Integration of Febio as an Instructional Tool in the Undergraduate Biomechanics Curriculum.

Computer simulations play an important role in a range of biomedical engineering applications. Thus, it is important that biomedical engineering students engage with modeling in their undergraduate education and establish an understanding of its practice. In addition, computational tools enhance active learning and complement standard pedagogical approaches to promote student understanding of course content. Herein, we describe the development and implementation of learning modules for computational modeling and simulation (CM&S) within an undergraduate biomechanics course. We developed four CM&S learning modules that targeted predefined course goals and learning outcomes within the febio studio software. For each module, students were guided through CM&S tutorials and tasked to construct and analyze more advanced models to assess learning and competency and evaluate module effectiveness. Results showed that students demonstrated an increased interest in CM&S through module progression and that modules promoted the understanding of course content. In addition, students exhibited increased understanding and competency in finite element model development and simulation software use. Lastly, it was evident that students recognized the importance of coupling theory, experiments, and modeling and understood the importance of CM&S in biomedical engineering and its broad application. Our findings suggest that integrating well-designed CM&S modules into undergraduate biomedical engineering education holds much promise in supporting student learning experiences and introducing students to modern engineering tools relevant to professional development.

A New Method for Quantifying Abdominal Aortic Wall Shear Stress Using Phase Contrast Magnetic Resonance Imaging and the Womersley Solution.

Wall shear stress (WSS) is an important mediator of cardiovascular pathologies and there is a need for its reliable evaluation as a potential prognostic indicator. The purpose of this work was to develop a method that quantifies WSS from two-dimensional (2D) phase contrast magnetic resonance (PCMR) imaging derived flow waveforms, apply this method to PCMR data acquired in the abdominal aorta of healthy volunteers, and to compare PCMR-derived WSS values to values predicted from a computational fluid dynamics (CFD) simulation. The method uses PCMR-derived flow versus time waveforms constrained by the Womersley solution for pulsatile flow in a cylindrical tube. The method was evaluated for sensitivity to input parameters, intrastudy repeatability and was compared with results from a patient-specific CFD simulation. 2D-PCMR data were acquired in the aortas of healthy men (n = 12) and women (n = 15) and time-averaged WSS (TAWSS) was compared. Agreement was observed when comparing TAWSS between CFD and the PCMR flow-based method with a correlation coefficient of 0.88 (CFD: 15.0 ± 1.9 versus MRI: 13.5 ± 2.4 dyn/cm2) though comparison of WSS values between the PCMR-based method and CFD predictions indicate that the PCMR method underestimated instantaneous WSS by 3.7 ± 7.6 dyn/cm2. We found no significant difference in TAWSS magnitude between the sexes; 8.19 ± 2.25 versus 8.07 ± 1.71 dyn/cm2, p = 0.16 for men and women, respectively.

On the use of constrained reactive mixtures of solids to model finite deformation isothermal elastoplasticity and elastoplastic damage mechanics.

This study presents a framework for plasticity and elastoplastic damage mechanics by treating materials as reactive solids whose internal composition evolves in response to applied loading. Using the framework of constrained reactive mixtures, plastic deformation is accounted for by allowing loaded bonds within the material to break and reform in a stressed state. Bonds which break and reform represent a new generation with a new reference configuration, which is time-invariant and provided by constitutive assumption. The constitutive relation for the reference configuration of each generation may depend on the selection of a suitable yield measure. The choice of this measure and the resulting plastic flow conditions are constrained by the Clausius-Duhem inequality. We show that this framework remains consistent with classical plasticity approaches and principles. Verification of this reactive plasticity framework, which is implemented in the open source FEBio finite element software (febio.org), is performed against standard 2D and 3D benchmark problems. Damage is incorporated into this reactive framework by allowing loaded bonds to break permanently according to a suitable damage measure, where broken bonds can no longer store free energy. Validation is also demonstrated against experimental data for problems involving plasticity and plastic damage. This study demonstrates that it is possible to formulate simple elastoplasticity and elastoplastic damage models within a consistent framework which uses measures of material mass composition as theoretically observable state variables. This theoretical frame can be expanded in scope to account for more complex behaviors.

Impact of combined plaque structural stress and wall shear stress on coronary plaque progression, regression, and changes in composition.

AIMS: The focal distribution of atherosclerotic plaques suggests that local biomechanical factors may influence plaque development. METHODS AND RESULTS: We studied 40 patients at baseline and over 12 months by virtual-histology intravascular ultrasound and bi-plane coronary angiography. We calculated plaque structural stress (PSS), defined as the mean of the maximum principal stress at the peri-luminal region, and wall shear stress (WSS), defined as the parallel frictional force exerted by blood flow on the endothelial surface, in areas undergoing progression or regression. Changes in plaque area, plaque burden (PB), necrotic core (NC), fibrous tissue (FT), fibrofatty tissue, and dense calcium were calculated for each co-registered frame. A total of 4029 co-registered frames were generated. In areas with progression, high PSS was associated with larger increases in NC and small increases in FT vs. low PSS (difference in ΔNC: 0.24 ± 0.06 mm2; P < 0.0001, difference in ΔFT: -0.15 ± 0.08 mm2; P = 0.049). In areas with regression, high PSS was associated with increased NC and decreased FT (difference in ΔNC: 0.15 ± 0.04; P = 0.0005, difference in ΔFT: -0.31 ± 0.06 mm2; P < 0.0001). Low WSS was associated with increased PB vs. high WSS in areas with progression (difference in ΔPB: 3.3 ± 0.4%; P < 0.001) with a similar pattern observed in areas with regression (difference in ΔPB: 1.2 ± 0.4%; P = 0.004). Plaque structural stress and WSS were largely independent of each other (R2 = 0.002; P = 0.001). CONCLUSION: Areas with high PSS are associated with compositional changes consistent with increased plaque vulnerability. Areas with low WSS are associated with more plaque growth in areas that progress and less plaque loss in areas that regress. The interplay of PSS and WSS may govern important changes in plaque size and composition.

Disturbed Flow Promotes Arterial Stiffening Through Thrombospondin-1.

BACKGROUND: Arterial stiffness and wall shear stress are powerful determinants of cardiovascular health, and arterial stiffness is associated with increased cardiovascular mortality. Low and oscillatory wall shear stress, termed disturbed flow (d-flow), promotes atherosclerotic arterial remodeling, but the relationship between d-flow and arterial stiffness is not well understood. The objective of this study was to define the role of d-flow on arterial stiffening and discover the relevant signaling pathways by which d-flow stiffens arteries. METHODS: D-flow was induced in the carotid arteries of young and old mice of both sexes. Arterial stiffness was quantified ex vivo with cylindrical biaxial mechanical testing and in vivo from duplex ultrasound and compared with unmanipulated carotid arteries from 80-week-old mice. Gene expression and pathway analysis was performed on endothelial cell-enriched RNA and validated by immunohistochemistry. In vitro testing of signaling pathways was performed under oscillatory and laminar wall shear stress conditions. Human arteries from regions of d-flow and stable flow were tested ex vivo to validate critical results from the animal model. RESULTS: D-flow induced arterial stiffening through collagen deposition after partial carotid ligation, and the degree of stiffening was similar to that of unmanipulated carotid arteries from 80-week-old mice. Intimal gene pathway analyses identified transforming growth factor-ß pathways as having a prominent role in this stiffened arterial response, but this was attributable to thrombospondin-1 (TSP-1) stimulation of profibrotic genes and not changes to transforming growth factor-ß. In vitro and in vivo testing under d-flow conditions identified a possible role for TSP-1 activation of transforming growth factor-ß in the upregulation of these genes. TSP-1 knockout animals had significantly less arterial stiffening in response to d-flow than wild-type carotid arteries. Human arteries exposed to d-flow had similar increases TSP-1 and collagen gene expression as seen in our model. CONCLUSIONS: TSP-1 has a critical role in shear-mediated arterial stiffening that is mediated in part through TSP-1's activation of the profibrotic signaling pathways of transforming growth factor-ß. Molecular targets in this pathway may lead to novel therapies to limit arterial stiffening and the progression of disease in arteries exposed to d-flow.

An endovascular model of ischemic myopathy from peripheral arterial disease.

OBJECTIVE: Peripheral arterial disease (PAD) is a significant age-related medical condition with limited pharmacologic options. Severe PAD, termed critical limb ischemia, can lead to amputation. Skeletal muscle is the end organ most affected by PAD, leading to ischemic myopathy and debility of the patient. Currently, there are not any therapeutics to treat ischemic myopathy, and proposed biologic agents have not been optimized owing to a lack of preclinical models of PAD. Because a large animal model of ischemic myopathy may be useful in defining the optimal dosing and delivery regimens, the objective was to create and to characterize a swine model of ischemic myopathy that mimics patients with severe PAD. METHODS: Yorkshire swine (N = 8) underwent acute right hindlimb ischemia by endovascular occlusion of the external iliac artery. The effect of ischemia on limb function, perfusion, and degree of ischemic myopathy was quantified by weekly gait analysis, arteriography, hindlimb blood pressures, femoral artery duplex ultrasound scans, and histologic examination. Animals were terminated at 5 (n = 5) and 6 (n = 3) weeks postoperatively. Ossabaw swine (N = 8) fed a high-fat diet were used as a model of metabolic syndrome for comparison of arteriogenic recovery and validation of ischemic myopathy. RESULTS: There was persistent ischemia in the right hindlimb, and occlusion pressures were significantly depressed compared with the untreated left hindlimb out to 6 weeks (systolic blood pressure, 31 ± 21 vs 83 ± 15 mm Hg, respectively; P = .0007). The blood pressure reduction resulted in a significant increase of ischemic myopathy in the gastrocnemius muscle in the treated limb. Gait analysis revealed a functional deficit of the right hindlimb immediately after occlusion that improved rapidly during the first 2 weeks. Peak systolic velocity values in the right common femoral artery were severely diminished throughout the entire study (P < .001), and the hemodynamic environment after occlusion was characterized by low and oscillatory wall shear stress. Finally, the internal iliac artery on the side of the ischemic limb underwent significant arteriogenic remodeling (1.8× baseline) in the Yorkshire but not in the Ossabaw swine model. CONCLUSIONS: This model uses endovascular technology to produce the first durable large animal model of ischemic myopathy. Acutely (first 2 weeks), this model is associated with impaired gait but no tissue loss. Chronically (2-6 weeks), this model delivers persistent ischemia, resulting in ischemic myopathy similar to that seen in PAD patients. This model may be of use for testing novel therapeutics including biologic therapies for promoting neovascularization and arteriogenesis.

Fibrin Network Changes in Neonates after Cardiopulmonary Bypass.

BACKGROUND: Quantitative and qualitative differences in the hemostatic systems exist between neonates and adults, including the presence of "fetal" fibrinogen, a qualitatively dysfunctional form of fibrinogen that exists until 1 yr of age. The consequences of "fetal" fibrinogen on clot structure in neonates, particularly in the context of surgery-associated bleeding, have not been well characterized. Here, the authors examine the sequential changes in clotting components and resultant clot structure in a small sample of neonates undergoing cardiac surgery and cardiopulmonary bypass (CPB). METHODS: Blood samples were collected from neonates (n = 10) before surgery, immediately after CPB, and after the transfusion of cryoprecipitate (i.e., adult fibrinogen component). Clots were formed from patient samples or purified neonatal and adult fibrinogen. Clot structure was analyzed using confocal microscopy. RESULTS: Clots formed from plasma obtained after CPB and after transfusion were more porous than baseline clots. Analysis of clots formed from purified neonatal and adult fibrinogen demonstrated that at equivalent fibrinogen concentrations, neonatal clots lack three-dimensional structure, whereas adult clots were denser with significant three-dimensional structure. Clots formed from a combination of purified neonatal and adult fibrinogen were less homogenous than those formed from either purified adult or neonatal fibrinogen. CONCLUSIONS: The results of this study confirm that significant differences exist in clot structure between neonates and adults and that neonatal and adult fibrinogen may not integrate well. These findings suggest that differential treatment strategies for neonates should be pursued to reduce the demonstrated morbidity of blood product transfusion.

An assessment of intra-patient variability on observed relationships between wall shear stress and plaque progression in coronary arteries.

BACKGROUND: Wall shear stress (WSS) has been associated with sites of plaque localization and with changes in plaque composition in human coronary arteries. Different values have been suggested for categorizing WSS as low, physiologic or high; however, uncertainties in flow rates, both across subjects and within a given individual, can affect the classification of WSS and thus influence the observed relationships between local hemodynamics and plaque changes over time. This study examines the effects of uncertainties in flow rate boundary conditions upon WSS values and investigates the influence of this variability on the observed associations of WSS with changes in VH-IVUS derived plaque components. METHODS: Three patients with coronary artery disease underwent baseline and 12 month follow-up angiography and virtual histology-intravascular ultrasound (VH-IVUS) measurements. Coronary artery models were reconstructed from the data and models with and without side-branches were created. Patient-specific Doppler ultrasound (DUS) data were employed as inflow boundary conditions and computational fluid dynamics was used to calculate the WSS in each model. Further, the influence of representative coronary artery flow waveforms upon WSS values was investigated and the concept of treating WSS using relative, rather than actual, values was explored. RESULTS: Models that included side-branch outflows and subject-specific DUS velocities were considered to be the reference cases. Hemodynamic differences were caused by the exclusion of side-branches and by imposing alternative velocity waveforms. One patient with fewer side-branches and a scaled generic waveform had little deviation from the reference case, while another patient with several side-branches excluded showed much larger departures from the reference situation. Differences between models and the respective reference cases were reduced when data were analyzed using relative, rather than actual, WSS. CONCLUSIONS: When considering individual subjects, large variations in patient-specific flow rates and exclusion of multiple side-branches in computational models can cause significant differences in observed associations between plaque evolution and ranges of computed WSS. These differences may contribute to the large variability typically found among subjects in pooled populations. Relative WSS may be more useful than actual WSS as a correlative variable when there is a large degree of uncertainty in flow rate data.

Influence of Material Parameter Variability on the Predicted Coronary Artery Biomechanical Environment via Uncertainty Quantification.

Central to the clinical adoption of patient-specific modeling strategies is demonstrating that simulation results are reliable and safe. Indeed, simulation frameworks must be robust to uncertainty in model input(s), and levels of confidence should accompany results. In this study, we applied a coupled uncertainty quantification-finite element (FE) framework to understand the impact of uncertainty in vascular material properties on variability in predicted stresses. Univariate probability distributions were fit to material parameters derived from layer-specific mechanical behavior testing of human coronary tissue. Parameters were assumed to be probabilistically independent, allowing for efficient parameter ensemble sampling. In an idealized coronary artery geometry, a forward FE model for each parameter ensemble was created to predict tissue stresses under physiologic loading. An emulator was constructed within the UncertainSCI software using polynomial chaos techniques, and statistics and sensitivities were directly computed. Results demonstrated that material parameter uncertainty propagates to variability in predicted stresses across the vessel wall, with the largest dispersions in stress within the adventitial layer. Variability in stress was most sensitive to uncertainties in the anisotropic component of the strain energy function. Moreover, unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter that describes the contribution of the embedded fibers to the overall artery stiffness. Results from a patient-specific coronary model confirmed many of these findings. Collectively, these data highlight the impact of material property variation on uncertainty in predicted artery stresses and present a pipeline to explore and characterize forward model uncertainty in computational biomechanics.

Influence of material parameter variability on the predicted coronary artery biomechanical environment via uncertainty quantification.

Central to the clinical adoption of patient-specific modeling strategies is demonstrating that simulation results are reliable and safe. Indeed, simulation frameworks must be robust to uncertainty in model input(s), and levels of confidence should accompany results. In this study, we applied a coupled uncertainty quantification-finite element (FE) framework to understand the impact of uncertainty in vascular material properties on variability in predicted stresses. Univariate probability distributions were fit to material parameters derived from layer-specific mechanical behavior testing of human coronary tissue. Parameters were assumed to be probabilistically independent, allowing for efficient parameter ensemble sampling. In an idealized coronary artery geometry, a forward FE model for each parameter ensemble was created to predict tissue stresses under physiologic loading. An emulator was constructed within the UncertainSCI software using polynomial chaos techniques, and statistics and sensitivities were directly computed. Results demonstrated that material parameter uncertainty propagates to variability in predicted stresses across the vessel wall, with the largest dispersions in stress within the adventitial layer. Variability in stress was most sensitive to uncertainties in the anisotropic component of the strain energy function. Moreover, unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter that describes the contribution of the embedded fibers to the overall artery stiffness. Results from a patient-specific coronary model confirmed many of these findings. Collectively, these data highlight the impact of material property variation on uncertainty in predicted artery stresses and present a pipeline to explore and characterize forward model uncertainty in computational biomechanics.