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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Variations in properties, active behavior, injury, scarring, and/or disease can all cause a tissue's mechanical behavior to be heterogeneous. Advances in imaging technology allow for accurate full-field displacement tracking of both in vitro and in vivo deformation from an applied load. While detailed strain fields provide some insight into tissue behavior, material properties are usually determined by fitting stress-strain behavior with a constitutive equation. However, the determination of the mechanical behavior of heterogeneous soft tissue requires a spatially varying constitutive equation (i.e., one in which the material parameters vary with position). We present an approach that computationally dissects the sample domain into many homogeneous subdomains, wherein subdomain boundaries are formed by applying a betweenness based graphical analysis to the deformation gradient field to identify locations with large discontinuities. This novel partitioning technique successfully determined the shape, size and location of regions with locally similar material properties for: (1) a series of simulated soft tissue samples prescribed with both abrupt and gradual changes in anisotropy strength, prescribed fiber alignment, stiffness, and nonlinearity, (2) tissue analogs (PDMS and collagen gels) which were tested biaxially and speckle tracked (3) and soft tissues which exhibited a natural variation in properties (cadaveric supraspinatus tendon), a pathologic variation in properties (thoracic aorta containing transmural plaque), and active behavior (contracting cardiac sheet). The routine enables the dissection of samples computationally rather than physically, allowing for the study of small tissues specimens with unknown and irregular inhomogeneity.

The Pacinian corpuscle (PC) is a dermal mechanoreceptor that responds to high-frequency (20-1000 Hz) vibrations. The PC's structure allows transmission of vibrations through its layers (lamellae) to the centrally-located nerve fiber (neurite). This work combines mechanical models of the PC with an electrochemical model of peripheral nerves to simulate the tactile response of the entire system. A three-stage model of response to a vibratory input was developed, consisting of (1) outer core mechanics, (2) inner core mechanics, and (3) neurite electrochemistry. The model correctly predicts the band-pass nature of the PC's frequency response, showing that the PC structure can amplify oscillatory strains within its target frequency band. Specifically, strain induced by a vibratory stimulus is amplified by a factor of 8-12 from the PC surface to the neurite. Our results also support the hypothesis that PC rapid adaptation is affected by the lamellar structures without requiring neuronal adaptivity. Simulated different-sized PCs showed a shift in frequency response, suggesting that clusters of different-sized PCs could enable more nuanced tactile encoding than uniform clusters. By modeling the PC's mechano-to-neural transduction, we can begin to characterize the mechanosensation of other receptors to understand how multiple receptors interact to create our sensation of touch.

The stress in a cell due to extracellular mechanical stimulus is determined by its mechanical properties, and the structural organization of many adherent cells suggests that their properties are anisotropic. This anisotropy may significantly influence the cells' mechanotransductive response to complex loads, and has important implications for development of accurate models of tissue biomechanics. Standard methods for measuring cellular mechanics report linear moduli that cannot capture large-deformation anisotropic properties, which in a continuum mechanics framework are best described by a strain energy density function (SED). In tissues, the SED is most robustly measured using biaxial testing. Here, we describe a cellular microbiaxial stretching (CμBS) method that modifies this tissue-scale approach to measure the anisotropic elastic behavior of individual vascular smooth muscle cells (VSMCs) with nativelike cytoarchitecture. Using CμBS, we reveal that VSMCs are highly anisotropic under large deformations. We then characterize a Holzapfel–Gasser–Ogden type SED for individual VSMCs and find that architecture-dependent properties of the cells can be robustly described using a formulation solely based on the organization of their actin cytoskeleton. These results suggest that cellular anisotropy should be considered when developing biomechanical models, and could play an important role in cellular mechano-adaptation.

The Pacinian corpuscle (PC) is a cutaneous mechanoreceptor sensitive to high-frequency vibrations (20–1000 Hz). 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 5 mm H 2 O (49 Pa), 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 ± 0.41 mm and short-axis lengths of 1.45 ± 0.22 mm, we calculated a Young’s modulus of 1.40 ± 0.86 kPa. 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.

Healthy subjects performed lumbar flexion and were assessed by video fluoroscopy to measure the in vivo kinematics of the lower lumbar motion segments.Fifteen healthy subjects (8 male, 7 female, 28 ± 10 years) performed lumbar flexion and extension back to neutral while their vertebrae were imaged. The sagittal plane vertebral margins of L3-S1 were identified. Lumbar angle, segmental margin strains, axial displacements, anterior-posterior (A-P) translations, and segmental rotations over the course of flexion were measured.L4-L5 had the largest posterior margin Green strain (65%). Each segment displayed more axial displacement than A-P translation. Peak vertebral angulation occurred at approximately 75% of peak flexion during the extension phase.L4-L5 exhibited the largest anterior and posterior margin strains (29 and 65%, respectively). Strains in the disc during in vivo lumbar flexion are due to both angular rotation and linear translation.

The spinal facet capsular ligament (FCL) is primarily comprised of heterogeneous arrangements of collagen fibers. This complex fibrous structure and its evolution under loading play a critical role in determining the mechanical behavior of the FCL. A lack of analytical tools to characterize the spatial anisotropy and heterogeneity of the FCL's microstructure has limited the current understanding of its structure–function relationships. Here, the collagen organization was characterized using spatial correlation analysis of the FCL's optically obtained fiber orientation field. FCLs from the cervical and lumbar spinal regions were characterized in terms of their structure, as was the reorganization of collagen in stretched cervical FCLs. Higher degrees of intra- and intersample heterogeneity were found in cervical FCLs than in lumbar specimens. In the cervical FCLs, heterogeneity was manifested in the form of curvy patterns formed by collections of collagen fibers or fiber bundles. Tensile stretch, a common injury mechanism for the cervical FCL, significantly increased the spatial correlation length in the stretch direction, indicating an elongation of the observed structural features. Finally, an affine estimation for the change of correlation length under loading was performed which gave predictions very similar to the actual values. These findings provide structural insights for multiscale mechanical analyses of the FCLs from various spinal regions and also suggest methods for quantitative characterization of complex tissue patterns.

The lumbar facet capsular ligament (FCL) primarily consists of aligned type I collagen fibers that are mainly oriented across the joint. The aim of this study was to characterize and incorporate in-plane local fiber structure into a multiscale finite element model to predict the mechanical response of the FCL during in vitro mechanical tests, accounting for the heterogeneity in different scales. Characterization was accomplished by using entire-domain polarization-sensitive optical coherence tomography to measure the fiber structure of cadaveric lumbar FCLs ( $$n=6$$ ). Our imaging results showed that fibers in the lumbar FCL have a highly heterogeneous distribution and are neither isotropic nor completely aligned. The averaged fiber orientation was $$+9.3^{\circ }$$ ( $$+29.9^{\circ }$$ in the inferior region and $$+5.1^{\circ }$$ in the middle and superior regions), with respect to lateral–medial direction (superior–medial to inferior–lateral). These imaging data were used to construct heterogeneous structural models, which were then used to predict experimental gross force–strain behavior and the strain distribution during equibiaxial and strip biaxial tests. For equibiaxial loading, the structural model fit the experimental data well but underestimated the lateral–medial forces by $$\sim $$ 16% on average. We also observed pronounced heterogeneity in the strain field, with stretch ratios for different elements along the lateral–medial axis of sample typically ranging from about 0.95 to 1.25 during a 12% strip biaxial stretch in the lateral–medial direction. This work highlights the multiscale structural and mechanical heterogeneity of the lumbar FCL, which is significant both in terms of injury prediction and microstructural constituents’ (e.g., neurons) behavior.

Background Context The lumbar facet capsular ligament (FCL) is a posterior spinal ligament with a complex structure and kinematic profile. The FCL has a curved geometry, multiple attachment sites, and preferentially aligned collagen fiber bundles on the posterior surface that are innervated with mechanoreceptive nerve endings. Spinal flexion induces three-dimensional (3D) deformations, requiring the FCL to maintain significant tensile and shear loads. Previous works aimed to study 3D facet joint kinematics during flexion, but to our knowledge none have reported localized FCL surface deformations likely created by this complex structure. Purpose The purpose of this study was to elucidate local deformations of both the posterior and anterior surfaces of the lumbar FCL to understand the distribution and magnitude of in-plane and through-plane deformations, including the prevalence of shear. Study Design/Setting The FCL anterior and posterior surface deformations were quantified through creation of a finite element model simulating facet joint flexion using a realistic geometry, physiological kinematics, and fitted constitutive material. Methods Geometry was obtained from the micro-CT data of a healthy L3–L4 facet joint capsule (n=1); kinematics were extracted from sagittal plane fluoroscopic data of healthy volunteers (n=10) performing flexion; and average material properties were determined from planar biaxial extension tests of L4–L5 FCLs (n=6). All analyses were performed with the non-linear finite element solver, FEBio. A grid of equally spaced 3×3 nodes on the posterior surface identified regional differences within the strain fields and was used to create comparisons against previously published experimental data. This study was funded by the National Institutes of Health and the authors have no disclosures. Results Inhomogeneous in-plane and through-plane shear deformations were prominent through the middle body of the FCL on both surfaces. Anterior surface deformations were more pronounced because of the small width of the joint space, whereas posterior surface deformations were more diffuse because the larger area increased deformability. We speculate these areas of large deformation may provide this proprioceptive system with an excellent measure of spinal motion. Conclusions We found that in-plane and through-plane shear deformations are widely present in finite element simulations of a lumbar FCL during flexion. Importantly, we conclude that future studies of the FCL must consider the effects of both shear and tensile deformations.

The lumbar facet capsular ligament (FCL) articulates with six degrees of freedom during spinal motions of flexion/extension, lateral bending, and axial rotation. The lumbar FCL is composed of highly aligned collagen fiber bundles on the posterior surface (oriented primarily laterally between the rigid articular facets) and irregularly oriented elastin on the anterior surface. Because the FCL is a capsule, it has multiple insertion sites across the lumbar facet joint, which, along with its material structure, give rise to complicated deformations in vivo. We performed planar equibiaxial mechanical tests on excised healthy cadaveric lumbar FCLs (n=6) to extract normal and shear reaction forces, and fit sample-specific two-fiber-family finite element models to the experimental force data. An eight-parameter anisotropic, hyperelastic model was used. Shear forces at maximum extension (mean values of 1.68 N and 3.01 N in the two directions) were of comparable magnitude to the normal forces perpendicular to the aligned collagen fiber bundles (4.67 N) but smaller than normal forces in the fiber direction (16.11 N). Inclusion of the experimental shear forces in the model optimization yielded fits with highly aligned fibers oriented at a specific angle across all samples, typically with one fiber population aligned nearly horizontally and the other at an oblique angle. Conversely, models fit to only the normal force data resulted in a broad range of fiber angles with low specificity. We found that shear forces generated through planar equibiaxial extension aided the model fit in describing the anisotropic nature of the FCL surface.

The mechanical properties of soft tissues depend on the collagen fiber network and the surrounding non-fibrillar matrix. The mechanical role of non-fibrillar material remains poorly understood. Our recent study (Lake and Barocas, Ann Biomed Eng 2011) introduced collagen-agarose co-gels as a simple experimental model system to evaluate the mechanical contribution of non-fibrillar matrix, and evaluated co-gel properties in uniaxial tension. In this study, we utilized similar co-gels to examine collagen-matrix interaction in tissues subjected to incremental stress-relaxation indentation tests. Mechanical testing was performed using two orthogonal custom test devices, and polarized light imaging was used to quantify 3D collagen fiber kinematics under load. The addition of agarose led to concentration-dependent changes in the time-dependent mechanical response and magnitude/spread of collagen fiber reorganization of tissue analogs. Specifically, peak/relaxed loads increased, and relaxation rate decreased, with increasing agarose concentration. In addition, increasing agarose content led to larger magnitude changes in orientation direction and alignment strength that were more localized near the indenter. Results suggest that non-fibrillar material significantly contributes to the behavior of co-gels in indentation, likely by reducing permeability and resisting volume change, thereby providing insight into the properties of artificial and native tissues subjected to non-tensile loading.

Purpose To study the impact of altitude on the intraocular pressure (IOP) in an eye with an intravitreal gas bubble. Methods A mathematical model was developed to simulate intravitreal gas bubble expansion caused by change in altitude. Mechanical deformation of the eye was simulated using a finite-element model. Intraocular pressure-driven changes in aqueous humor flow were also considered. Two cases were studied: 1) ascent from sea level to 3,000 ft followed by immediate return to sea level and 2) ascent to 3,000 ft followed by prolonged exposure to 3,000 ft. The effect of IOP-lowering medications was studied by changing the model parameters. Results The IOP increase was directly related to the initial bubble size when ascent to 3,000 ft was simulated. When prolonged exposure to high altitude was modeled, loss of aqueous humor led to a less elevated value of IOP. In a typical simulated case, when the outflow facility was increased, the predicted IOP rise was reduced by 28%. Conclusion Theoretical modeling of an eye with an intravitreal gas bubble can help an ophthalmologist evaluate the impact of altitude-induced IOP changes. Our model suggests that IOP-lowering drugs could help manage altitude-induced IOP changes in the presence of intravitreal gas bubbles.

Human dermal fibroblasts entrapped in fibrin gels cast in cross-shaped (cruciform) geometries with 1:1 and 1:0.5 ratios of arm widths were studied to assess whether tension and alignment of the cells and fibrils affected ECM deposition. The cruciforms of contrasting geometry (symmetric vs. asymmetric), which developed different fiber alignment patterns, were harvested at 2, 5, and 10 weeks of culture. Cruciforms were subjected to planar biaxial testing, polarimetric imaging, DNA and biochemical analyses, histological staining, and SEM imaging. As the cruciforms compacted and developed fiber alignment, fibrin was degraded, and elastin and collagen were produced in a geometry-dependent manner. Using a continuum mechanical model that accounts for direction-dependent stress due to cell traction forces and cell contact guidance with aligned fibers that occurs in the cruciforms, the mechanical stress environment was concluded to influence collagen deposition, with deposition being the greatest in the narrow arms of the asymmetric cruciform where stress was predicted to be the largest.

To compare iris cross-sectional area and thickness in the accommodated and unaccommodated states in controls versus patients with pigment dispersion syndrome (PDS) and to quantify short-term response of the iris to accommodation.Thirty-three patients with PDS and 17 control subjects were examined with ultrasound biomicroscopy. A radial image of the iris and ciliary body was taken at the temporal quadrant before and after accommodation with the patient looking at a standardized target. Iris thickness was measured from a line perpendicular to the iris from points on the trabecular meshwork 500, 1000, and 3000 μm from the scleral spur. Ciliary body thickness was measured 500 μm posterior to the scleral spur. Independent sample t tests (2-sided) compared iris thickness and cross-sectional area between groups.All participants were of European descent. Mean age was 45.6 ± 5.4 years (mean ± 95% confidence interval) in the PDS group and 34.9 ± 5.5 in the controls. Mean refractive error was -4.26 ± 1.0 diopters in the PDS group and -4.83 ± 1.0 diopters in the controls (P=0.499). There was no significant difference in iris cross-sectional area in the accommodated and unaccommodated states between the 3 groups. For all quantities measured (iris thickness at 500, 1000, 3000 μm; iris cross-sectional area; ciliary body thickness and area), there was no significant difference between the control group and the PDS group (P0.35).Iris cross-sectional area and thickness and ciliary body thickness were similar in the accommodated and unaccommodated states in PDS and controls. This result provides further suggestive evidence that nongeometrical factors contribute to the development of PDS.

Cell-mediated compaction of the extracellular matrix (ECM) plays a critical role in tissue engineering, wound healing, embryonic development, and many disease states. The ECM is compacted as a result of cellular traction forces. We hypothesize that a cell mechanically remodels the nearby ECM until some target conditions are obtained, and then the cell stops compacting. A key feature of this hypothesis is that ECM compaction primarily occurs in the pericellular region and the properties of the ECM in the pericellular region govern cellular force generation. We developed a mathematical model to describe the amount of macroscopic compaction of cell-populated collagen gels in terms of the initial cell and collagen densities, as well as the final conditions of the pericellular environment (defined as the pericellular volume where the collagen is compacted (V(*)) and the mass of collagen within this volume (m(*))). This model qualitatively predicts the effects of varying initial cell and collagen concentrations on the extent of gel compaction, and by fitting V(*) and m(*), provides reasonable quantitative agreement with the extent of gel compaction observed in experiments with endothelial cells and fibroblasts. Microscopic analysis of compacted gels supports the assumption that collagen compaction occurs primarily in the pericellular environment.

Structural models of tissue mechanics, in which the tissue is represented as a sum or integral of fiber contributions for a distribution of fiber orientations, are a popular tool to represent the complex mechanical behavior of soft tissues. A significant practical challenge, however, is evaluation of the integral that defines the stress. Numerical integration is accurate but computationally demanding, posing an impediment to incorporation of structural models into large-scale finite element simulations. In this paper, a closed-form analytic evaluation of the integral is derived for fibers distributed according to a von Mises distribution and an exponential fiber stress-strain law.

Background/aims: To determine whether the volume of the posterior chamber changes during pupillary dilation. Methods: Eyes with anatomically narrow angles underwent ultrasound biomicroscopy of the posterior chamber and pupillary margin under dark- and light-room conditions to assess changes in posterior chamber anatomy and volume. All examinations were stored as real-time video. A frame-by-frame analysis was performed using a macro written for the ImageJ image-processing software. Results: Thirteen eyes were assessed. The mean patient age was 63.0 (SD 10.0) years, and the mean refractive error was 1.1 (1.9) dioptres. The horizontal mean pupillary diameter was 2.3 (0.6) mm and 3.5 (0.5) mm under light- and dark-room conditions, respectively (p −7 , paired t test). The mean posterior chamber volumes were unchanged under light and dark conditions (3.76 (1.09) vs 3.63 (0.78) mm 3 , p = 0.22, paired t test). Volumes were greater under light conditions in eight eyes and under dark conditions in five eyes. Conclusions: The volume of the posterior chamber does not change significantly during dilation.

Heart valve replacements composed of living tissue that can adapt, repair, and grow with a patient would provide a more clinically beneficial option than current inert replacements. Bioartificial valves were produced by entrapping human dermal fibroblasts within a fibrin gel. Using a mold design that presents appropriate mechanical constraints to the cell-induced fibrin gel compaction, gross fiber alignment (commissure-to-commissure alignment in the leaflets and circumferential alignment in the root) and the basic geometry of a native aortic valve were obtained. After static incubation on the mold in complete medium supplemented with transforming growth factor beta 1, insulin, and ascorbate, collagen fibers produced by the entrapped cells were found to coalign with the fibrin based on histological analyses. The resultant tensile mechanical properties were anisotropic. Ultimate tensile strength and tensile modulus of the leaflets in the commissural direction were 0.53 and 2.34 MPa, respectively. The constructs were capable of withstanding backpressure commensurate with porcine aortic valves in regurgitation tests (330 mmHg) and opened and closed under physiological pressure swings of 10 and 20 mmHg, respectively. These data support proof of principle of using cell-remodeled fibrin gel to produce tissue-engineered valve replacements.

A variety of macromolecules accumulate in the glomerular mesangium in many different diseases, but the physics of the transport of these molecules within the mesangial matrix has not been extensively studied. We present a computational model of convection and diffusion within the porous mesangial matrix and apply this model to the specific instance of immunoglobulin A (IgA) transport in IgA nephropathy. We examine the influence of physiological factors including glomerular basement membrane (GBM) thickness and mesangial matrix density on the total accumulation of IgA. Our results suggest that IgA accumulation can be understood by relating convection and diffusion, thus demonstrating the importance of intrinsic glomerular factors.

The need for corneas suitable for transplantation, combined with the decreasing supply, has fueled interest in the development of a corneal replacement. In this study, a collagen-sponge-based stromal equivalent, consisting of human corneal fibroblasts cultured on a type I collagen sponge, was maintained in culture for up to 21 days and characterized with respect to mechanical properties and cellular behavior. The Young's modulus of the stromal equivalent varied from 95 to 370 Pa, and its permeability varied from 5.3 x 10(-8) - 4.2 x 10(-7) m4 N(-1) s(-1). The greatest changes occurred during the first few days in culture, but the mechanical properties continued to change during the entire 21 days. Cell traction stress, determined from sponge compaction and DNA count, decreased during the compaction process with the maximum traction value the initial value of 6.6 +/- 2.9 x 10(-3) Pacm3 cell(-1). Microarray data showed that the expression level of fibronectin, decorin sulfate, collagenase, and gelatinase A was upregulated at day 14 in the sponge. This suggested that the repair fibroblast phenotype was being expressed by the fibroblasts. Additional analysis suggested that a subpopulation of cells expressed the myofibroblast phenotype.

Current models used in our laboratory to assess the migration and traction of a population of cells within biopolymer gels are extended to investigate temporal changes in these parameters during compaction of mechanically constrained gels. The random cell migration coefficient, micro (t) is calculated using a windowing technique by regressing the mean-squared displacement of cells tracked at high magnification in three dimensions with a generalized least squares algorithm for a subset of experimental time intervals, and then shifting the window interval-by-interval until all time points are analyzed. The cell traction parameter, tau(0)(t), is determined by optimizing the solution of our anisotropic biphasic theory to tissue equivalent compaction. The windowing technique captured simulated sinusoidal and step changes in cell migration superposed on a persistent random walk in simulated cell movement. The optimization software captured simulated time dependence of compaction on cell spreading. Employment of these techniques on experimental data using rat dermal fibroblasts (RDFs) and human foreskin fibroblasts (HFFs) demonstrated that these cells exhibit different migration-traction relationships. Rat dermal fibroblast migration was negatively correlated to traction, suggesting migration was not the driving force for compaction with these cells, whereas human foreskin fibroblast migration was positively correlated to traction.

A method to impose and measure a one dimensional strain field via confined compression of a tissue-equivalent and measure the resulting cell and collagen fibril alignment was developed. Strain was determined locally by the displacement of polystyrene beads dispersed and entrapped within the network of collagen fibrils along with the cells, and it was correlated to the spatial variation of collagen network birefringence and concentration. Alignment of fibroblasts and smooth muscle cells was determined based on the long axis of elongated cells. Cell and collagen network alignment were observed normal to the direction of compression after a step strain and increased monotonically up to 50% strain. These results were independent of time after straining over 24 hr despite continued cell motility after responding instantly to the step strain with a change in alignment by deforming/convecting with the strained network. Since the time course of cell alignment followed that of strain and not stress which, due to the viscoelastic fluid-like nature of the network relaxes completely within the observation period, these results imply cell alignment in a compacting tissue-equivalent is due to fibril alignment associated with anisotropic network strain. Estimation of a contact guidance sensitivity parameter indicates that both cell types align to a greater extent than the surrounding fibrils.

We proposed and tested a method by which surface strains of biological tissues can be captured without the use of fiducial markers by instead, utilizing the inherent structure of the tissue. We used polarization-sensitive optical coherence tomography (PS OCT) to obtain volumetric data through the thickness and across a partial surface of the lumbar facet capsular ligament (FCL) during three cases of static bending. Reflectivity and phase retardance were calculated from two polarization channels, and a power spectrum analysis was performed on each a-line to extract the dominant banding frequency (a measure of degree of fiber alignment) through the maximum value of the power spectrum (maximum power). Maximum powers of all a-lines for each case were used to create 2D visualizations, which were subsequently tracked via digital image correlation. In-plane strains were calculated from measured 2D deformations and converted to 3D surface strains by including out-of-plane motion obtained from the PS OCT image. In-plane strains correlated with 3D strains (R2 ≥ 0.95). Using PS OCT for marker-free motion tracking of biological tissues is a promising new technique because it relies on the structural characteristics of the tissue to monitor displacement instead of external fiducial markers.

Soft-tissue characterization using planar biaxial testing and nominal stress–strain curves usually relies on certain conditions1: The sample should have a shape, (e.g., square or cruciform) that tends to produce homogeneous strain fields in the central region. If the sample is fibrous, the fiber orientation should be known and aligned with the axes of the test system. Strain should be measured far from any rigid boundary, such as a grip or attachment to bone. These criteria are often met (e.g., Refs. [3–9]), but for some tissue types, meeting one or more criteria is impossible. The tissue may, for example, be too small to allow isolation of a sample that is large enough for biaxial testing and is shaped to create a homogeneous strain region in the center. Aligning the material axes does not allow a biaxial test to generate planar shear strain [10]. Furthermore, if the material axes are improperly aligned, the variation in tissue response will increase, which could hinder elucidation of complex behaviors such as coupling between the two directions [10]. Other groups [e.g., Ref. 10] have used biaxial testing to good effect for off-axis fibrous samples. This is only effective, however, when the fiber orientation is known. When fiber orientation is unknown and/or the objective is to determine the fiber orientation, as in the current study, force-stretch data alone are insufficient. It also may be undesirable or even impossible to remove the tissue from bone, which restricts one's ability to align the tissue fiber direction with the testing apparatus and leads to inhomogeneity of the strain field. An example of these challenges is found in the AF of the intervertebral disk, particularly if one seeks to do single lamella experiments. Although some single lamella experiments have been performed in uniaxial [11–13] and biaxial modes [14–16], testing with intact bone [12–14,16] is attractive both because of direct relevance to in vivo loading and because of minimized tissue damage. Figure ​Figure11 shows a lamella of AF attached to axial vertebral bone. This geometry is not conducive to a homogeneous strain field, and the principal fiber direction does not align with the axes of the testing apparatus. Fig. 1 Lamella of the AF. The sample is attached to bone, labeled, and is anisotropic with fibers aligned 30 deg from the horizontal testing axis, along the dotted line. The dissected tissue is too small to be removed from the bone and cut to align the ... Sample geometries that produce inhomogeneous strain fields pose a considerable challenge to the investigator, but the advent of image-correlation-based methods for tracking motion over the entire tissue during testing [17–24] present new opportunities. The approach of simulating the experiment and then iterating over the model parameters to determine a best fit has been used in elastography [25,26] as well as indentation [27] and can be applied to tissue testing as well. In this study, we demonstrate the use of combined displacement field data, grip force-stretch data, and FE modeling to determine tissue properties from a biaxial test.

To investigate the contribution of three anatomical and physiologic factors (dilator thickness, dynamic pupillary block, and iris compressibility) to changes in iris configuration and anterior chamber angle during pupil dilation.A MATHEMATICAL MODEL OF THE ANTERIOR SEGMENT BASED ON THE AVERAGE VALUES OF OCULAR DIMENSIONS WAS DEVELOPED TO SIMULATE PUPIL DILATION. TO CHANGE THE PUPIL DIAMETER FROM 3.0 TO 5.4 MM IN 10 SECONDS, ACTIVE DILATOR CONTRACTION WAS APPLIED BY IMPOSING STRESS IN THE DILATOR REGION. THREE SETS OF PARAMETERS WERE VARIED IN THE SIMULATIONS: (1) a thin (4 μm, 1% of full thickness) versus a thick dilator (covering the full thickness iris) to quantify the effects of dilator anatomy, (2) in the presence (+PB) versus absence of pupillary block (-PB) to quantify the effect of dynamic motion of aqueous humor from the posterior to the anterior chamber, and (3) a compressible versus an incompressible iris to quantify the effects of iris volume change. Changes in the apparent iris-lens contact and angle open distance (AOD500) were calculated for each case.The thin case predicted a significant increase (average 700%) in iris curvature compared with the thick case (average 70%), showing that the anatomy of dilator plays an important role in iris deformation during dilation. In the presence of pupillary block (+PB), AOD500 decreased 25% and 36% for the compressible and incompressible iris, respectively.Iris bowing during dilation was driven primarily by posterior location of the dilator muscle and by dynamic pupillary block, but the effect of pupillary block was not as large as that of the dilator anatomy according to the quantified values of AOD500. Incompressibility of the iris, in contrast, had a relatively small effect on iris curvature but a large effect on AOD500; thus, we conclude that all three effects are important.

In addition to their obvious biological roles in tissue function, cells often play a significant mechanical role through a combination of passive and active behaviors. This study focused on the passive mechanical contribution of cells in tissues by improving our multiscale model via the addition of cells, which were treated as dilute spherical inclusions. The first set of simulations considered a rigid cell, with the surrounding ECM modeled as (1) linear elastic, (2) Neo-Hookean, and (3) a fiber network. Comparison with the classical composite theory for rigid inclusions showed close agreement at low cell volume fraction. The fiber network case exhibited nonlinear stress–strain behavior and Poisson's ratios larger than the elastic limit of 0.5, characteristics similar to those of biological tissues. The second set of simulations used a fiber network for both the cell (simulating cytoskeletal filaments) and matrix, and investigated the effect of varying relative stiffness between the cell and matrix, as well as the effect of a cytoplasmic pressure to enforce incompressibility of the cell. Results showed that the ECM network exerted negligible compression on the cell, even when the stiffness of fibers in the network was increased relative to the cell. Introduction of a cytoplasmic pressure significantly increased the stresses in the cell filament network, and altered how the cell changed its shape under tension. Findings from this study have implications on understanding how cells interact with their surrounding ECM, as well as in the context of mechanosensation.

In Part 1 of this work, we formulated and analyzed a mathematical model for our fibroblast-populated collagen microsphere (FPCM) assay of cell traction forces (Moon and Tranquillo, 1993). In this assay, the FPCM diameter decreases with time as the cells compact the gel by exerting traction on collagen fibrils. In Part I we demonstrated that the diameter reduction profiles for varied initial cell concentration and varied initial FPCM diameter are qualitatively consistent with the model predictions. We show here in Part 2 how predictions of a model similar to that of Part 1, along with the determination of the growth parameters of the cells and the viscoelastic parameters of the gel, allow us to estimate the magnitude of a cell traction parameter, the desired objective index of cell traction forces. The model is based on a monophasic continuum-mechanical theory of cell-extracellular matrix (ECM) mechanical interactions, with a species conservation equation for cells (1), a mass conservation equation for ECM (2), and a mechanical force balance for the cell/ECM composite (3). Using a constant-stress rheometer and a fluids spectrometer in creep and oscillatory shear modes, respectively, we establish and characterize the linear viscoelastic regime for the reconstituted type I collagen gel used in our FPCM traction assay and in other assays of cell-collagen mechanical interactions. Creep tests are performed on collagen gel specimens in a state resembling that in our FPCM traction assay (initially uncompacted, and therefore nearly isotropic and at a relatively low collagen concentration of 2.1 mg/ml), yielding measurements of the zero shear viscosity, μ 0 (7.4 x 10 6 Poise), and the steady-state creep compliance, J c 0 . The shear modulus, G (155 dynes/cm 2 ), is then determined from the inverse of J e 0 in the linear viscoelastic regime. Oscillatory shear tests are performed in strain sweep mode, indicating linear viscoelastic behavior up to shear strains of approximately 10 percent. We discuss the estimation of Poisson's ratio, v, which along with G and μ 0 specifies the assumed isotropic, linear viscoelastic stress tensor for the cell/collagen gel composite which appears in (3). The proliferation rate of fibroblasts in free floating collagen gel (appearing in (1)) is characterized by direct cell counting, yielding an estimate of the first-order growth rate constant, k (5.3 X 10 -6 s -1 ). These independently measured and estimated parameter values allow us to estimate that the cell traction parameter, τ 0 , defined in the active stress tensor which also appears in (3), is in the range of 0.00007-0.0002 dyne cm 4 /mg collagen cell. This value is in agreement with a reported measure of traction obtained directly via isometric force measurement across a slab of fibroblast-containing collagen gel.

A model is developed and analyzed for type IV collagen turnover in the kidney glomerular basement membrane (GBM), which is the primary structural element in the glomerular capillary wall. The model incorporates strain dependence in both deposition and removal of the GBM, leading to an equilibrium tissue strain at which deposition and removal are balanced. The GBM thickening decreases tissue strain per unit of transcapillary pressure drop according to the law of Laplace, but increases the transcapillary pressure drop required to maintain glomerular filtration. The model results are in agreement with the observed GBM alterations in Alport syndrome and thin basement membrane disease, and the model-predicted linear relation between the inverse capillary radius and inverse capillary thickness at equilibrium is consistent with published data on different mammals. In addition, the model predicts a minimum achievable strain in the GBM based on the geometry, properties, and mechanical environment; that is, an infinitely thick GBM would still experience a finite strain. Although the model assumptions would be invalid for an extremely thick GBM, the minimum achievable strain could be significant in diseases, such as Alport syndrome, characterized by focal GBM thickening. Finally, an examination of reasonable values for the model parameters suggests that the oncotic pressure drop—the osmotic pressure difference between the plasma and the filtrate due to large molecules—plays an important role in setting the GBM strain and, thus, leakage of protein into the urine may be protective against some GBM damage.

While several studies have evaluated how the degree of collagen alignment affects the response of soft tissues to tensile loading, the role of fibrillar organization in indentation is less understood. Collagen-based tissue-equivalents (TEs) provide a convenient model system to explore structure-function relationships since their microstructural properties can be easily controlled during fabrication. The purpose of this study was to evaluate the role of initial collagen alignment on the mechanical and structural behavior of soft tissues subjected to indentation using TEs as a model system. Cell-compacted TEs with either isotropic or highly anisotropic fiber alignment were subjected to four-step incremental stress-relaxation indentation tests. The mechanical properties, collagen reorganization and 2D strain patterns were quantified at each indentation step and compared between groups. While no differences were seen in the peak force response, significant differences were seen in relaxation behavior, fiber kinematics and tissue strain. Specifically, highly aligned samples exhibited a slower relaxation rate, smaller changes in collagen fiber orientation, larger changes in strength of alignment, and larger strain magnitudes compared to isotropic samples. Results demonstrate the significant role that microstructural organization plays in mediating the response of soft tissues to a non-tensile (i.e., indentation) mechanical stimulus.

The vitreous humor liquefies with age and readily sloshes during eye motion. The objective was to develop a computational model to determine the effect of sloshing on intravitreal drug transport for transscleral and intra-vitreal drug sources at various locationsA finite element model based on a telescopic implicit envelope tracking scheme was developed to model drug dispersion. Flow velocities due to saccadic oscillations were solved for and were used to simulate drug dispersion.Saccades induced a three-dimensional flow field that indicates intense drug dispersion in the vitreous. Model results showed that the time scale for transport decreased for the sloshing vitreous when compared to static vitreous. Macular concentrations for the sloshing vitreous were found be much higher than that for the static vitreous. For low viscosities the position of the intravitreal source did not have a big impact on drug distribution.Model results show that care should be taken when extrapolating animal data, which are mostly done on intact vitreous, to old patients whose vitreous might be a liquid. The decrease in drug transport time scales and changes in localized concentrations should be considered when deciding on treatment modalities and dosing strategies.

Elastography, which is the imaging of soft tissues on the basis of elastic modulus (or, more generally, stiffness) has become increasingly popular in the last decades and holds promise for application in many medical areas. Most of the attention has focused on inhomogeneous materials that are locally isotropic, the intent being to detect a (stiff) tumor within a (compliant) tissue. Many tissues of mechanical interest, however, are anisotropic, so a method capable of determining material anisotropy would be attractive. We present here an approach to determine the mechanical anisotropy of inhomogeneous, anisotropic tissues, by directly solving the finite element representation of the Cauchy stress balance in the tissue. The method divides the sample domain into subdomains assumed to have uniform properties and solves for the material constants in each subdomain. Two-dimensional simulated experiments on linear anisotropic inhomogeneous systems demonstrate the ability of the method, and simulated experiments on a nonlinear model demonstrate the ability of the method to capture anisotropy qualitatively even though only a linear model is used in the inverse problem. As with any inverse problem, ill-posedness is a serious concern, and multiple tests may need to be done on the same sample to determine the properties with confidence.

The fibroblast-populated collagen lattice is an attractive model tissue for in vitro studies of cell behavior and as the basis for bioartificial tissues. In spite of its simplicity—containing only collagen and cells—the system is surprisingly difficult to describe mechanically because of the ability of the cells to remodel the matrix, including compaction at short times and synthesis and/or degradation (and cell proliferation) at longer times. The objectives of this work were to measure the equilibrium modulus of fibroblast-populated gels with different collagen and cell concentrations, and to use that characterization as the basis for a theoretical model that could be used to predict gel mechanics based on conditions. Although many observations were as expected (e.g., the gel compacts more when there are more cells in it, and the gel is stiffer when there is more collagen in it), an unexpected result arose: the final modulus of the gel was not dependent solely on the final composition. Even if it compacted more than a gel that was originally at a high collagen concentration, a gel that started at a low collagen concentration remained less stiff than the higher-concentration gel. In light of these results and experimental studies by others, we propose a model in which the gel compaction is not homogeneous but consists instead of extreme densification near the cells in an otherwise unchanged matrix. By treating the dense regions as spherical inclusions, we used classical composite material theory to develop an expression for the modulus of a compacted gel based on the initial collagen density and the final inclusion (i.e., cell) density. The new model fit the data for moderately compacted gels well but broke down, as expected, for larger volume fractions at which the underlying model assumptions did not apply.

While it is firmly established that the mechanical behavior of most biological tissues, including bioengineered tissues, is governed by an underlying network of protein fibers, it is still not clear how best to obtain and utilize structural information to predict mechanical response. In this paper, methods are presented to (1) quantify the fiber arrangement in a tissue from different imaging tools, (2) incorporate that structure into a multiscale model, and (3) solve the model equations to predict both the microscopic and the macroscopic tissue response. In principle these concepts could be applied to any tissue (incorporating the specific tissue components as needed), but for demonstration purposes, the focus of the current work is on cell-compacted collagen gel, a model engineered tissue.

Though it is widely accepted that fiber alignment has a great influence on the mechanical anisotropy of tissues, a systematic study of the influence of fiber alignment on the macroscopic mechanical behavior by native tissues is precluded due to their predefined microstructure and heterogeneity. Such a study is possible using collagen-based bioartificial tissues that allow for alignment to be prescribed during their fabrication. To generate a systemic variation of strength of fiber alignment, we made cruciform tissue constructs in Teflon molds that had arms of different aspect ratios. We implemented our anisotropic biphasic theory of tissue-equivalent mechanics to simulate the compaction by finite element analysis. Prior to tensile testing, the construct geometry was standardized by cutting test samples with a 1:1 cruciform punch after releasing constructs from the molds. Planar biaxial testing was performed on these samples, after stretching them to their in-mold dimensions to recover in-mold alignment, to observe the macroscopic mechanical response with simultaneous fiber alignment imaging using a polarimetry system. We found that the strength of fiber alignment of the samples prior to release from the molds linearly increased with anisotropy of the mold. In testing after release, modulus ratio (modulus in fiber direction/modulus in normal direction) was greater as the initial strength of fiber alignment increased, that is, as the aspect ratio increased. We also found that the fiber alignment strength and modulus ratio increased in a hyperbolic fashion with stretching for a sample of given aspect ratio.