research

Computational Biomechanics

Research in the Musculoskeletal Research Laboratories has historically focused on the biomechanics and healing of musculoskeletal soft tissues, in particular the ligaments of the knee. Over the past five years, the research focus has expanded considerably to include hard tissue as well as cardiovascular tissues including the heart, coronary arteries and smaller vessels involved in angiogenesis.

Muskuloskeletal Research Laboratory

Computational Biomechanics



Extracellular matrix density regulates the rate of neovessel growth and branching in sprouting angiogenesis
L.T. Edgar, C.J. Underwood, J.E. Guilkey, J.B. Hoying, J.A. Weiss. In PLOS one, Vol. 9, No. 1, 2014.
DOI: 10.1371/journal.pone.0085178

Angiogenesis is regulated by the local microenvironment, including the mechanical interactions between neovessel sprouts and the extracellular matrix (ECM). However, the mechanisms controlling the relationship of mechanical and biophysical properties of the ECM to neovessel growth during sprouting angiogenesis are just beginning to be understood. In this research, we characterized the relationship between matrix density and microvascular topology in an in vitro 3D organ culture model of sprouting angiogenesis. We used these results to design and calibrate a computational growth model to demonstrate how changes in individual neovessel behavior produce the changes in vascular topology that were observed experimentally. Vascularized gels with higher collagen densities produced neovasculatures with shorter vessel lengths, less branch points, and reduced network interconnectivity. The computational model was able to predict these experimental results by scaling the rates of neovessel growth and branching according to local matrix density. As a final demonstration of utility of the modeling framework, we used our growth model to predict several scenarios of practical interest that could not be investigated experimentally using the organ culture model. Increasing the density of the ECM significantly reduced angiogenesis and network formation within a 3D organ culture model of angiogenesis. Increasing the density of the matrix increases the stiffness of the ECM, changing how neovessels are able to deform and remodel their surroundings. The computational framework outlined in this study was capable of predicting this observed experimental behavior by adjusting neovessel growth rate and branching probability according to local ECM density, demonstrating that altering the stiffness of the ECM via increasing matrix density affects neovessel behavior, thereby regulated vascular topology during angiogenesis.




A computational model of in vitro angiogenesis based on extracellular matrix fiber orientation
L.T. Edgar, S.C. Sibole, C.J. Underwood, J.E. Guilkey, J.A. Weiss. In Computer Methods in Biomechanical and Biomedical Engineering, Vol. 16, No. 7, pp. 790--801. 2013.
DOI: 10.1080/10255842.2012.662678

Recent interest in the process of vascularisation within the biomedical community has motivated numerous new research efforts focusing on the process of angiogenesis. Although the role of chemical factors during angiogenesis has been well documented, the role of mechanical factors, such as the interaction between angiogenic vessels and the extracellular matrix, remains poorly understood. In vitro methods for studying angiogenesis exist; however, measurements available using such techniques often suffer from limited spatial and temporal resolutions. For this reason, computational models have been extensively employed to investigate various aspects of angiogenesis. This paper outlines the formulation and validation of a simple and robust computational model developed to accurately simulate angiogenesis based on length, branching and orientation morphometrics collected from vascularised tissue constructs. Microvessels were represented as a series of connected line segments. The morphology of the vessels was determined by a linear combination of the collagen fibre orientation, the vessel density gradient and a random walk component. Excellent agreement was observed between computational and experimental morphometric data over time. Computational predictions of microvessel orientation within an anisotropic matrix correlated well with experimental data. The accuracy of this modelling approach makes it a valuable platform for investigating the role of mechanical interactions during angiogenesis.



 
Biomechanical analysis of acetabular revision constructs: is pelvic discontinuity best treated with bicolumnar or traditional unicolumnar fixation?
J.M. Gililland, L.A. Anderson, H.B. Henninger, E.N. Kubiak, C.L. Peters. In Journal of Arthoplasty, Vol. 28, No. 1, pp. 178--186. 2013.
DOI: 10.1016/j.arth.2012.04.031

Pelvic discontinuity in revision total hip arthroplasty presents problems with component fixation and union. A construct was proposed based on bicolumnar fixation for transverse acetabular fractures. Each of 3 reconstructions was performed on 6 composite hemipelvises: (1) a cup-cage construct, (2) a posterior column plate construct, and (3) a bicolumnar construct (no. 2 plus an antegrade 4.5-mm anterior column screw). Bone-cup interface motions were measured, whereas cyclical loads were applied in both walking and descending stair simulations. The bicolumnar construct provided the most stable construct. Descending stair mode yielded more significant differences between constructs. The bicolumnar construct provided improved component stability. Placing an antegrade anterior column screw through a posterior approach is a novel method of providing anterior column support in this setting.




Finite element predictions of cartilage contact mechanics in hips with retroverted acetabula
C.R. Henak, Carruth E, A.E. Anderson, M.D. Harris, B.J. Ellis, C.L. Peters, J.A. Weiss. In Osteoarthritis and Cartilage, Vol. 21, pp. 1522-1529. 2013.
DOI: 10.1016/j.joca.2013.06.008

Background
A contributory factor to hip osteoarthritis (OA) is abnormal cartilage mechanics. Acetabular retroversion, a version deformity of the acetabulum, has been postulated to cause OA via decreased posterior contact area and increased posterior contact stress. Although cartilage mechanics cannot be measured directly in vivo to evaluate the causes of OA, they can be predicted using finite element (FE) modeling.

Objective
The objective of this study was to compare cartilage contact mechanics between hips with normal and retroverted acetabula using subject-specific FE modeling.

Methods
Twenty subjects were recruited and imaged: 10 with normal acetabula and 10 with retroverted acetabula. FE models were constructed using a validated protocol. Walking, stair ascent, stair descent and rising from a chair were simulated. Acetabular cartilage contact stress and contact area were compared between groups.

Results
Retroverted acetabula had superomedial cartilage contact patterns, while normal acetabula had widely distributed cartilage contact patterns. In the posterolateral acetabulum, average contact stress and contact area during walking and stair descent were 2.6–7.6 times larger in normal than retroverted acetabula (P ≤ 0.017). Conversely, in the superomedial acetabulum, peak contact stress during walking was 1.2–1.6 times larger in retroverted than normal acetabula (P ≤ 0.044). Further differences varied by region and activity.

Conclusions
This study demonstrated superomedial contact patterns in retroverted acetabula vs widely distributed contact patterns in normal acetabula. Smaller posterolateral contact stress in retroverted acetabula than in normal acetabula suggests that increased posterior contact stress alone may not be the link between retroversion and OA.



 
Specimen-specific predictions of contact stress under physiological loading in the human hip: validation and sensitivity studies
C.R. Henak, A.K. Kapron, B.J. Ellis, S.A. Maas, A.E. Anderson, J.A. Weiss. In Biomechanics and Modeling in Mechanobiology, pp. 1-14. 2013.
DOI: 10.1007/s10237-013-0504-1

Hip osteoarthritis may be initiated and advanced by abnormal cartilage contact mechanics, and finite element (FE) modeling provides an approach with the potential to allow the study of this process. Previous FE models of the human hip have been limited by single specimen validation and the use of quasi-linear or linear elastic constitutive models of articular cartilage. The effects of the latter assumptions on model predictions are unknown, partially because data for the instantaneous behavior of healthy human hip cartilage are unavailable. The aims of this study were to develop and validate a series of specimen-specific FE models, to characterize the regional instantaneous response of healthy human hip cartilage in compression, and to assess the effects of material nonlinearity, inhomogeneity and specimen-specific material coefficients on FE predictions of cartilage contact stress and contact area. Five cadaveric specimens underwent experimental loading, cartilage material characterization and specimen-specific FE modeling. Cartilage in the FE models was represented by average neo-Hookean, average Veronda Westmann and specimen- and region-specific Veronda Westmann hyperelastic constitutive models. Experimental measurements and FE predictions compared well for all three cartilage representations, which was reflected in average RMS errors in contact stress of less than 25 %. The instantaneous material behavior of healthy human hip cartilage varied spatially, with stiffer acetabular cartilage than femoral cartilage and stiffer cartilage in lateral regions than in medial regions. The Veronda Westmann constitutive model with average material coefficients accurately predicted peak contact stress, average contact stress, contact area and contact patterns. The use of subject- and region-specific material coefficients did not increase the accuracy of FE model predictions. The neo-Hookean constitutive model underpredicted peak contact stress in areas of high stress. The results of this study support the use of average cartilage material coefficients in predictions of cartilage contact stress and contact area in the normal hip. The regional characterization of cartilage material behavior provides the necessary inputs for future computational studies, to investigate other mechanical parameters that may be correlated with OA and cartilage damage in the human hip. In the future, the results of this study can be applied to subject-specific models to better understand how abnormal hip contact stress and contact area contribute to OA.



 
Relationship of the intercondylar roof and the tibial footprint of the ACL: implications for ACL reconstruction
P.T. Scheffel, H.B. Henninger, R.T. Burks. In American Journal of Sports Medicine, Vol. 41, No. 2, pp. 396--401. 2013.
DOI: 10.1177/0363546512467955

Background: Debate exists on the proper relation of the anterior cruciate ligament (ACL) footprint with the intercondylar notch in anatomic ACL reconstructions. Patient-specific graft placement based on the inclination of the intercondylar roof has been proposed. The relationship between the intercondylar roof and native ACL footprint on the tibia has not previously been quantified.

Hypothesis: No statistical relationship exists between the intercondylar roof angle and the location of the native footprint of the ACL on the tibia.

Study Design: Case series; Level of evidence, 4.

Methods: Knees from 138 patients with both lateral radiographs and MRI, without a history of ligamentous injury or fracture, were reviewed to measure the intercondylar roof angle of the femur. Roof angles were measured on lateral radiographs. The MRI data of the same knees were analyzed to measure the position of the central tibial footprint of the ACL (cACL). The roof angle and tibial footprint were evaluated to determine if statistical relationships existed.

Results: Patients had a mean ± SD age of 40 ± 16 years. Average roof angle was 34.7° ± 5.2° (range, 23°-48°; 95% CI, 33.9°-35.5°), and it differed by sex but not by side (right/left). The cACL was 44.1% ± 3.4% (range, 36.1%-51.9%; 95% CI, 43.2%-45.0%) of the anteroposterior length of the tibia. There was only a weak correlation between the intercondylar roof angle and the cACL (R = 0.106). No significant differences arose between subpopulations of sex or side.

Conclusion: The tibial footprint of the ACL is located in a position on the tibia that is consistent and does not vary according to intercondylar roof angle. The cACL is consistently located between 43.2% and 45.0% of the anteroposterior length of the tibia. Intercondylar roof–based guidance may not predictably place a tibial tunnel in the native ACL footprint. Use of a generic ACL footprint to place a tibial tunnel during ACL reconstruction may be reliable in up to 95% of patients.



 
Evaluation of a post-processing approach for multiscale analysis of biphasic mechanics of chondrocytes
S.C. Sibole, S.A. Maas, J.P. Halloran, J.A. Weiss, A. Erdemir. In Computer Methods in Biomechanical and Biomedical Engineering, Vol. 16, No. 10, pp. 1112--1126. 2013.
DOI: 10.1080/10255842.2013.809711
PubMed ID: 23809004

Understanding the mechanical behaviour of chondrocytes as a result of cartilage tissue mechanics has significant implications for both evaluation of mechanobiological function and to elaborate on damage mechanisms. A common procedure for prediction of chondrocyte mechanics (and of cell mechanics in general) relies on a computational post-processing approach where tissue-level deformations drive cell-level models. Potential loss of information in this numerical coupling approach may cause erroneous cellular-scale results, particularly during multiphysics analysis of cartilage. The goal of this study was to evaluate the capacity of first- and second-order data passing to predict chondrocyte mechanics by analysing cartilage deformations obtained for varying complexity of loading scenarios. A tissue-scale model with a sub-region incorporating representation of chondron size and distribution served as control. The post-processing approach first required solution of a homogeneous tissue-level model, results of which were used to drive a separate cell-level model (same characteristics as the sub-region of control model). The first-order data passing appeared to be adequate for simplified loading of the cartilage and for a subset of cell deformation metrics, for example, change in aspect ratio. The second-order data passing scheme was more accurate, particularly when asymmetric permeability of the tissue boundaries was considered. Yet, the method exhibited limitations for predictions of instantaneous metrics related to the fluid phase, for example, mass exchange rate. Nonetheless, employing higher order data exchange schemes may be necessary to understand the biphasic mechanics of cells under lifelike tissue loading states for the whole time history of the simulation.




Surgical technique: talar neck osteotomy to lengthen the medial column after a malunited talar neck fracture
T. Suter, A. Barg, M. Knupp, H.B. Henninger, B. Hintermann. In Clinical Orthopaedics & Related research, Vol. 471, No. 4, pp. 1356--1364. 2013.
DOI: 10.1080/10255842.2013.809711
PubMed ID: 23809004

Understanding the mechanical behaviour of chondrocytes as a result of cartilage tissue mechanics has significant implications for both evaluation of mechanobiological function and to elaborate on damage mechanisms. A common procedure for prediction of chondrocyte mechanics (and of cell mechanics in general) relies on a computational post-processing approach where tissue-level deformations drive cell-level models. Potential loss of information in this numerical coupling approach may cause erroneous cellular-scale results, particularly during multiphysics analysis of cartilage. The goal of this study was to evaluate the capacity of first- and second-order data passing to predict chondrocyte mechanics by analysing cartilage deformations obtained for varying complexity of loading scenarios. A tissue-scale model with a sub-region incorporating representation of chondron size and distribution served as control. The post-processing approach first required solution of a homogeneous tissue-level model, results of which were used to drive a separate cell-level model (same characteristics as the sub-region of control model). The first-order data passing appeared to be adequate for simplified loading of the cartilage and for a subset of cell deformation metrics, for example, change in aspect ratio. The second-order data passing scheme was more accurate, particularly when asymmetric permeability of the tissue boundaries was considered. Yet, the method exhibited limitations for predictions of instantaneous metrics related to the fluid phase, for example, mass exchange rate. Nonetheless, employing higher order data exchange schemes may be necessary to understand the biphasic mechanics of cells under lifelike tissue loading states for the whole time history of the simulation.




Biomechanical evaluation of subpectoral biceps tenodesis: dual suture anchor versus interference screw fixation
R.Z. Tashjian, H.B. Henninger. In Journal of Shoulder and Elbow Surgery, Vol. 22, No. 10, pp. 1408–-1412. 2013.
DOI: 10.1016/j.jse.2012.12.039

Background
Subpectoral biceps tenodesis has been reliably used to treat a variety of biceps tendon pathologies. Interference screws have been shown to have superior biomechanical properties compared to suture anchors; although, only single anchor constructs have been evaluated in the subpectoral region. The purpose of this study was to compare interference screw fixation with a suture anchor construct, using 2 anchors for a subpectoral tenodesis.

Methods
A subpectoral biceps tenodesis was performed using either an interference screw (8 × 12 mm; Arthrex) or 2 suture anchors (Mitek G4) with #2 FiberWire (Arthrex) in a Krackow and Bunnell configuration in seven pairs of human cadavers. The humerus was inverted in an Instron and the biceps tendon was loaded vertically. Displacement driven cyclic loading was performed followed by failure loading.

Results
Suture anchor constructs had lower stiffness upon initial loading (P = .013). After 100 cycles, the stiffness of the suture anchor construct "softened" (decreased 9%, P < .001), whereas the screw construct was unchanged (0.4%, P = .078). Suture anchors had significantly higher ultimate failure strain than the screws (P = .003), but ultimate failure loads were similar between constructs: 280 ± 95 N (screw) vs 310 ± 91 N (anchors) (P = .438).

Conclusion
The interference screw was significantly stiffer than the suture anchor construct. Ultimate failure loads were similar between constructs, unlike previous reports indicating interference screws had higher ultimate failure loads compared to suture anchors. Neither construct was superior with regards to stress; although, suture anchors could withstand greater elongation prior to failure.



 
The geometry and biomechanics of normal and pathomorphologic human hips
M.D. Harris. Note: Ph.D. Thesis, Department of Bioengineering, University of Utah, 2013.

 
Cartilage and labrum mechanics in the normal and pathomorphologic human hip
C.R. Henak. Note: Ph.D. Thesis, Department of Bioengineering, University of Utah, 2013.


Statistical Shape Modeling of Cam Femoroacetabular Impingement
M.D. Harris, M. Datar, R.T. Whitaker, E.R. Jurrus, C.L. Peters, A.E. Anderson. In Journal of Orthopaedic Research, Vol. 31, No. 10, pp. 1620--1626. 2013.
DOI: 10.1002/jor.22389

Statistical shape modeling (SSM) was used to quantify 3D variation and morphologic differences between femurs with and without cam femoroacetabular impingement (FAI). 3D surfaces were generated from CT scans of femurs from 41 controls and 30 cam FAI patients. SSM correspondence particles were optimally positioned on each surface using a gradient descent energy function. Mean shapes for groups were defined. Morphological differences between group mean shapes and between the control mean and individual patients were calculated. Principal component analysis described anatomical variation. Among all femurs, the first six modes (or principal components) captured significant variations, which comprised 84% of cumulative variation. The first two modes, which described trochanteric height and femoral neck width, were significantly different between groups. The mean cam femur shape protruded above the control mean by a maximum of 3.3 mm with sustained protrusions of 2.5–3.0 mm along the anterolateral head-neck junction/distal anterior neck. SSM described variations in femoral morphology that corresponded well with areas prone to damage. Shape variation described by the first two modes may facilitate objective characterization of cam FAI deformities; variation beyond may be inherent population variance. SSM could characterize disease severity and guide surgical resection of bone.




Lateral ventricle morphology analysis via mean latitude axis
B. Paniagua, A. Lyall, J.-B. Berger, C. Vachet, R.M. Hamer, S. Woolson, W. Lin, J. Gilmore, M. Styner. In Proceedings of SPIE 8672, Biomedical Applications in Molecular, Structural, and Functional Imaging, 86720M, 2013.
DOI: 10.1117/12.2006846
PubMed ID: 23606800

Statistical shape analysis has emerged as an insightful method for evaluating brain structures in neuroimaging studies, however most shape frameworks are surface based and thus directly depend on the quality of surface alignment. In contrast, medial descriptions employ thickness information as alignment-independent shape metric. We propose a joint framework that computes local medial thickness information via a mean latitude axis from the well-known spherical harmonic (SPHARM-PDM) shape framework. In this work, we applied SPHARM derived medial representations to the morphological analysis of lateral ventricles in neonates. Mild ventriculomegaly (MVM) subjects are compared to healthy controls to highlight the potential of the methodology. Lateral ventricles were obtained from MRI scans of neonates (9- 144 days of age) from 30 MVM subjects as well as age- and sex-matched normal controls (60 total). SPHARM-PDM shape analysis was extended to compute a mean latitude axis directly from the spherical parameterization. Local thickness and area was straightforwardly determined. MVM and healthy controls were compared using local MANOVA and compared with the traditional SPHARM-PDM analysis. Both surface and mean latitude axis findings differentiate successfully MVM and healthy lateral ventricle morphology. Lateral ventricles in MVM neonates show enlarged shapes in tail and head. Mean latitude axis is able to find significant differences all along the lateral ventricle shape, demonstrating that local thickness analysis provides significant insight over traditional SPHARM-PDM. This study is the first to precisely quantify 3D lateral ventricle morphology in MVM neonates using shape analysis.




A new discrete element analysis method for predicting hip joint contact stresses
C.L. Abraham, S.A. Maas, J.A. Weiss, B.J. Ellis, C.L. Peters, A.E. Anderson. In Journal of Biomechanics, Vol. 46, No. 6, pp. 1121--1127. 2013.
DOI: 10.1016/j.jbiomech.2013.01.012

Quantifying cartilage contact stress is paramount to understanding hip osteoarthritis. Discrete element analysis (DEA) is a computationally efficient method to estimate cartilage contact stresses. Previous applications of DEA have underestimated cartilage stresses and yielded unrealistic contact patterns because they assumed constant cartilage thickness and/or concentric joint geometry. The study objectives were to: (1) develop a DEA model of the hip joint with subject-specific bone and cartilage geometry, (2) validate the DEA model by comparing DEA predictions to those of a validated finite element analysis (FEA) model, and (3) verify both the DEA and FEA models with a linear-elastic boundary value problem. Springs representing cartilage in the DEA model were given lengths equivalent to the sum of acetabular and femoral cartilage thickness and gap distance in the FEA model. Material properties and boundary/loading conditions were equivalent. Walking, descending, and ascending stairs were simulated. Solution times for DEA and FEA models were ∼7 s and ∼65 min, respectively. Irregular, complex contact patterns predicted by DEA were in excellent agreement with FEA. DEA contact areas were 7.5%, 9.7% and 3.7% less than FEA for walking, descending stairs, and ascending stairs, respectively. DEA models predicted higher peak contact stresses (9.8–13.6 MPa) and average contact stresses (3.0–3.7 MPa) than FEA (6.2–9.8 and 2.0–2.5 MPa, respectively). DEA overestimated stresses due to the absence of the Poisson's effect and a direct contact interface between cartilage layers. Nevertheless, DEA predicted realistic contact patterns when subject-specific bone geometry and cartilage thickness were used. This DEA method may have application as an alternative to FEA for pre-operative planning of joint-preserving surgery such as acetabular reorientation during peri-acetabular osteotomy.




Three-dimensional Quantification of Femoral Head Shape in Controls and Patients with Cam-type Femoroacetabular Impingement
M.D. Harris, S.P. Reese, C.L. Peters, J.A. Weiss, A.E. Anderson. In Annals of Biomedical Engineering, Vol. 41, No. 6, pp. 1162--1171. 2013.
DOI: 10.1007/s10439-013-0762-1

An objective measurement technique to quantify 3D femoral head shape was developed and applied to normal subjects and patients with cam-type femoroacetabular impingement (FAI). 3D reconstructions were made from high-resolution CT images of 15 cam and 15 control femurs. Femoral heads were fit to ideal geometries consisting of rotational conchoids and spheres. Geometric similarity between native femoral heads and ideal shapes was quantified. The maximum distance native femoral heads protruded above ideal shapes and the protrusion area were measured. Conchoids provided a significantly better fit to native femoral head geometry than spheres for both groups. Cam-type FAI femurs had significantly greater maximum deviations (4.99 ± 0.39 mm and 4.08 ± 0.37 mm) than controls (2.41 ± 0.31 mm and 1.75 ± 0.30 mm) when fit to spheres or conchoids, respectively. The area of native femoral heads protruding above ideal shapes was significantly larger in controls when a lower threshold of 0.1 mm (for spheres) and 0.01 mm (for conchoids) was used to define a protrusion. The 3D measurement technique described herein could supplement measurements of radiographs in the diagnosis of cam-type FAI. Deviations up to 2.5 mm from ideal shapes can be expected in normal femurs while deviations of 4–5 mm are characteristic of cam-type FAI.



 
Subject-specific analysis of joint contact mechanics: application to the study of osteoarthritis and surgical planning
C.R. Henak, A.E. Anderson, J.A. Weiss. In Journal of Biomechanical Engineering, Vol. 135, No. 2, 2013.
DOI: 10.1115/1.4023386
PubMed ID: 23445048

Advances in computational mechanics, constitutive modeling, and techniques for subject-specific modeling have opened the door to patient-specific simulation of the relationships between joint mechanics and osteoarthritis (OA), as well as patient-specific preoperative planning. This article reviews the application of computational biomechanics to the simulation of joint contact mechanics as relevant to the study of OA. This review begins with background regarding OA and the mechanical causes of OA in the context of simulations of joint mechanics. The broad range of technical considerations in creating validated subject-specific whole joint models is discussed. The types of computational models available for the study of joint mechanics are reviewed. The types of constitutive models that are available for articular cartilage are reviewed, with special attention to choosing an appropriate constitutive model for the application at hand. Issues related to model generation are discussed, including acquisition of model geometry from volumetric image data and specific considerations for acquisition of computed tomography and magnetic resonance imaging data. Approaches to model validation are reviewed. The areas of parametric analysis, factorial design, and probabilistic analysis are reviewed in the context of simulations of joint contact mechanics. Following the review of technical considerations, the article details insights that have been obtained from computational models of joint mechanics for normal joints; patient populations; the study of specific aspects of joint mechanics relevant to OA, such as congruency and instability; and preoperative planning. Finally, future directions for research and application are summarized.



 
Effect of Elastin Digestion on the Quasi-Static Tensile Response of Medial Collateral Ligament
H.B. Henninger, C.J. Underwood, S.J. Romney, G.L. Davis, J.A. Weiss. In Journal of Orthopaedic Research, pp. (published online). 2013.
DOI: 10.1002/jor.22352

Elastin is a structural protein that provides resilience to biological tissues. We examined the contributions of elastin to the quasi-static tensile response of porcine medial collateral ligament through targeted disruption of the elastin network with pancreatic elastase. Elastase concentration and treatment time were varied to determine a dose response. Whereas elastin content decreased with increasing elastase concentration and treatment time, the change in peak stress after cyclic loading reached a plateau above 1 U/ml elastase and 6 h treatment. For specimens treated with 2 U/ml elastase for 6 h, elastin content decreased approximately 35%. Mean peak tissue strain after cyclic loading (4.8%, p ≥ 0.300), modulus (275 MPa, p ≥ 0.114) and hysteresis (20%, p ≥ 0.553) were unaffected by elastase digestion, but stress decreased significantly after treatment (up to 2 MPa, p ≤ 0.049). Elastin degradation had no effect on failure properties, but tissue lengthened under the same pre-stress. Stiffness in the linear region was unaffected by elastase digestion, suggesting that enzyme treatment did not disrupt collagen. These results demonstrate that elastin primarily functions in the toe region of the stress–strain curve, yet contributes load support in the linear region. The increase in length after elastase digestion suggests that elastin may pre-stress and stabilize collagen crimp in ligaments




Effects of decorin proteoglycan on fibrillogenesis, ultrastructure, and mechanics of type I collagen gels
S.P. Reese, C.J. Underwood, J.A. Weiss. In Matrix Biology, pp. (in press). 2013.
DOI: 10.1016/j.matbio.2013.04.004

The proteoglycan decorin is known to affect both the fibrillogenesis and the resulting ultrastructure of in vitro polymerized collagen gels. However, little is known about its effects on mechanical properties. In this study, 3D collagen gels were polymerized into tensile test specimens in the presence of decorin proteoglycan, decorin core protein, or dermatan sulfate (DS). Collagen fibrillogenesis, ultrastructure, and mechanical properties were then quantified using a turbidity assay, 2 forms of microscopy (SEM and confocal), and tensile testing. The presence of decorin proteoglycan or core protein decreased the rate and ultimate turbidity during fibrillogenesis and decreased the number of fibril aggregates (fibers) compared to control gels. The addition of decorin and core protein increased the linear modulus by a factor of 2 compared to controls, while the addition of DS reduced the linear modulus by a factor of 3. Adding decorin after fibrillogenesis had no effect, suggesting that decorin must be present during fibrillogenesis to increase the mechanical properties of the resulting gels. These results show that the inclusion of decorin proteoglycan during fibrillogenesis of type I collagen increases the modulus and tensile strength of resulting collagen gels. The increase in mechanical properties when polymerization occurs in the presence of the decorin proteoglycan is due to a reduction in the aggregation of fibrils into larger order structures such as fibers and fiber bundles.




Micromechanical model of a surrogate for collagenous soft tissues: development, validation, and analysis of mesoscale size effects
S.P. Reese, B.J. Ellis, J.A. Weiss. In Biomechanics and Modeling in Mechanobiology, pp. (in press). 2013.
DOI: 10.1007/s10237-013-0475-2

Aligned, collagenous tissues such as tendons and ligaments are composed primarily of water and type I collagen, organized hierarchically into nanoscale fibrils, microscale fibers and mesoscale fascicles. Force transfer across scales is complex and poorly understood. Since innervation, the vasculature, damage mechanisms and mechanotransduction occur at the microscale and mesoscale, understanding multiscale interactions is of high importance. This study used a physical model in combination with a computational model to isolate and examine the mechanisms of force transfer between scales. A collagen-based surrogate served as the physical model. The surrogate consisted of extruded collagen fibers embedded within a collagen gel matrix. A micromechanical finite element model of the surrogate was validated using tensile test data that were recorded using a custom tensile testing device mounted on a confocal microscope. Results demonstrated that the experimentally measured macroscale strain was not representative of the microscale strain, which was highly inhomogeneous. The micromechanical model, in combination with a macroscopic continuum model, revealed that the microscale inhomogeneity resulted from size effects in the presence of a constrained boundary. A sensitivity study indicated that significant scale effects would be present over a range of physiologically relevant inter-fiber spacing values and matrix material properties. The results indicate that the traditional continuum assumption is not valid for describing the macroscale behavior of the surrogate and that boundary-induced size effects are present.




Inverse Electrocardiographic Source Localization of Ischemia: An Optimization Framework and Finite Element Solution
D. Wang, R.M. Kirby, R.S. MacLeod, C.R. Johnson. In Journal of Computational Physics, Vol. 250, Academic Press, pp. 403--424. 2013.
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2013.05.027

With the goal of non-invasively localizing cardiac ischemic disease using bodysurface potential recordings, we attempted to reconstruct the transmembrane potential (TMP) throughout the myocardium with the bidomain heart model. The task is an inverse source problem governed by partial differential equations (PDE). Our main contribution is solving the inverse problem within a PDE-constrained optimization framework that enables various physically-based constraints in both equality and inequality forms. We formulated the optimality conditions rigorously in the continuum before deriving finite element discretization, thereby making the optimization independent of discretization choice. Such a formulation was derived for the L2-norm Tikhonov regularization and the total variation minimization. The subsequent numerical optimization was fulfilled by a primal-dual interior-point method tailored to our problem's specific structure. Our simulations used realistic, fiberincluded heart models consisting of up to 18,000 nodes, much finer than any inverse models previously reported. With synthetic ischemia data we localized ischemic regions with roughly a 10% false-negative rate or a 20% false-positive rate under conditions up to 5% input noise. With ischemia data measured from animal experiments, we reconstructed TMPs with roughly 0.9 correlation with the ground truth. While precisely estimating the TMP in general cases remains an open problem, our study shows the feasibility of reconstructing TMP during the ST interval as a means of ischemia localization.