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Tissue growth and remodeling (GR) is often central to disease etiology and progression, so understanding GR is essential for understanding disease and developing effective therapies. While the state-of-the-art in this regard is animal and cellular models, recent advances in computational tools offer another avenue to investigate GR. A major challenge for computational models is bridging from the cellular scale (at which changes are actually occurring) to the macroscopic, geometric-scale (at which physiological consequences arise). Thus, many computational models simplify one scale or another in the name of computational tractability. In this work, we develop a discrete-continuum modeling scheme for analyzing GR, in which we apply changes directly to the discrete cell and extracellular matrix (ECM) architecture and pass those changes up to a finite-element macroscale geometry. We demonstrate the use of the model in three case-study scenarios: the media of a thick-walled artery, and the media and adventitia of a thick-walled artery, and chronic dissection of an arterial wall. We analyze each case in terms of the new and insightful data that can be gathered from this technique, and we compare our results from this model to several others. STATEMENT OF SIGNIFICANCE: This work is significant in that it provides a framework for combining discrete, microstructural- and cellular-scale models to the growth and remodeling of large tissue structures (such as the aorta). It is a significant advance in that it couples the microscopic remodeling with an existing macroscopic finite element model, making it relatively easy to use for a wide range of conceptual models. It has the potential to improve understanding of many growth and remodeling processes, such as organ formation during development and aneurysm formation, growth, and rupture.

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.

Statistical shape modeling (SSM) is an emerging tool for risk assessment of thoracic aortic aneurysm. However, the head branches of the aortic arch are often excluded in SSM. We introduced an SSM strategy based on principal component analysis that accounts for aortic branches and applied it to a set of patient scans. Computational fluid dynamics were performed on the reconstructed geometries to identify the extent to which branch model accuracy affects the calculated wall shear stress (WSS) and pressure. Surface-averaged and location-specific values of pressure did not change significantly, but local WSS error was high near branches when inaccurately modeled.

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.

Degeneration of the lumbar spine, and especially how that degeneration may lead to pain, remains poorly understood. In particular, the mechanics of the facet capsular ligament may contribute to low back pain, but the mechanical changes that occur in this ligament with spinal degeneration are unknown. Additionally, the highly nonlinear, heterogeneous, and anisotropic nature of the facet capsular ligament makes understanding mechanical changes more difficult. Clinically, magnetic resonance imaging (MRI)-based signs of degeneration in the facet joint and the intervertebral disc (IVD) correlate. Therefore, this study examined how the nonlinear, heterogeneous mechanics of the facet capsular ligament change with degeneration of the lumbar spine as characterized using MRI. Cadaveric human spines were imaged via MRI, and the L2-L5 facet joints and IVDs were scored using the Fujiwara and Pfirrmann grading systems. Then, the facet capsular ligament was isolated and biaxially loaded. The nonlinear mechanical properties of the ligament were obtained using a nonlinear generalized anisotropic inverse mechanics analysis (nGAIM). Then a Holzapfel–Gasser–Ogden (HGO) model was fit to the stress–strain data obtained from nGAIM. The facet capsular ligament is stiffer and more anisotropic at larger Pfirrmann grades and higher Fujiwara scores than at lower grades and scores. Analysis of ligament heterogeneity showed all tissues are highly heterogeneous, but no distinct spatial patterns of heterogeneity were found. These results show that degeneration of the lumbar spine including the facet capsular ligament appears to be occurring as a whole joint phenomenon and advance our understanding of lumbar spine degeneration.

BACKGROUND: The ring-pull test, where a ring of tissue is hooked via two pins and stretched, is a popular biomechanical test, especially for small arteries. Although convenient and reliable, the ring test produces inhomogeneous strain, making determination of material parameters non-trivial. OBJECTIVE: To determine correction factors between ring-pull-estimated and true tissue properties. METHODS: A finite-element model of ring pulling was constructed for a sample with nonlinear, anisotropic mechanical behavior typical of arteries. The pin force and sample cross-section were used to compute an apparent modulus at small and large strain, which were compared to the specified properties. The resulting corrections were validated with experiments on porcine and ovine arteries. The correction was further applied to experiments on mouse aortic rings to determine material and failure properties. RESULTS: Calculating strain based on centerline stretch rather than inner-wall or outer-wall stretch afforded better estimation of tissue properties. Additional correction factors were developed based on ring wall thickness H, centerline ring radius R(c), and pin radius a. The corrected estimates for tissue properties were in good agreement with uniaxial stretch experiments. CONCLUSIONS: The computed corrections improved estimation of tissue material properties for both the small-strain (toe) modulus and the large-strain (lockout) modulus. When measuring tensile strength, one should minimize H/a to ensure that peak stress occurs at the sample midplane rather than near the pin. In this scenario, tensile strength can be estimated accurately by using inner-wall stretch at the midplane and the corrected properties.

Despite its importance in physiological processes and tissue engineering, the mechanism underlying cell contact guidance in an aligned fibrillar network has defied elucidation due to multiple interdependent signals that such a network presents to cells, namely, anisotropy of adhesion, porosity and mechanical behaviour. A microstructural–mechanical model of fibril networks was used to assess the relative magnitudes of these competing signals in networks of varied alignment strength based on idealized cylindrical pseudopods projected into the aligned and orthogonal directions and computing the anisotropy of metrics chosen for adhesion, porosity and mechanical behaviour: cylinder–fibre contact area for adhesion, persistence length of pores for porosity and total force to displace fibres from the cylindrical volume as well as network stiffness experienced upon cylinder retraction for mechanical behaviour. The signals related to mechanical anisotropy are substantially higher than adhesion and porosity anisotropy, especially at stronger network alignments, although their signal to noise (S/N) values are substantially lower. The former finding is consistent with a recent report that fibroblasts can sense fibril alignment via anisotropy of network mechanical resistance, and the model reveals this can be due to either mechanical resistance to pseudopod protrusion or retraction given their signal and S/N values are similar.

Percutaneous pulmonary valve implantation (PPVI) is a non-surgical treatment in which a stented valve is delivered via catheter to replace a stenosed or leaky pulmonary valve. Stent oversizing is used to anchor the valve within the right ventricular outflow tract (RVOT), but overexpansion may interfere with adjoining structures specifically the aortic root and coronary arteries. Potential devastating consequences include distortion of the aortic sinus, causing aortic valve insufficiency, and/or compression of the coronary arteries. Because the outcome of PPVI is determined by the patient’s anatomy, we propose a method that uses patient-specific finite-element (FE) models constructed from pre-procedural cross-sectional CT scan images to evaluate these potential risks prior to clinical intervention. In five cases from an ongoing retrospective study, our preliminary results demonstrate our model’s ability to accurately identify the risk of aortic valve insufficiency as a consequence of the PPVI procedure.

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.

To use computational methods to explore geometric, mechanical, and fluidic biomarkers that could correlate with mouse lifespan in the Fbln4Image-based, mouse-specific fluid-structure-interaction models were developed for Fbln4Comparing the different geometrical and biofluidic biomarkers to the mouse lifespan, it was found that mean oscillatory shear index (OSIThe 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.

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.

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.

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.

The heterogeneous, nonlinear, anisotropic material behavior of biological tissues makes precise definition of an accurate constitutive model difficult. One possible solution to this issue would be to define microstructural elements and perform fully coupled multiscale simulation. However, for complex geometries and loading scenarios, the computational costs of such simulations can be prohibitive. Ideally then, we should seek a method that contains microstructural detail, but leverages the speed of classical continuum-based finite-element (FE) modeling. In this work, we demonstrate the use of the Holzapfel-Gasser-Ogden (HGO) model (Holzapfel et al. in J. Elast. 61:1–48, 2000; Gasser et al. in J. R. Soc. Interface 3(6):15–35, 2006) to fit the behavior of microstructural network models. We show that Delaunay microstructural networks can be fit to the HGO strain energy function by calculating fiber network strain energy and average fiber stretch ratio. We then use the HGO constitutive model in a FE framework to improve the speed of our hybrid model, and demonstrate that this method, combined with a material property update scheme, can match a full multiscale simulation. This method gives us flexibility in defining complex FE simulations that would be impossible, or at least prohibitively time consuming, in multiscale simulation, while still accounting for microstructural heterogeneity.

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.

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.

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.

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.

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.

The effect of a double-walled stent-graft (DWSG) design on arterial compliance was evaluated using pulse wave velocity (PWV) measurements in an in vitro mock arterial flow loop. The DWSG prototype was compared to a rigid stent-graft and to an unstented aorta model. The time delay between two pressure sensors a fixed distance apart was used to calculate PWV. Latex tubing simulated the compliant aorta, and a needle valve provided downstream resistance. A series of pulse rates and stroke volumes was applied to enable measurements at different mean pressures for the same system. PWV for the rigid stent-graft was higher than in the other two cases across all mean pressures. The DWSG exhibited behavior similar to the unstented model, demonstrating the capability of the DWSG to maintain aortic compliance in patients requiring an aortic stent-graft.

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 facet capsular ligament’s (FCL) 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, bending stiffness, facet joint space, and FCL stretch. Range of motion (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.

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.

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.

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.

Tension pneumothorax, a major preventable cause of battlefield death, often arises from chest trauma and is treated by needle decompression to release trapped air from the pleural cavity. Surgical simulation mannequins are often employed to train medical personnel to perform this procedure properly. Accurate reproduction of the mechanical behavior of the parietal pleura, especially in response to needle penetration, is essential to maximize the fidelity of these surgical simulators. To date, however, the design of pleura-simulating material has been largely empirical and based on subjective practitioner feel rather than on the tissue properties, which have remained unknown. In this study, we performed uniaxial extension tests on samples of cadaveric human parietal pleura. We found that the pleura was highly nonlinear and mildly anisotropic, being roughly twice as stiff in the direction parallel to the ribs vs. perpendicular to the ribs (large-strain modulus = 20.44 vs. 11.49MPa). We also did not find significant correlations for most pleural properties with age or BMI, but it must be recognized that the age range (59 ± 9.5 yrs) and BMI range (31 ± 5.3) of the donors in our study was not what one might expect from combatants, and there could be differences for younger, lighter individuals. We found a significantly higher low-strain modulus in the diabetic donors (0.213 vs. 0.100MPa), consistent with the general tendency of tissue to stiffen in diabetes. The nonlinearity and tensile strength should be considered in material design and selection for future surgical simulators.

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.

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.

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 ( κsub ), as a function of the Young's modulus of the substrate ( E Y ), which yields the relation, κ sub = R s E Y , 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.

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.

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.

Signaling molecules stored in cellular granules serve a broad range of functional purposes. Serotonin, for example, is involved in the regulation of behavior, cognitive function, and hemostasis. Understanding serotonin release from platelet granules can provide valuable fundamental information about the exocytotic process and help elucidate potential abnormalities of diseased platelets. Experimentally, carbon-fiber microelectrochemistry has been utilized to characterize the dynamic behavior of serotonin secretion from individual platelets. The objectives of this study were (1) to develop a finite-element model of the carbon-fiber microelectrode experiment and (2) to predict the effect of the postulated core-halo granule microstructure and rate of fusion pore expansion on the resulting amperometric signal. The model confirmed that the core-halo microstructure is consistent with the observed amperometric spike profiles. Further, it showed that the ratio of pore diameter to granule diameter, rather than the rate of pore expansion, dictates the profile shape. Understanding the driving forces for chemical messenger delivery from platelet granules has implications for understanding abnormalities in diseased platelets as well as other exocytotic cells.

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure-function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.

Quantification of the mechanical behavior of soft tissues is challenging due to their anisotropic, heterogeneous, and nonlinear nature. We present a method for the “computational dissection” of a tissue, by which we mean the use of computational tools both to identify and to analyze regions within a tissue sample that have different mechanical properties. The approach employs an inverse technique applied to a series of planar biaxial experimental protocols. The aggregated data from multiple protocols provide the basis for (1) segmentation of the tissue into regions of similar properties, (2) linear analysis for the small-strain behavior, assuming uniform, linear, anisotropic behavior within each region, (3) subsequent nonlinear analysis following each individual experimental protocol path and using local linear properties, and (4) construction of a strain energy data set W(E) at every point in the material by integrating the differential stress-strain functions along each strain path. The approach has been applied to simulated data and captures not only the general nonlinear behavior but also the regional differences introduced into the simulated tissue sample.

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.