statistical shape and density modeling (SSDM) of pQCT data, we have identified morphological risk factors that show a strong correlation to tibia stress fracture outcomes. We have also shown that the spectral content of pQCT is strongly correlated to tibia stress fracture injury. It is likely that bone morphology influences stress and strain fields throughout the bone.8 Additionally, peak skeletal stresses, which yield higher rates of micro-fractures, are likely better correlates of injury risk than non-site specific bone stress metrics. Finite element models (FEM) can be developed to determine peak stresses and peak stress locations of the tibia for a given load using whole bone CT scans. However, researchers typically acquire pQCT scans at specific locations (e.g., 4, 14, 38 and 66% tibia length) of tibia when assessing bone morphology, bypassing the more tedious nature of full CT scans. Therefore, the objective of this study is to develop a subject-specific 3D reconstruction of the tibia using only a few CT images for the prediction of peak stresses and locations. The future goal would be to correlate these measures to tibia stress fracture outcome to assess the risk of this type of injury for new military cohorts. METHODS Experimental Design and Procedure Participants Sixty-three healthy college male participants were recruited. The means and standard deviations (SDs) of age, body mass, and body height of participants were 21(2) years, 78.4(10.2) kg, and 180.4(6.3) cm, respectively. Participants were classified as low risk for cardiovascular diseases according to American College of Sports Medicine (ACSM) guidelines9 and free from known musculoskeletal injury. All participants met military enlistment standards in terms of physical condition, and age, body mass, and body height of participants were comparable to those of military recruits entering U.S. Army Basic Training.10 Approvals from the Ball State University Institutional Research Board and Human Research Protection Office at the U.S. Army Medical Research and Materiel Command were obtained prior to commencing the study. CT Measurements A GE Light Speed VCT scanner (GE HealthCare, General Electric Company, Chicago, IL, USA) was used to perform CT imaging. During the CT scanning, participants’ bilateral tibial CTs were recorded through axial plane scans. CT tube potential was set at 120 peak kilo-voltage (kVp), and the tube current-time product was set at 144.54 milliampere-seconds (mAs). The slice thickness was 0.625 mm. The field of view was 15 cm × 15 cm. 2D to 3D Image Reconstruction A full 3D model of the tibia is generated from standard CT cross-section data through an interpolation algorithm. Standard cross-sections collected in CT analysis are 4%, 14%, 38%, and 66% of the tibial length. Building a 3D FE model from 2D CT slices could bypass the need to perform a full CT scan of each individual in the future. The final reconstructed FE model can be used to calculate the stress and strain of the tibia due to applied loads. A full CT scan of a typical subject is processed in the 3D reconstruction algorithm below. Scans were taken at an in-plane resolution of 0.293 cm/pixel and an axial resolution of 0.625 mm/step. The standard axial site cross-sectional images for the subject are shown in Figure 1 (4%, 14%, 38%, and 66% tibial length). FIGURE 1. View largeDownload slide Cross-sectional CT images at standard axial sites of the tibia. FIGURE 1. View largeDownload slide Cross-sectional CT images at standard axial sites of the tibia. The CT images of the full tibia were converted into a quadrilateral mesh, where the vertices store x-, y-, and density- (ρ-) values. The routines used to convert the images to the mesh are adopted from the standard suite of subroutines previously published.11,12 Figure 2 shows an example quadrilateral mesh for the 66% tibial length CT image. A convergence study was conducted where it was found that the calculation of peak stress and location converged at 9 radial and 72 circumferential nodes as shown in Figure 2. An FE model is then developed utilizing the full CT stack by connecting the quadrilaterals from one cross-section to the next, along the axis of the tibia as shown in Figure 3. The resulting inter-connection produces a solid, 3D hexahedral mesh of the tibia. The density of each hexahedron is interpolated from the density map of each cross-section. FIGURE 2. View largeDownload slide Example cross-section (66% tibia length) showing the quadrilateral mesh and density map. FIGURE 2. View largeDownload slide Example cross-section (66% tibia length) showing the quadrilateral mesh and density map. FIGURE 3. View largeDownload slide The 3D mesh is generated by connecting quadrilaterals along the axis of the tibia. FIGURE 3. View largeDownload slide The 3D mesh is generated by connecting quadrilaterals along the axis of the tibia. The advantages of using the quadrilateral mesh are: (1) The shape and density, i.e., topography, of the bone can be quantified; (2) The conversion of an axial sequence of quadrilateral mesh leads to a straightforward auto-generation of an FE model of the tibia. To transform the mesh data for the standard tibial length cross-sections (4%, 14%, 38%, and 66% tibial length) into a complete 3D model, we use the pseudo-inverse. Specifically, let Xi represent a 1D array (vector) of the x-, y-, and ρ-data for every vertex of cross-section i. Then, let A=[X1,X2,X3,…,XN] be an array that contains the vertex data for all N cross-sections of the image stack, and let B=[X4%,X14%,X38%,X66%] be an array that contains the vertex data for only the cross-sections that correspond to the standard axial sites. The array A can be calculated from B assuming a linear transformation of the form A = B*T, where T is the transformation matrix. The transformation matrix can be calculated as T=pinv(B)∗A (1) where pinv represents the Moore-Penrose pseudo-inverse operator. The pseudo-inverse optimizes T so that |A – B*T| is minimized. Therefore, to calculate the approximation of the full CT data, AT=B⋅T (2) The density-weighted, spatially-normalized error between the full CT data and the subset-approximated CT data is ε=∑iδi⋅Ri∑iδi (3) where the difference metrics are δi=(xi,Data−xi,Trans)2+(yi,Data−yi,Trans)2 (4) and Ri= |ρi,Data−ρi,Trans | (5) for all vertices of each cross-sectional mesh i. For qualitative comparison, the full tibia CT and transformed tibia using the transformation matrix T are shown in Figure 4. FIGURE 4. View largeDownload slide Tibia meshes for raw full tibia CT data and full tibia reconstructed from method described in this study. Both bone shape and density are in good qualitative agreement. FIGURE 4. View largeDownload slide Tibia meshes for raw full tibia CT data and full tibia reconstructed from method described in this study. Both bone shape and density are in good qualitative agreement. Following the above calculations, A and AT were then converted into hexahedral 3D FE models. The hexahedra were constructed by connecting sequential quadrilaterals. The density values for each hexahedron were used to approximate material properties according to Kaneko et al.13 The proximal end of the tibia diaphysis model is held fixed, while a transverse load can be applied at the base of the tibia. The FE model is used to calculate peak tensile stresses, the location of peak tensile stresses, and the maximum deflection of both the full CT model and subset-approximated model. Finite Element Methods The finite element (FE) method is a well-developed technique to calculate stress, strain, and displacement of a structure. In part, any structure can be thought of as an assembly of springs, dampers, and masses. For static loads (inertial forces are ignored), the governing equation of this system is the balance of internal forces (e.g., spring force) and external forces (e.g., ground reaction forces). For a linear spring with spring constant k and an end load F, this relationship becomes F = k*u, where u is the compression or extension of the spring. As multiple springs and multiple forces are added to the system, this equation takes on a matrix form, so that F = K*u. While it is straightforward to solve this equation for most simple structures, it may not be straightforward for complex structures such as the skeleton, or organs of the human body. The power of the FE method is that it reduces complex geometries into the spring matrix equation listed above, by using interpolation, numerical integration, and linear algebra. For the purposes of our work, we will closely follow the numerical methods shown in a standard text on the FE method14. The model will solve the static displacements, stresses, and strains of the structure composed of linear hexahedral elements, linear materials (Hooke’s Law), fixed boundary conditions, and simple end loads (forces, moments). RESULTS The density-weighted, spatially-normalized error between the full CT data and the subset-approximated CT data is shown in Figure 5. Overall, the calculated errors were small, and as to be expected, the error at the 4, 14, 38, and 66% tibial length were the smallest and the largest error occurred toward the proximal epiphysis. FIGURE 5. View largeDownload slide The density-weighted, spatially-normalized error between the full CT data and the subset-approximated CT data. FIGURE 5. View largeDownload slide The density-weighted, spatially-normalized error between the full CT data and the subset-approximated CT data. From the tibia CT images for each individual in the cohort, we determined the location and value of peak tensile stresses for an FE model derived from the full CT stack, and for a model from the reconstructed tibia. A static ankle load equivalent to walking (3,700 N) was applied to the full model and reconstructed model for each subject to compare peak stress and location of peak stress. The results of this comparison are shown in Figure 6 for peak stresses and Figure 7 for the location of peak stresses. In the left panel of each figure, the x-axis is the result from the reconstructed model and the y-axis is the result from the full CT model. In the right panel of each figure, there is a histogram of the percent difference between the reconstructed and full CT dataset models. For peak stress, the mean percent difference was 0.62% with a standard deviation of 8.27%. For the location of peak stress, the mean percent difference −0.88% with a standard deviation of 8.06%. FIGURE 6. View largeDownload slide (A) Comparison of peak stresses computed from the reconstructed (x-axis) and raw (y-axis) CT dataset. The data were fit with linear regression, where the model parameters and fit are shown above the figure (n = 63). (B) Histogram of the percent difference in peak stress between the reconstructed and raw model. FIGURE 6. View largeDownload slide (A) Comparison of peak stresses computed from the reconstructed (x-axis) and raw (y-axis) CT dataset. The data were fit with linear regression, where the model parameters and fit are shown above the figure (n = 63). (B) Histogram of the percent difference in peak stress between the reconstructed and raw model. FIGURE 7. View largeDownload slide (A) Comparison of the location of peak stresses calculated from the reconstructed (x-axis) and raw CT (y-axis) datasets. The data were fit using linear regression, with the model parameters and fit shown above the figure (n = 63). (B) Histogram of the percent difference in location of peak stress between the reconstructed and raw model. FIGURE 7. View largeDownload slide (A) Comparison of the location of peak stresses calculated from the reconstructed (x-axis) and raw CT (y-axis) datasets. The data were fit using linear regression, with the model parameters and fit shown above the figure (n = 63). (B) Histogram of the percent difference in location of peak stress between the reconstructed and raw model. DISCUSSION The novelty of this work is a proof-of-concept of the ability to perform 3D reconstruction of the tibia using only a few 2D CT slices. The use of full bone CT scans is useful in constructing FE models of the tibia.11,12,15,16 However, full CT scans are cumbersome and often a few pQCT slices, typically at 4, 14, 38, and 66%, are acquired when analysing bone morphology. Therefore, it is advantageous to be able to accurately reconstruct the whole tibia 3D with only a few 2D CT scans. Using a transformation matrix methodology allowed for the rapid development of subject-specific 3D tibia meshes. The reconstructed tibias were able to replicate shape, density, and mechanical response with similar accuracy as a 3D mesh developed from a full stack of tibia slices and was significantly better than a spline extrapolation method that we also performed (data not shown). In literature, FE models of the tibia have been shown to elucidate the mechanics of stress fracture injury.8,11,12,15,16 Rapid development of subject-specific models can provide even great insights into injury mechanisms. The accuracy of the mechanical response of the 3D reconstruction was tested by comparing peak stress and peak stress location between the raw and reconstructed models, which showed a small error respectively. Additionally, peak stresses were similar to what has been estimated in literature for walking while carrying loads.11,12,15 Location of peak stresses ranged on average from roughly 25–70% of tibia slice. It has been shown that morphological variations at the 38 and 66% slice can predict adult fracture risk,17 which is consistent with peak stress occurring in this range. Peripheral Quantitative Computed Tomography (pQCT) data should be able to capture the influence of highly focal stress concentrations. Ideally, microcomputed tomography (μCT) would be used for this purpose. However, Schmidt et al18 reported that pQCT yielded satisfactory results in precision and accuracy when compared to μCT. There could be differences in density measures between pQCT and μCT, but the differences in density are mainly due to differences in machine calibration. However, these kind of differences would be considered systematic errors, which would not affect the outcomes of the modeling and simulations. There are a few limitations in the current study. The transformation matrix essentially extrapolates the bone structure near the proximal epiphysis resulting in larger errors than in other tibia locations. Although, the error was low, the proximal epiphysis reconstruction still could be improved with an additional slice beyond the 66% tibial length. Secondly, the transformation matrix was only tested at 4, 14, 38, and 66% (i.e., standard pQCT locations), therefore the transformation matrix developed here would only work for these slice locations. However, the methodology could be repeated for other combinations of tibial location, but the accuracy of such transformations would need to first be verified. Lastly, the transformation was not applied to an independent dataset, which should be done in the future for a true validation of the methodology. The ultimate goal of this work is to significantly reduce the occurrence of stress fracture injury. Those who are at high risk for stress injury would be identified and provided an alternate training until ready to enter BCT. The current methodology also allows for the future diagnoses of likely areas of tibial stress fracture. One strength of the current approach is that researchers can determine stress fracture risk by acquiring only a few pQCT scans at specific locations of tibia (e.g., 4, 14, 38 and 66% tibia length). Individuals identified as high risk prior to training could be monitored more frequently for bone health and placed on a modified training program to prevent overuse injuries. CONCLUSIONS In conclusion, we have developed a methodology allowing for the rapid development of subject-specific 3D tibia meshes from a transformation of 2D CT images. Subject-specific tibia models can provide even great insights into the mechanisms of stress fracture injury, which are common in military and athletic settings. Rapid development of 3D tibia models allows for the future work of determining a correlation between peak stress and/or peak stress region to stress fracture outcomes. This would include incorporating subject-specific tibia meshes into whole body models to determine bone stresses and resultant injury outcomes during realistic cyclic loading conditions seen in military training and athletics. Previous Presentations This work was orally presented at the 2017 Military Health System Research Symposium, Kissimmee, FL (Abstract number: MHSRS-17–0782). Funding This work was supported by the United States Army Medical Research and Materiel Command under contract numbers W81XWH-14-C-0061, W81XWH-08-1-0587, and W81XWH-15-1-0006. This supplement was sponsored by the Office of the Secretary of Defense for Health Affairs. References 1 Evans RK , Antczak AJ , Lester M , Yanovich R , Israeli E , Moran DS : Effects of a 4-month recruit training program on markers of bone metabolism . Med Sci Sports Exerc 2008 ; 40 : S660 – 70 . (in eng). Google Scholar Crossref Search ADS PubMed 2 Evans RK , Negus C , Antczak AJ , Yanovich R , Israeli E , Moran DS : Sex differences in parameters of bone strength in new recruits: beyond bone density . Med Sci Sports Exerc 2008 ; 40 : S645 – 53 . Google Scholar Crossref Search ADS PubMed 3 Evans RK , Negus CH , Centi AJ , Spiering BA , Kraemer WJ , Nindl BC : Peripheral QCT sector analysis reveals early exercise-induced increases in tibial bone mineral density . J Musculoskelet Neuronal Interact 2012 ; 12 : 155 – 64 . Google Scholar PubMed 4 Jepsen KJ , Centi A , Duarte GF , et al. : Biological constraints that limit compensation of a common skeletal trait variant lead to inequivalence of tibial function among healthy young adults . J Bone Mineral Res 2011 ; 26 : 2872 – 85 . Google Scholar Crossref Search ADS 5 Jepsen KJ , Duarte GF , Antczak AJ , et al. : Building a weak skeleton relative to body size during growth increases fracture risk in adults . J Bone Mineral Res 2010 ; 25 : S370 . Available at https://onlinelibrary.wiley.com/doi/abs/10.1002/jbmr.5650251305; accessed April 5, 2018. Google Scholar Crossref Search ADS 6 Jepsen KJ , Evans R , Negus CH , et al. : Variation in tibial functionality and fracture susceptibility among healthy, young adults arises from the acquisition of biologically distinct sets of traits . J Bone Mineral Res 2013 ; 28 : 1290 – 1300 . Google Scholar Crossref Search ADS 7 Negus CH , Izard RM , Greeves JP , Evans RK , Fraser WD : A 14-week initial military training regimen led to distal trabecularization and diaphyseal cortical thickening in tibiae of men and women . J Bone Mineral Res 2011 ; 26 : S254 . Available at https://onlinelibrary.wiley.com/toc/15234681/26/S1; accessed April 5, 2018. 8 Meardon SA , Willson JD , Gries SR , Kernozek TW , Derrick TR : Bone stress in runners with tibial stress fracture . Clin Biomechan (Bristol, Avon) 2015 ; 30 : 895 – 902 . (in eng). Google Scholar Crossref Search ADS 9 Pescatello L : ACSM’s Guidelines for Exercise Testing and Prescription , 9th ed. , Philadelphia , Lippincott Williams & Wilkins , 2014 . 10 Sharp MA : Physical fitness and occupational performance of women in the U.S. Army . Work 1994 ; 4 : 80 – 92 . (in eng). Google Scholar PubMed 11 Wang H , Dueball S : The effect of drop-landing height on tibia bone strain . J Biomed Sci Eng 2017 ; 10 : 10 – 20 . Google Scholar Crossref Search ADS 12 Wang H , Kia M , Dickin DC : Influences of load carriage and physical activity history on tibia bone strain . J Sport Health Sci 2016 Available at https://www.sciencedirect.com/science/article/pii/S2095254616300990; accessed April 5, 2018. 13 Kaneko TS , Pejcic MR , Tehranzadeh J , Keyak JH : Relationships between material properties and CT scan data of cortical bone with and without metastatic lesions . Med Eng Phys 2003 ; 25 : 445 – 54 . (in eng). Google Scholar Crossref Search ADS PubMed 14 Cook RD , Malkus DS , Plesha ME , Witt RJ : Concepts and Applications of Finite Element Analysis , 4th ed. , USA , John Wiley & Sons , 2002 . 15 Xu C , Silder A , Zhang J , et al. : An integrated musculoskeletal-finite-element model to evaluate effects of load carriage on the tibia during walking . J Biomech Eng 2016 ; 138 : 1 – 11 . Available at http://biomechanical.asmedigitalcollection.asme.org/article.aspx?articleid=2537122; accessed April 5, 2018. Google Scholar Crossref Search ADS 16 Xu C , Silder A , Zhang J , Reifman J , Unnikrishnan G : A cross-sectional study of the effects of load carriage on running characteristics and tibial mechanical stress: implications for stress-fracture injuries in women . BMC Musculoskelet Disord 2017 ; 18 : 125 . Available at https://bmcmusculoskeletdisord.biomedcentral.com/articles/10.1186/s12891-017-1481-9; accessed April 5, 2018. Google Scholar Crossref Search ADS PubMed 17 Dennison EM , Jameson KA , Edwards MH , Denison HJ , Aihie Sayer A , Cooper C : Peripheral quantitative computed tomography measures are associated with adult fracture risk: the Hertfordshire Cohort Study . Bone 2014 ; 64 : 13 – 17 . Google Scholar Crossref Search ADS PubMed 18 Schmidt C , Priemel M , Kohler T , et al. : Precision and accuracy of peripheral quantitative computed tomography (pQCT) in the mouse skeleton compared with histology and microcomputed tomography (microCT) . J Bone Miner Res 2003 ; 18 : 1486 – 1496 . Google Scholar Crossref Search ADS PubMed Author notes The views, opinions and/or findings contained in this report are those of the authors and should not be construed as an official Department of the Army position, policy or decision unless so designated by other documentation. Cleared for public release by the United States Army Medical Research and Materiel Command on February 26, 2016. © Association of Military Surgeons of the United States 2019. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
TI - 3D Tibia Reconstruction Using 2D Computed Tomography Images
JF - Military Medicine
DO - 10.1093/milmed/usy379
DA - 2019-03-01
UR - https://www.deepdyve.com/lp/oxford-university-press/3d-tibia-reconstruction-using-2d-computed-tomography-images-Vry8xSEXm0
SP - 621
VL - 184
IS - Supplement_1
DP - DeepDyve
ER -