Publications by authors named "Victor H Barocas"

121 Publications

In Situ Lumbar Facet Capsular Ligament Strains Due to Joint Pressure and Residual Strain.

J Biomech Eng 2022 06;144(6)

Department of Biomedical Engineering, University of Minnesota, Twin Cities, Minneapolis, MN 55455.

The lumbar facet capsular ligament, which surrounds and limits the motion of each facet joint in the lumbar spine, has been recognized as being mechanically significant and has been the subject of multiple mechanical characterization studies in the past. Those studies, however, were performed on isolated tissue samples and thus could not assess the mechanical state of the ligament in vivo, where the constraints of attachment to rigid bone and the force of the joint pressure lead to nonzero strain even when the spine is not loaded. In this work, we quantified these two effects using cadaveric lumbar spines (five spines, 20 total facet joints harvested from L2 to L5). The effect of joint pressure was measured by injecting saline into the joint space and tracking the 3D capsule surface motion via digital image correlation, and the prestrain due to attachment was measured by dissecting a large section of the tissue from the bone and by tracking the motion between the on-bone and free states. We measured joint pressures of roughly 15-40 kPa and local first principal strains of up to 25-50% when 0.3 mL of saline was injected into the joint space; the subsequent increase in pressure and strain were more modest for further increases in injection volume, possibly due to leakage of fluid from the joint. The largest stretches were in the bone-to-bone direction in the portions of the ligament spanning the joint space. When the ligament was released from the vertebrae, it shrank by an average of 4-5%, with local maximum (negative) principal strain values of up to 30%, on average. Based on these measurements and previous tests on isolated lumbar facet capsular ligaments, we conclude that the normal in vivo state of the facet capsular ligament is in tension, and that the collagen in the ligament is likely uncrimped even when the spine is not loaded.
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http://dx.doi.org/10.1115/1.4053993DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8990720PMC
June 2022

Experimental and Mouse-Specific Computational Models of the Fbln4 Mouse to Identify Potential Biomarkers for Ascending Thoracic Aortic Aneurysm.

Cardiovasc Eng Technol 2022 Jan 22. Epub 2022 Jan 22.

Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN, 55455, USA.

Purpose: To use computational methods to explore geometric, mechanical, and fluidic biomarkers that could correlate with mouse lifespan in the Fbln4 mouse. Mouse lifespan was used as a surrogate for risk of a severe cardiovascular event in cases of ascending thoracic aortic aneurysm.

Methods: Image-based, mouse-specific fluid-structure-interaction models were developed for Fbln4 mice (n = 10) at ages two and six months. The results of the simulations were used to quantify potential biofluidic biomarkers, complementing the geometrical biomarkers obtained directly from the images.

Results: Comparing the different geometrical and biofluidic biomarkers to the mouse lifespan, it was found that mean oscillatory shear index (OSI) and minimum time-averaged wall shear stress (TAWSS) at six months showed the largest correlation with lifespan (r = 0.70, 0.56), with both correlations being positive (i.e., mice with high OSI and high TAWSS tended to live longer). When change between two and six months was considered, the change in TAWSS showed a much stronger correlation than OSI (r = 0.75 vs. 0.24), and the correlation was negative (i.e., mice with increasing TAWSS over this period tended to live less long).

Conclusion: The results highlight potential biomarkers of ATAA outcomes that can be obtained through noninvasive imaging and computational simulations, and they illustrate the potential synergy between small-animal and computational models.
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http://dx.doi.org/10.1007/s13239-021-00600-4DOI Listing
January 2022

Characterizing Tissue Remodeling and Mechanical Heterogeneity in Cerebral Aneurysms.

J Vasc Res 2022 10;59(1):34-42. Epub 2021 Nov 10.

Department of Biomedical Engineering, University of Minnesota Twin Cities, Minneapolis, Minnesota, USA.

Accurately assessing the complex tissue mechanics of cerebral aneurysms (CAs) is critical for elucidating how CAs grow and whether that growth will lead to rupture. The factors that have been implicated in CA progression - blood flow dynamics, immune infiltration, and extracellular matrix remodeling - all occur heterogeneously throughout the CA. Thus, it stands to reason that the mechanical properties of CAs are also spatially heterogeneous. Here, we present a new method for characterizing the mechanical heterogeneity of human CAs using generalized anisotropic inverse mechanics, which uses biaxial stretching experiments and inverse analyses to determine the local Kelvin moduli and principal alignments within the tissue. Using this approach, we find that there is significant mechanical heterogeneity within a single acquired human CA. These results were confirmed using second harmonic generation imaging of the CA's fiber architecture and a correlation was observed. This approach provides a single-step method for determining the complex heterogeneous mechanics of CAs, which has important implications for future identification of metrics that can improve accuracy in prediction risk of rupture.
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http://dx.doi.org/10.1159/000519694DOI Listing
February 2022

Local tissue heterogeneity may modulate neuronal responses via altered axon strain fields: insights about innervated joint capsules from a computational model.

Biomech Model Mechanobiol 2021 Dec 12;20(6):2269-2285. Epub 2021 Sep 12.

Department of Biomedical Engineering, College of Science and Engineering, University of Minnesota, Nils Hasselmo Hall, 312 Church St SE, Minneapolis, MN, USA.

In innervated collagenous tissues, tissue scale loading may contribute to joint pain by transmitting force through collagen fibers to the embedded mechanosensitive axons. However, the highly heterogeneous collagen structures of native tissues make understanding this relationship challenging. Recently, collagen gels with embedded axons were stretched and the resulting axon signals were measured, but these experiments were unable to measure the local axon strain fields. Computational discrete fiber network models can directly determine axon strain fields due to tissue scale loading. Therefore, this study used a discrete fiber network model to identify how heterogeneous collagen networks (networks with multiple collagen fiber densities) change axon strain due to tissue scale loading. In this model, a composite cylinder (axon) was embedded in a Delaunay network (collagen). Homogeneous networks with a single collagen volume fraction and two types of heterogeneous networks with either a sparse center or dense center were created. Measurements of fiber forces show higher magnitude forces in sparse regions of heterogeneous networks and uniform force distributions in homogeneous networks. The average axon strain in the sparse center networks decreases when compared to homogeneous networks with similar collagen volume fractions. In dense center networks, the average axon strain increases compared to homogeneous networks. The top 1% of axon strains are unaffected by network heterogeneity. Based on these results, the interaction of tissue scale loading, collagen network heterogeneity, and axon strains in native musculoskeletal tissues should be considered when investigating the source of joint pain.
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http://dx.doi.org/10.1007/s10237-021-01506-9DOI Listing
December 2021

Residual stress and osmotic swelling of the periodontal ligament.

Biomech Model Mechanobiol 2021 Dec 7;20(6):2047-2059. Epub 2021 Aug 7.

Department of Biomedical Engineering, University of Minnesota-Twin Cities, Minneapolis, USA.

Osmotic swelling and residual stress are increasingly recognized as important factors in soft tissue biomechanics. Little attention has been given to residual stress in periodontal ligament (PDL) biomechanics despite its rapid growth and remodeling potential. Those tissues that bear compressive loads, e.g., articular cartilage, intervertebral disk, have received much attention related to their capacities for osmotic swelling. To understand residual stress and osmotic swelling in the PDL, it must be asked (1) to what extent, if any, does the PDL exhibit residual stress and osmotic swelling, and (2) if so, whether residual stress and osmotic swelling are mechanically significant to the PDL's stress/strain behavior under external loading. Here, we incrementally built a series of computer models that were fit to uniaxial loading, osmotic swelling and residual stretch data. The models were validated with in vitro shear tests and in vivo tooth-tipping data. Residual stress and osmotic swelling models were used to analyze tension and compression stress (principal stress) effects in PDL specimens under external loads. Shear-to-failure experiments under osmotic conditions were performed and modeled to determine differences in mechanics and failure of swollen periodontal ligament. Significantly higher failure shear stresses in swollen PDL suggested that osmotic swelling reduced tension and thus had a strengthening effect. The in vivo model's first and third principal stresses were both higher with residual stress and osmotic swelling, but smooth stress gradients prevailed throughout the three-dimensional PDL anatomy. The addition of PDL stresses from residual stress and osmotic swelling represents a unique concept in dental biomechanics.
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http://dx.doi.org/10.1007/s10237-021-01493-xDOI Listing
December 2021

Through-thickness regional variation in the mechanical characteristics of the lumbar facet capsular ligament.

Biomech Model Mechanobiol 2021 Aug 31;20(4):1445-1457. Epub 2021 Mar 31.

Biomedical Engineering, University of Minnesota, 312 Church St. SE, 7-105 Nils Hasselmo Hall, Minneapolis, MN, 55455, USA.

The human lumbar facet capsule, with the facet capsular ligament (FCL) that forms its primary constituent, is a common source of lower back pain. Prior studies on the FCL were limited to in-plane tissue behavior, but due to the presence of two distinct yet mechanically different regions, a novel out-of-plane study was conducted to further characterize the roles of the collagen and elastin regions. An experimental technique, called stretch-and-bend, was developed to study the tension-compression asymmetry of the FCL due to varying collagen fiber density throughout the thickness of the tissue. Each healthy excised cadaveric FCL sample was tested in four conditions depending on primary collagen fiber alignment and regional loading. Our results indicate that the FCL is stiffest when the collagen fibers (1) are aligned in the direction of loading, (2) are in tension, and (3) are stretched - 16% from its off-the-bone, undeformed state. An optimization routine was used to fit a four-parameter anisotropic, hyperplastic model to the experimental data. The average elastin modulus, E, and the average collagen fiber modulus, ξ, were 13.15 ± 3.59 kPa and 18.68 ± 13.71 MPa (95% CI), respectively.
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http://dx.doi.org/10.1007/s10237-021-01455-3DOI Listing
August 2021

An Experimental-Computational Approach to Quantify Blood Rheology in Sickle Cell Disease.

Biophys J 2020 12 20;119(11):2307-2315. Epub 2020 Oct 20.

Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota. Electronic address:

In sickle cell disease, aberrant blood flow due to oxygen-dependent changes in red cell biomechanics is a key driver of pathology. Most studies to date have focused on the potential role of altered red cell deformability and blood rheology in precipitating vaso-occlusive crises. Numerous studies, however, have shown that sickle blood flow is affected even at high oxygen tensions, suggesting a potentially systemic role for altered blood flow in driving pathologies, including endothelial dysfunction, ischemia, and stroke. In this study, we applied a combined experimental-computation approach that leveraged an experimental platform that quantifies sickle blood velocity fields under a range of oxygen tensions and shear rates. We computationally fitted a continuum model to our experimental data to generate physics-based parameters that capture patient-specific rheological alterations. Our results suggest that sickle blood flow is altered systemically, from the arterial to the venous circulation. We also demonstrated the application of this approach as a tool to design patient-specific transfusion regimens. Finally, we demonstrated that patient-specific rheological parameters can be combined with patient-derived vascular models to identify patients who are at higher risk for cerebrovascular complications such as aneurysm and stroke. Overall, this study highlights that sickle blood flow is altered systemically, which can drive numerous pathologies, and this study demonstrates the potential utility of an experimentally parameterized continuum model as a predictive tool for patient-specific care.
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http://dx.doi.org/10.1016/j.bpj.2020.10.011DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7732763PMC
December 2020

Vibrotactile perception in Dupuytren disease.

J Plast Surg Hand Surg 2021 Feb 12;55(1):32-40. Epub 2020 Oct 12.

Twin Cities Orthopaedics, Edina, MN, USA.

Purpose: Dupuytren disease (DD) has been associated with enlarged Pacinian corpuscles (PCs) and with PCs having a greater number of lamellae. Based on these associations, we hypothesized that subjects with DD would have altered sensitivity to high-frequency vibrations and that the changes would be more prominent at 250 Hz, where healthy subjects demonstrate the highest sensitivity.

Methods: A novel device was created to deliver vibrations of specific frequencies and amplitudes to the fingers and palm. Using a Psi-marginal adaptive algorithm, vibrotactile perception thresholds (VPTs) were determined in 36 subjects with DD and 74 subjects without DD. Experiments were performed at 250 Hz and 500 Hz at the fingertip and palm. The VPTs were statistically analyzed with respect to disease status, age, gender, location tested, and frequency tested.

Results: We found that VPT increases with age, which agrees with findings by others. Women showed greater sensitivity (i.e. lower VPT) than men. Men exhibited lower sensitivity in DD versus healthy subjects, but the results were not statistically significant. In subjects with DD presenting unilaterally, the unaffected hand was more sensitive than the affected hand, in particular for a 250 Hz stimulus applied to the finger.

Conclusions: The data on vibration sensitivity obtained from a large group of subjects with and without DD present interesting trends that may serve as a useful reference to future DD researchers. Understanding additional symptoms of DD may facilitate development of novel diagnostic or prognostic protocols.
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http://dx.doi.org/10.1080/2000656X.2020.1828898DOI Listing
February 2021

Conceptual Framework Development for a Double-Walled Aortic Stent-Graft to Manage Blood Pressure.

J Med Device 2020 Sep 31;14(3):031005. Epub 2020 Jul 31.

Department of Biomedical Engineering, University of Minnesota, 312 Church Street SE Hasselmo Hall, 7-105, Minneapolis, MN 55455.

A double-walled stent-graft (DWSG) design with a compressible gas layer was conceived with the goal of treating hypertension in patients receiving an aortic stent-graft. Early prototypes were developed to evaluate the design concept through static measurements from a finite element (FE) model and quasi-static inflation experiments, and through dynamic measurements from an in vitro flow loop and the three-element Windkessel model. The amount of gas in the gas layer and the properties of the flexible inner wall were the primary variables evaluated in this study. Properties of the inner wall had minimal effect on DWSG behavior, but increased gas charge led to increased fluid capacitance and larger reduction in peak and pulse pressures. In the flow loop, placement of the DWSG decreased pulse pressure by over 20% compared to a rigid stent-graft. Capacitance measurements were consistent across all methods, with the maximum capacitance estimated at 0.07 mL/mmHg for the largest gas charge in the 15 cm long prototype. Windkessel model predictions for in vivo performance of a DWSG placed in the aorta of a hypertensive patient showed pulse pressure reduction of 14% compared to a rigid stent-graft case, but pressures never returned to unstented values. These results indicate that the DWSG design has potential to be developed into a new treatment for hypertensive patients requiring an aortic intervention.
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http://dx.doi.org/10.1115/1.4047873DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7477714PMC
September 2020

Investigation of Pathophysiological Aspects of Aortic Growth, Remodeling, and Failure Using a Discrete-Fiber Microstructural Model.

J Biomech Eng 2020 11;142(11)

Department of Biomedical Engineering, University of Minnesota-Twin Cities, 7-105 Nils Hasselmo Hall, 312 Church St SE, Minneapolis, MN 55455.

Aortic aneurysms are inherently unpredictable. One can never be sure whether any given aneurysm may rupture or dissect. Clinically, the criteria for surgical intervention are based on size and growth rate, but it remains difficult to identify a high-risk aneurysm, which may require intervention before the cutoff criteria, versus an aneurysm than can be treated safely by more conservative measures. In this work, we created a computational microstructural model of a medial lamellar unit (MLU) incorporating (1) growth and remodeling laws applied directly to discrete, individual fibers, (2) separate but interacting fiber networks for collagen, elastin, and smooth muscle, (3) active and passive smooth-muscle cell mechanics, and (4) failure mechanics for all three fiber types. The MLU model was then used to study different pathologies and microstructural anomalies that may play a role in vascular growth and failure. Our model recapitulated many aspects of arterial remodeling under hypertension with no underlying genetic syndrome including remodeling dynamics, tissue mechanics, and failure. Syndromic effects (smooth muscle cell (SMC) dysfunction or elastin fragmentation) drastically changed the simulated remodeling process, tissue behavior, and tissue strength. Different underlying pathologies were able to produce similarly dilatated vessels with different failure properties, providing a partial explanation for the imperfect nature of aneurysm size as a predictor of outcome.
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http://dx.doi.org/10.1115/1.4048031DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7580844PMC
November 2020

Glomerular filtration and podocyte tensional homeostasis: importance of the minor type IV collagen network.

Biomech Model Mechanobiol 2020 Dec 27;19(6):2433-2442. Epub 2020 May 27.

Department of Biomedical Engineering, University of Minnesota, 7-105 Nils Hasselmo Hall, 312 Church St SE, Minneapolis, MN, 55455, USA.

The minor type IV collagen chain, which is a significant component of the glomerular basement membrane in healthy individuals, is known to assemble into large structures (supercoils) that may contribute to the mechanical stability of the collagen network and the glomerular basement membrane as a whole. The absence of the minor chain, as in Alport syndrome, leads to glomerular capillary demise and eventually to kidney failure. An important consideration in this problem is that the glomerular capillary wall must be strong enough to withstand the filtration pressure and porous enough to permit filtration at reasonable pressures. In this work, we propose a coupled feedback loop driven by filtration demand and tensional homeostasis of the podocytes forming the outer portion of the glomerular capillary wall. Briefly, the deposition of new collagen increases the stiffness of basement membrane, helping to stress shield the podocytes, but the new collagen also decreases the permeability of the basement membrane, requiring an increase in capillary transmural pressure drop to maintain filtration; the resulting increased pressure outweighs the increased glomerular basement membrane stiffness and puts a net greater stress demand on the podocytes. This idea is explored by developing a multiscale simulation of the capillary wall, in which a macroscopic (µm scale) continuum model is connected to a set of microscopic (nm scale) fiber network models representing the collagen network and the podocyte cytoskeleton. The model considers two cases: healthy remodeling, in which the presence of the minor chain allows the collagen volume fraction to be increased by thickening fibers, and Alport syndrome remodeling, in which the absence of the minor chain allows collagen volume fraction to be increased only by adding new fibers to the network. The permeability of the network is calculated based on previous models of flow through a fiber network, and it is updated for different fiber radii and volume fractions. The analysis shows that the minor chain allows a homeostatic balance to be achieved in terms of both filtration and cell tension. Absent the minor chain, there is a fundamental change in the relation between the two effects, and the system becomes unstable. This result suggests that mechanobiological or mechanoregulatory therapies may be possible for Alport syndrome and other minor chain collagen diseases of the kidney.
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http://dx.doi.org/10.1007/s10237-020-01347-yDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7606712PMC
December 2020

An inter-species computational analysis of vibrotactile sensitivity in Pacinian and Herbst corpuscles.

R Soc Open Sci 2020 Apr 29;7(4):191439. Epub 2020 Apr 29.

Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN, USA.

Vibration sensing is ubiquitous among vertebrates, with the sensory end organ generally being a multilayered ellipsoidal structure. There is, however, a wide range of sizes and structural arrangements across species. In this work, we applied our earlier computational model of the Pacinian corpuscle to predict the sensory response of different species to various stimulus frequencies, and based on the results, we identified the optimal frequency for vibration sensing and the bandwidth over which frequencies should be most detectable. We found that although the size and layering of the corpuscles were very different, almost all of the 19 species studied showed very similar sensitivity ranges. The human and goose were the notable exceptions, with their corpuscle tuned to higher frequencies (130-170 versus 40-50 Hz). We observed no correlation between animal size and any measure of corpuscle geometry in our model. Based on the results generated by our computational model, we hypothesize that lamellar corpuscles across different species may use different sizes and structures to achieve similar frequency detection bands.
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http://dx.doi.org/10.1098/rsos.191439DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7211856PMC
April 2020

Asymmetric in-plane shear behavior of isolated cadaveric lumbar facet capsular ligaments: Implications for subject specific biomechanical models.

J Biomech 2020 05 22;105:109814. Epub 2020 Apr 22.

University of Minnesota, Biomedical Engineering, 312 Church St. SE, 7-105 Nils Hasselmo Hall, Minneapolis, MN 55455, United States. Electronic address:

The facet capsular ligaments (FCLs) flank the spinous process on the posterior aspect of the spine. The lumbar FCL is collagenous, with collagen fibers aligned primarily bone-to-bone (medial-lateral) and experiences significant shear, especially during spinal flexion and extension. We characterized the mechanical response of the lumbar FCL to in-plane shear, and we evaluated that response in the context of the fiber architecture. In-plane shear tests with both positive and negative shear (i.e., corresponding to flexion and to extension) were performed on eight cadaveric human L4-L5 FCLs. Our most striking observation was subject-dependent asymmetry in the response. All samples showed a toe region of low stiffness, transitioning to greater stiffness at higher strains, for both shear directions. Different samples showed profoundly different transition strains, with some samples stiffening more rapidly in positive shear and some in negative shear. This unpredictable asymmetry, which did not correlate with age, side, or degeneration state, suggesting that collagen fibers in the FCL are sometimes aligned at a slight positive angle from the bone-to-bone axis and sometimes at a negative angle. Fitting the experimental data to a fiber-composite-based finite element model supported this idea, yielding optimal fits with positive or negative off-axis fiber directions (-40° to +40°). Subsequent examination of selected FCLs by small-angle x-ray scattering (SAXS) showed a similar variability in fiber direction. We conclude that small individual differences in lumbar FCL architecture may have a significant effect on lumbar FCL mechanics, especially at moderate strains.
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http://dx.doi.org/10.1016/j.jbiomech.2020.109814DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7336028PMC
May 2020

Ex Vivo Mechanical Tests and Multiscale Computational Modeling Highlight the Importance of Intramural Shear Stress in Ascending Thoracic Aortic Aneurysms.

J Biomech Eng 2019 Oct 1. Epub 2019 Oct 1.

Department of Biomedical Engineering, University of Minnesota, 7-105 Nils Hasselmo Hall, 312 Church St. SE, Minneapolis, MN 55455.

Ascending thoracic aortic aneurysms (ATAAs) are anatomically complex in terms of architecture and geometry, and both complexities contribute to unpredictability of ATAA dissection and rupture in vivo. The goal of this work was to examine the mechanism of ATAA failure using a combination of detailed mechanical tests on human tissue and a multiscale computational model. We used (1) multiple, geometrically diverse, mechanical tests to characterize tissue properties, (2) a multiscale computational model to translate those results into a broadly usable form, and (3) a model-based computer simulation of the response of an ATAA to the stresses generated by the blood pressure. Mechanical tests were performed in uniaxial extension, biaxial extension, shear lap, and peel geometries. ATAA tissue was strongest in circumferential extension and weakest in shear, presumably because of the collagen and elastin in the arterial lamellae. A multiscale, fiber-based model using different fiber properties for collagen, elastin, and interlamellar connections was specified to match all of the experimental data with one parameter set. Finally, this model was used to simulate ATAA inflation using a realistic geometry. The predicted tissue failure occurred in regions of high stress, as expected; initial failure events involved almost entirely interlamellar connections, consistent with arterial dissection - the elastic lamellae remain intact, but the connections between them fail. The failure of the interlamellar connections, paired with the weakness of the tissue under shear loading, is suggestive that shear stress within the tissue may contribute to ATAA dissection.
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http://dx.doi.org/10.1115/1.4045270DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7104749PMC
October 2019

Modeling distributed forces within cell adhesions of varying size on continuous substrates.

Cytoskeleton (Hoboken) 2019 11 6;76(11-12):571-585. Epub 2019 Nov 6.

Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota.

Cell migration and traction are essential to many biological phenomena, and one of their key features is sensitivity to substrate stiffness, which biophysical models, such as the motor-clutch model and the cell migration simulator can predict and explain. However, these models have not accounted for the finite size of adhesions, the spatial distribution of forces within adhesions. Here, we derive an expression that relates varying adhesion radius ( R) and spatial distribution of force within an adhesion (described by s) to the effective substrate stiffness ( κ ), as a function of the Young's modulus of the substrate ( E ), which yields the relation, , for two-dimensional cell cultures. Experimentally, we found that a cone-shaped force distribution ( s = 1.05) can describe the observed displacements of hydrogels deformed by adherent U251 glioma cells. Also, we found that the experimentally observed adhesion radius increases linearly with the cell protrusion force, consistent with the predictions of the motor-clutch model with spatially distributed clutches. We also found that, theoretically, the influence of one protrusion on another through a continuous elastic environment is negligible. Overall, we conclude cells can potentially control their own interpretation of the mechanics of the environment by controlling adhesion size and spatial distribution of forces within an adhesion.
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http://dx.doi.org/10.1002/cm.21561DOI Listing
November 2019

Effects of Collagen Heterogeneity on Myocardial Infarct Mechanics in a Multiscale Fiber Network Model.

J Biomech Eng 2019 May 29. Epub 2019 May 29.

Department of Bioengineering, Clemson University, 401-3 Rhodes Engineering Research Center, 118 Engineering Service Drive, Clemson, SC 29631.

The scar that forms after a myocardial infarction is often characterized by a highly disordered architecture but generally exhibits some degree of collagen fiber orientation, with a resulting mechanical anisotropy. When viewed in finer detail, however, the heterogeneity of the sample is clear, with different subregions exhibiting different fiber orientations. In this work, we used a multiscale finite-element model to explore the consequences of the heterogeneity in terms of mechanical behavior. To do so, we used previously obtained fiber alignment maps of rat myocardial scar slices (n = 15) to generate scar-specific finite-element meshes that were populated with fiber models based on the local alignment state. These models were then compared to isotropic models with the same sample shape and fiber density, and to homogeneous models with the same sample shape, fiber density, and average fiber alignment as the scar-specific models. All simulations involved equibiaxial extension of the sample with free motion in the third dimension. We found that heterogeneity led to a lower degree of mechanical anisotropy and a higher level of local stress concentration than the corresponding homogeneous model, and also that fibers failed in the heterogeneous model at much lower macroscopic strains than in the isotropic and homogeneous models. Taken together, these results suggest that scar heterogeneity may impair myocardial mechanical function both in terms of anisotropy and strength, and that individual variations in scar heterogeneity could be an important consideration for understanding scar remodeling and designing therapeutic interventions for patients after myocardial infarction.
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http://dx.doi.org/10.1115/1.4043865DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6807994PMC
May 2019

Mechanical Performance of Posterior Spinal Instrumentation and Growing Rod Implants: Experimental and Computational Study.

Spine (Phila Pa 1976) 2019 Sep;44(18):1270-1278

Department of Orthopaedic Surgery, Medical School, University of Minnesota, Minneapolis, Minnesota.

Study Design: Experimental and computational study of posterior spinal instrumentation and growing rod constructs per ASTM F1717-15 vertebrectomy methodology for static compressive bending.

Objective: Assess mechanical performance of standard fusion instrumentation and growing rod constructs.

Summary Of Background Data: Growing rod instrumentation utilizes fewer anchors and spans longer distances, increasing shared implant loads relative to fusion. There is a need to evaluate growing rod's mechanical performance. ASTM F1717-15 standard assesses performance of spinal instrumentation; however, effects of growing rods with side-by-side connectors have not been evaluated.

Methods: Standard and growing rod constructs were tested per ASTM F1717-15 methodology; setup was modified for growing rod constructs to allow for connector offset. Three experimental groups (standard with active length 76 mm, and growing rods with active lengths 76 and 376 mm; n = 5/group) were tested; stiffness, yield load, and load at maximum displacement were calculated. Computational models were developed and used to locate stress concentrations.

Results: For both constructs at 76 mm active length, growing rod stiffness (49 ± 0.8 N/mm) was significantly greater than standard (43 ± 0.4 N/mm); both were greater than growing rods at 376 mm (10 ± 0.3 N/mm). No significant difference in yield load was observed between growing rods (522 ± 12 N) and standard (457 ± 19 N) constructs of 76 mm. Growing rod constructs significantly decreased from 76 mm (522 ± 12 N) to 376 mm active length (200 ± 2 N). Maximum load of growing rods at 76 mm (1084 ± 11 N) was significantly greater than standard at 76 mm (1007 ± 7 N) and growing rods at 376 mm active length (392 ± 5 N). Simulations with active length of 76 mm were within 10% of experimental mechanical characteristics; stress concentrations were at the apex and cranial to connector-rod interaction for standard and growing rod models, respectively.

Conclusion: Growing rod constructs are stronger and stiffer than spinal instrumentation constructs; with an increased length accompanied a decrease in strength. Growing rod construct stress concentration locations observed during computational simulation are consistent with clinically observed failure locations.

Level Of Evidence: 5.
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http://dx.doi.org/10.1097/BRS.0000000000003061DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6722018PMC
September 2019

Computational and Psychophysical Experiments on the Pacinian Corpuscle's Ability to Discriminate Complex Stimuli.

IEEE Trans Haptics 2019 Oct-Dec;12(4):635-644. Epub 2019 Mar 26.

Recognizing and discriminating vibrotactile stimuli is an essential function of the Pacinian corpuscle. This function has been studied at length in both a computational and an experimental setting, but the two approaches have rarely been compared, especially when the computational model has a high level of structural detail. In this paper, we explored whether the predictions of a multiscale, multiphysical computational model of the Pacinian corpuscle can predict the outcome of a corresponding psychophysical experiment. The discrimination test involved either two simple stimuli with frequency in the 160-500 Hz range, or two complex stimuli formed by combining the waveforms for a 100-Hz stimulus with a second stimulus in the 160-500 Hz range. The subjects' ability to distinguish between the simple stimuli increased as the frequency increased, a result consistent with the model predictions for the same stimuli. The model also predicted correctly that subjects would find the complex stimuli more difficult to distinguish than the simple ones and also that the discriminability of the complex stimuli would show no trend with frequency difference.
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http://dx.doi.org/10.1109/TOH.2019.2903500DOI Listing
May 2020

Editors' Choice Papers for 2018.

J Biomech Eng 2019 Mar 6. Epub 2019 Mar 6.

240 Skirkanich Hall 210 S. 33rd Street philadelphia, PA 19104-6321.

No abstract.
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http://dx.doi.org/10.1115/1.4043072DOI Listing
March 2019

The role of the facet capsular ligament in providing spinal stability.

Comput Methods Biomech Biomed Engin 2018 Oct;21(13):712-721

b Department of Rehabilitation Medicine , University of Minnesota , Minneapolis , MN , USA.

Low back pain (LBP) is the most common type of pain in America, and spinal instability is a primary cause. The facet capsular ligament (FCL) encloses the articulating joints of the spine and is of particular interest due to its high innervation - as instability ensues, high stretch values likely are a cause of this pain. Therefore, this work investigated the FCL's role in providing stability to the lumbar spine. A previously validated finite element model of the L4-L5 spinal motion segment was used to simulate pure moment bending in multiple planes. FCL failure was simulated and the following outcome measures were calculated: helical axes of motion, range of motion (ROM), bending stiffness, facet joint space, and FCL stretch. ROM increased, bending stiffness decreased, and altered helical axis patterns were observed with the removal of the FCL. Additionally, a large increase in FCL stretch was measured with diminished FCL mechanical competency, providing support that the FCL plays an important role in spinal stability.
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http://dx.doi.org/10.1080/10255842.2018.1514392DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6366332PMC
October 2018

Emergent structure-dependent relaxation spectra in viscoelastic fiber networks in extension.

Acta Biomater 2019 03 22;87:245-255. Epub 2019 Jan 22.

312 Church St. SE, Minneapolis, MN 55455, United States. Electronic address:

Viscoelasticity plays an important role in the mechanical behavior of biological tissues undergoing dynamic loading. Exploring viscoelastic relaxation spectra of the tissue is essential for predicting its mechanical response. Most load-bearing tissues, however, are also composed of networks of intertwined fibers and filaments of, e.g., collagen, elastin. In this work, we show how non-affine deformations within fiber networks affect the relaxation behavior of the material leading to the emergence of structure-dependent time scales in the relaxation spectra. In particular, we see two different contributions to the network relaxation process: a material contribution due to the intrinsic viscoelasticity of the fibers, and a kinematic contribution due to non-affine rearrangement of the network when different fibers relax at different rates. We also present a computational model to simulate viscoelastic relaxation of networks, demonstrating the emergent time scales and a pronounced dependence of the network relaxation behavior on whether components with different relaxation times percolate the network. Finally, we observe that the simulated relaxation spectrum for Delaunay networks is comparable to that measured experimentally for reconstituted collagen gels by others. STATEMENT OF SIGNIFICANCE: Viscoelasticty plays an important role in the mechanical behavior of biological tissues undergoing dynamic loading. Stress relaxation tests provide a convenient way to explore the viscoelastic behavior of the material, while providing an advantage of interrogating multiple time scales in a single experiment. Most load bearing tissues, however, are composed of networks of intertwined fibers and filaments. In the present study, we analyze how the network structure can affect the viscoelastic relaxation behavior of a tissue leading to the emergence of structure-based time scales in the relaxation spectra.
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http://dx.doi.org/10.1016/j.actbio.2019.01.027DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6467080PMC
March 2019

Image-based multi-scale mechanical analysis of strain amplification in neurons embedded in collagen gel.

Comput Methods Biomech Biomed Engin 2019 Feb 17;22(2):113-129. Epub 2018 Nov 17.

a Scientific Computational Research Center , Rensselaer Polytechnic Institute, Low Center for Industrial Innocation , Troy , NY , USA.

A general multi-scale strategy is presented for modeling the mechanical environment of a group of neurons that were embedded within a collagenous matrix. The results of the multi-scale simulation are used to estimate the local strains that arise in neurons when the extracellular matrix is deformed. The distribution of local strains was found to depend strongly on the configuration of the embedded neurons relative to the loading direction, reflecting the anisotropic mechanical behavior of the neurons. More importantly, the applied strain on the surrounding extracellular matrix is amplified in the neurons for all loading configurations that are considered. In the most severe case, the applied strain is amplified by at least a factor of 2 in 10% of the neurons' volume. The approach presented in this paper provides an extension to the capability of past methods by enabling the realistic representation of complex cell geometry into a multi-scale framework. The simulation results for the embedded neurons provide local strain information that is not accessible by current experimental techniques.
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http://dx.doi.org/10.1080/10255842.2018.1538414DOI Listing
February 2019

Multiscale modelling of the human lumbar facet capsular ligament: analysing spinal motion from the joint to the neurons.

J R Soc Interface 2018 11 14;15(148). Epub 2018 Nov 14.

Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455, USA

Due to its high level of innervation, the lumbar facet capsular ligament (FCL) is suspected to play a role in low back pain (LBP). The nociceptors in the lumbar FCL may experience excessive deformation and generate pain signals. As such, understanding the mechanical behaviour of the FCL, as well as that of its underlying nerves, is critical if one hopes to understand its role in LBP. In this work, we constructed a multiscale structure-based finite-element (FE) model of a lumbar FCL on a spinal motion segment undergoing physiological motions of flexion, extension, ipsilateral and contralateral bending, and ipsilateral axial rotation. Our FE model was created for a generic FCL geometry by morphing a previously imaged FCL anatomy onto an existing generic motion segment model. The fibre organization of the FCL in our models was subject-specific based on previous analysis of six dissected specimens. The fibre structures from those specimens were mapped onto the FCL geometry on the motion segment. A motion segment model was used to determine vertebral kinematics under specified spinal loading conditions, providing boundary conditions for the FCL-only multiscale FE model. The solution of the FE model then provided detailed stress and strain fields within the tissue. Lastly, we used this computed strain field and our previous studies of deformation of nerves embedded in fibrous networks during simple deformations (e.g. uniaxial stretch, shear) to estimate the nerve deformation based on the local tissue strain and fibre alignment. Our results show that extension and ipsilateral bending result in largest strains of the lumbar FCL, while contralateral bending and flexion experience lowest strain values. Similar to strain trends, we calculated that the stretch of the microtubules of the nerves, as well as the forces exerted on the nerves' membrane are maximal for extension and ipsilateral bending, but the location within the FCL of peak microtubule stretch differed from that of peak membrane force.
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http://dx.doi.org/10.1098/rsif.2018.0550DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6283995PMC
November 2018

Multiscale model of fatigue of collagen gels.

Biomech Model Mechanobiol 2019 Feb 27;18(1):175-187. Epub 2018 Aug 27.

Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN, 55455, USA.

Fatigue as a mode of failure becomes increasingly relevant with age in tissues that experience repeated fluctuations in loading. While there has been a growing focus on the mechanics of networks of collagen fibers, which are recognized as the predominant mechanical components of soft tissues, the network's fatigue behavior has received less attention. Specifically, it must be asked (1) how the fatigue of networks differs from that of its component fibers, and (2) whether this difference in fatigue behaviors is affected by changes in the network's architecture. In the present study, we simulated cyclic uniaxial loading of Voronoi networks to model fatigue experiments performed on reconstituted collagen gels. Collagen gels were cast into dog-bone shape molds and were tested on a uniaxial machine under a tension-tension cyclic loading protocol. Simulations were performed on networks modeled as trusses of, on average, 600 nonlinear elastic fibers connected at freely rotating pin-joints. We also simulated fatigue failure of Delaunay, and Erdős-Rényi networks, in addition to Voronoi networks, to compare fatigue behavior among different architectures. The uneven distribution of stresses within the fibers of the unstructured networks resulted in all three network geometries being more endurant than a single fiber or a regular lattice under cyclic loading. Among the different network geometries, for low to moderate external loads, the Delaunay networks showed the best fatigue behavior, while at higher loads, the Voronoi networks performed better.
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http://dx.doi.org/10.1007/s10237-018-1075-yDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6367047PMC
February 2019

Mechanics of a two-fiber model with one nested fiber network, as applied to the collagen-fibrin system.

Acta Biomater 2018 05 7;72:306-315. Epub 2018 Apr 7.

Department of Biomedical Engineering, University of Minnesota, Twin Cities, 7-105 Nils Hasselmo Hall, 312 Church Street SE, Minneapolis, MN 55455, USA. Electronic address:

The mechanical behavior of collagen-fibrin (col-fib) co-gels is both scientifically interesting and clinically relevant. Collagen-fibrin networks are a staple of tissue engineering research, but the mechanical consequences of changes in co-gel composition have remained difficult to predict or even explain. We previously observed fundamental differences in failure behavior between collagen-rich and fibrin-rich co-gels, suggesting an essential change in how the two components interact as the co-gel's composition changes. In this work, we explored the hypothesis that the co-gel behavior is due to a lack of percolation by the dilute component. We generated a series of computational models based on interpenetrating fiber networks. In these models, the major network component percolated the model space but the minor component did not, instead occupying a small island embedded within the larger network. Each component was assigned properties based on a fit of single-component gel data. Island size was varied to match the relative concentrations of the two components. The model predicted that networks rich in collagen, the stiffer component, would roughly match pure-collagen gel behavior with little additional stress due to the fibrin, as seen experimentally. For fibrin-rich gels, however, the model predicted a smooth increase in the overall network strength with added collagen, as seen experimentally but not consistent with an additive parallel model. We thus conclude that incomplete percolation by the low-concentration component of a co-gel is a major determinant of its macroscopic properties, especially if the low-concentration component is the stiffer component.

Statement Of Significance: Models for the behavior of fibrous networks have useful applications in many different fields, including polymer science, textiles, and tissue engineering. In addition to being important structural components in soft tissues and blood clots, these protein networks can serve as scaffolds for bioartificial tissues. Thus, their mechanical behavior, especially in co-gels, is both interesting from a materials science standpoint and significant with regard to tissue engineering.
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http://dx.doi.org/10.1016/j.actbio.2018.03.053DOI Listing
May 2018

Dicer1 Deficiency in the Idiopathic Pulmonary Fibrosis Fibroblastic Focus Promotes Fibrosis by Suppressing MicroRNA Biogenesis.

Am J Respir Crit Care Med 2018 08;198(4):486-496

1 Department of Medicine.

Rationale: The lung extracellular matrix (ECM) in idiopathic pulmonary fibrosis (IPF) mediates progression of fibrosis by decreasing fibroblast expression of miR-29 (microRNA-29), a master negative regulator of ECM production. The molecular mechanism is undefined. IPF-ECM is stiffer than normal. Stiffness drives fibroblast ECM production in a YAP (yes-associated protein)-dependent manner, and YAP is a known regulator of miR-29. Therefore, we tested the hypothesis that negative regulation of miR-29 by IPF-ECM was mediated by mechanotransduction of stiffness.

Objectives: To determine how IPF-ECM negatively regulates miR-29.

Methods: We decellularized lung ECM using detergents and prepared polyacrylamide hydrogels of defined stiffness by varying acrylamide concentrations. Mechanistic studies were guided by immunohistochemistry of IPF lung and used cell culture, RNA-binding protein assays, and xenograft models.

Measurements And Main Results: Contrary to our hypothesis, we excluded fibroblast mechanotransduction of ECM stiffness as the primary mechanism deregulating miR-29. Instead, systematic examination of miR-29 biogenesis revealed a microRNA processing defect that impeded processing of miR-29 into its mature bioactive forms. Immunohistochemical analysis of the microRNA processing machinery in IPF lung specimens revealed decreased Dicer1 expression in the procollagen-rich myofibroblastic core of fibroblastic foci compared with the focus perimeter and adjacent alveolar walls. Mechanistically, IPF-ECM increased association of the Dicer1 transcript with RNA binding protein AUF1 (AU-binding factor 1), and Dicer1 knockdown conferred primary human lung fibroblasts with cell-autonomous fibrogenicity in zebrafish and mouse lung xenograft models.

Conclusions: Our data identify suppression of fibroblast Dicer1 expression in the myofibroblast-rich IPF fibroblastic focus core as a central step in the mechanism by which the ECM sustains fibrosis progression in IPF.
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http://dx.doi.org/10.1164/rccm.201709-1823OCDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6118029PMC
August 2018

A finite-element model of mechanosensation by a Pacinian corpuscle cluster in human skin.

Biomech Model Mechanobiol 2018 Aug 17;17(4):1053-1067. Epub 2018 Mar 17.

Department of Biomedical Engineering, University of Minnesota, 7-105 Hasselmo Hall, 312 Church St. SE, Minneapolis, MN, 55455, USA.

The Pacinian corpuscle (PC) is the cutaneous mechanoreceptor responsible for sensation of high-frequency (20-1000 Hz) vibrations. PCs lie deep within the skin, often in multicorpuscle clusters with overlapping receptive fields. We developed a finite-element mechanical model of one or two PCs embedded within human skin, coupled to a multiphysics PC model to simulate action potentials elicited by each PC. A vibration was applied to the skin surface, and the resulting mechanical signal was analyzed using two metrics: the deformation amplitude ratio ([Formula: see text], [Formula: see text] and the phase shift of the vibration ([Formula: see text], [Formula: see text] between the stimulus and the PC. Our results showed that the amplitude attenuation and phase shift at a PC increased with distance from the stimulus to the PC. Differences in amplitude ([Formula: see text] and phase shift ([Formula: see text] between the two PCs in simulated clusters directly affected the interspike interval between the action potentials elicited by each PC ([Formula: see text]. While [Formula: see text] had a linear relationship with [Formula: see text], [Formula: see text]'s effect on [Formula: see text] was greater for lower values of [Formula: see text]. In our simulations, the separation between PCs and the distance of each PC from the stimulus location resulted in differences in amplitude and phase shift at each PC that caused [Formula: see text] to vary with PC location. Our results suggest that PCs within a cluster receive different mechanical stimuli which may enhance source localization of vibrotactile stimuli, drawing parallels to sound localization in binaural hearing.
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http://dx.doi.org/10.1007/s10237-018-1011-1DOI Listing
August 2018

Perspectives on Sharing Models and Related Resources in Computational Biomechanics Research.

J Biomech Eng 2018 02;140(2)

National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health, Bethesda, MD 20892.

The role of computational modeling for biomechanics research and related clinical care will be increasingly prominent. The biomechanics community has been developing computational models routinely for exploration of the mechanics and mechanobiology of diverse biological structures. As a result, a large array of models, data, and discipline-specific simulation software has emerged to support endeavors in computational biomechanics. Sharing computational models and related data and simulation software has first become a utilitarian interest, and now, it is a necessity. Exchange of models, in support of knowledge exchange provided by scholarly publishing, has important implications. Specifically, model sharing can facilitate assessment of reproducibility in computational biomechanics and can provide an opportunity for repurposing and reuse, and a venue for medical training. The community's desire to investigate biological and biomechanical phenomena crossing multiple systems, scales, and physical domains, also motivates sharing of modeling resources as blending of models developed by domain experts will be a required step for comprehensive simulation studies as well as the enhancement of their rigor and reproducibility. The goal of this paper is to understand current perspectives in the biomechanics community for the sharing of computational models and related resources. Opinions on opportunities, challenges, and pathways to model sharing, particularly as part of the scholarly publishing workflow, were sought. A group of journal editors and a handful of investigators active in computational biomechanics were approached to collect short opinion pieces as a part of a larger effort of the IEEE EMBS Computational Biology and the Physiome Technical Committee to address model reproducibility through publications. A synthesis of these opinion pieces indicates that the community recognizes the necessity and usefulness of model sharing. There is a strong will to facilitate model sharing, and there are corresponding initiatives by the scientific journals. Outside the publishing enterprise, infrastructure to facilitate model sharing in biomechanics exists, and simulation software developers are interested in accommodating the community's needs for sharing of modeling resources. Encouragement for the use of standardized markups, concerns related to quality assurance, acknowledgement of increased burden, and importance of stewardship of resources are noted. In the short-term, it is advisable that the community builds upon recent strategies and experiments with new pathways for continued demonstration of model sharing, its promotion, and its utility. Nonetheless, the need for a long-term strategy to unify approaches in sharing computational models and related resources is acknowledged. Development of a sustainable platform supported by a culture of open model sharing will likely evolve through continued and inclusive discussions bringing all stakeholders at the table, e.g., by possibly establishing a consortium.
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http://dx.doi.org/10.1115/1.4038768DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5821103PMC
February 2018

Tissue loading and microstructure regulate the deformation of embedded nerve fibres: predictions from single-scale and multiscale simulations.

J R Soc Interface 2017 10;14(135)

Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455, USA

Excessive deformation of nerve fibres (axons) in the spinal facet capsular ligaments (FCLs) can be a cause of pain. The axons are embedded in the fibrous extracellular matrix (ECM) of FCLs, so understanding how local fibre organization and micromechanics modulate their mechanical behaviour is essential. We constructed a computational discrete-fibre model of an axon embedded in a collagen fibre network attached to the axon by distinct fibre-axon connections. This model was used to relate the axonal deformation to the fibre alignment and collagen volume concentration of the surrounding network during transverse, axial and shear deformations. Our results showed that fibre alignment affects axonal deformation only during transverse and axial loading, but higher collagen volume concentration results in larger overall axonal strains for all loading cases. Furthermore, axial loading leads to the largest stretch of axonal microtubules and induces the largest forces on axon's surface in most cases. Comparison between this model and a multiscale continuum model for a representative case showed that although both models predicted similar averaged axonal strains, strain was more heterogeneous in the discrete-fibre model.
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http://dx.doi.org/10.1098/rsif.2017.0326DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5665822PMC
October 2017

Micropipette aspiration of the Pacinian corpuscle.

J Biomech 2017 10 20;63:104-109. Epub 2017 Aug 20.

Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN, USA. Electronic address:

The Pacinian corpuscle (PC) is a cutaneous mechanoreceptor sensitive to high-frequency vibrations (20-1000Hz). The PC is of importance due to its integral role in somatosensation and the critical need to understand PC function for haptic feedback system development. Previous theoretical and computational studies have modeled the physiological response of the PC to sustained or vibrating mechanical stimuli, but they have used estimates of the receptor's mechanical properties, which remain largely unmeasured. In this study, we used micropipette aspiration (MPA) to determine an apparent Young's modulus for PCs isolated from a cadaveric human hand. MPA was applied in increments of 5mm HO (49Pa), and the change in protrusion length of the PC into the pipette was recorded. The protrusion length vs. suction pressure data were used to calculate the apparent Young's modulus. Using 10 PCs with long-axis lengths of 2.99±0.41mm and short-axis lengths of 1.45±0.22mm, we calculated a Young's modulus of 1.40±0.86kPa. Our measurement is on the same order of magnitude as those approximated in previous models, which estimated the PC to be on the same order of magnitude as skin or isolated cells, so we recommend that a modulus in the kPa range be used in future studies.
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http://dx.doi.org/10.1016/j.jbiomech.2017.08.005DOI Listing
October 2017
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