A Systems Approach to Biomechanics, Mechanobiology, and Biotransport.

The human body represents a collection of interacting systems that range in scale from nanometers to meters. Investigations from a systems perspective focus on how the parts work together to enact changes across spatial scales, and further our understanding of how systems function and fail. Here, we highlight systems approaches presented at the 2022 Summer Biomechanics, Bio-engineering, and Biotransport Conference in the areas of solid mechanics; fluid mechanics; tissue and cellular engineering; biotransport; and design, dynamics, and rehabilitation; and biomechanics education. Systems approaches are yielding new insights into human biology by leveraging state-of-the-art tools, which could ultimately lead to more informed design of therapies and medical devices for preventing and treating disease as well as rehabilitating patients using strategies that are uniquely optimized for each patient. Educational approaches can also be designed to foster a foundation of systems-level thinking.

Effects of Porosity on Piezoelectric Characteristics of Polyvinylidene Fluoride Films for Biomedical Applications.

Objective: The objective of this work is to study the effects of porosity on mechanical and piezoelectric properties of polyvinylidene fluoride (PVDF) films for biomedical applications. Impact Statement: By investigating the piezoelectric properties of PVDF and the porosity effect on its electromechanical performance, there is potential for further development of PVDF as a hemodynamic sensor that can lead to further technological advancements in the biomedical field, benefiting patients and physicians alike. Introduction: PVDF thin films have shown potential in the application of hemodynamic flow sensing and monitoring the effects on blood flow caused by prosthetic valve implantation via the transcatheter aortic valve replacement operation. The piezoelectric performance of PVDF films can be influenced by the porosity of the material. Methods: In this study, strain tracking was performed on thin film PVDF specimens with various levels of porosity and pore sizes to determine the mechanical properties of the specimens. The mechanical properties were used to model the PVDF material in COMSOL multiphysics software, in which compression test simulations were performed to determine the piezoelectric coefficient d33 of the PVDF. Results: A decline in the elastic modulus was found to be highly inversely correlated with porosity of the specimens and the simulation results show that elastic modulus had a much greater effect on the piezoelectric properties than Poisson's ratio. Conclusion: A combination of experimental and computational techniques was able to characterize and correlate the mechanical properties of PVDF films of varying porosities to their piezoelectric properties.

Elucidating the signal for contact guidance contained in aligned fibrils with a microstructural-mechanical model.

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.

Computational and experimental comparison on the effects of flow-induced compression on the permeability of collagen gels.

Collagen is a naturally occurring polymer and is popular in tissue engineering due to its high biocompatibility, ubiquity throughout the body, and its porous nature. The transport properties of collagen help dictate the delivery of nutrients to tissues, and the mechanical properties can help improve the function of engineered tissues. The objective of this study is to investigate experimentally the change in permeability as collagen gels undergo flow-induced compression and compare these results with model predictions using a finite element model. We developed a horizontal apparatus to measure the hydraulic permeability of collagen gels undergoing flow-induced compression. The permeability of 1.98 mg/mL, 3.5 mg/mL, and 5 mg/mL collagen Type I rat tail hydrogels were determined experimentally by tracking the pressure drop across the gels as water flowed through the samples, which simultaneously compressed them under pressure. The Holmes-Mow model was used to fit the permeability as the gels underwent compression. A finite element model was created using FEBio to estimate the Young's modulus of collagen gels at the macroscopic level by fitting the experimental pressure vs. the compressive stretch ratio to the model. Our results suggest that the initial permeability of collagen gels decreased with increasing concentration, as expected. However, gels with a lower initial concentration compressed to a greater degree, resulting in smaller final permeabilities once fully compressed. Taken together, our work suggests that the treatment of a collagen gel as an isotropic, elastic material is sufficient to model its transport properties on a macroscopic level but is inadequate if more localized transport properties, which are dependent on network architecture (such as collagen alignment or inhomogeneous densification), are required.

Responses of ticks to immersion in hot bathing water: Effect of surface type, water temperature, and soap on tick motor control.

Preventing bites from undetected ticks through bathing practices would benefit public health, but the effects of these practices have been researched minimally. We immersed nymphal and adult hard ticks of species common in the eastern United States in tap water, using temperatures and durations that are realistic for human hot bathing. The effect of (a) different skin-equivalent surfaces (silicone and pig skin), and (b) water temperature was tested on Amblyomma americanum, Dermacentor variabilis and Ixodes scapularis nymphs. Overall, the type of surface had a much larger effect on the nymphs' tendency to stay in contact with the surface than water temperature did. Most nymphs that separated from the surface did so within the first 10 s of immersion, with the majority losing contact due to the formation of an air bubble between their ventral side and the test surface. In addition, adult Ixodes scapularis were tested for the effect of immersion time, temperature, and soap on tick responsiveness. Some individual adults moved abnormally or stopped moving as a result of longer or hotter immersion, but soap had little effect on responsiveness. Taken together, our results suggest that the surface plays a role in ticks' tendency to stay in contact; the use of different bath additives warrants further research. While water temperature did not have a significant short-term effect on tick separation, ticks that have not attached by their mouth parts may be rendered unresponsive and eventually lose contact with a person's skin in a hot bath. It should be noted that our research did not consider potential temperature effects on the pathogens themselves, as previous research suggests that some tickborne pathogens may become less hazardous even if the tick harboring them survives hot-water exposures and later bites the bather after remaining undetected.

Pandemic-Driven Online Teaching-The Natural Setting for a Flipped Classroom?

As the COVID-19 pandemic forced a sudden shift to online teaching and learning in April 2020, one of the more significant challenges faced by instructors is encouraging and maintaining student engagement in their online classes. This paper describes my experience of flipping an online classroom for a core Chemical Engineering Fluid Mechanics class to promote student engagement and collaboration in an online setting. Comparing exam scores with prior semesters involving in-person, traditional lecture-style classes suggests that students need a certain degree of adjustment to adapt to this new learning mode. A decrease in student rating of teaching (SRT) scores indicates that students largely prefer in-person, traditional lectures over an online flipped class, even though written comments in the SRT contained several responses favorable to flipping the class in an online setting. Overall, SRT scores on a department level also showed a similar decrease, which suggests students were less satisfied with the quality of teaching overall throughout the department, with this flipped method of instruction neither improving nor worsening student sentiment toward online learning. In addition, whereas most students liked the prerecorded lecture videos, they were less enthusiastic about using breakout rooms to encourage student collaboration and discussion. Further thought and discussion on best practices to facilitate online student interaction and collaboration are recommended, as online learning will likely continue to grow in popularity even when in-person instruction resumes after the pandemic.

Cell contact guidance via sensing anisotropy of network mechanical resistance.

Despite the ubiquitous importance of cell contact guidance, the signal-inducing contact guidance of mammalian cells in an aligned fibril network has defied elucidation. This is due to multiple interdependent signals that an aligned fibril network presents to cells, including, at least, anisotropy of adhesion, porosity, and mechanical resistance. By forming aligned fibrin gels with the same alignment strength, but cross-linked to different extents, the anisotropic mechanical resistance hypothesis of contact guidance was tested for human dermal fibroblasts. The cross-linking was shown to increase the mechanical resistance anisotropy, without detectable change in network microstructure and without change in cell adhesion to the cross-linked fibrin gel. This methodology thus isolated anisotropic mechanical resistance as a variable for fixed anisotropy of adhesion and porosity. The mechanical resistance anisotropy |Y*| -1 - |X*| -1 increased over fourfold in terms of the Fourier magnitudes of microbead displacement |X*| and |Y*| at the drive frequency with respect to alignment direction Y obtained by optical forces in active microrheology. Cells were found to exhibit stronger contact guidance in the cross-linked gels possessing greater mechanical resistance anisotropy: the cell anisotropy index based on the tensor of cell orientation, which has a range 0 to 1, increased by 18% with the fourfold increase in mechanical resistance anisotropy. We also show that modulation of adhesion via function-blocking antibodies can modulate the guidance response, suggesting a concomitant role of cell adhesion. These results indicate that fibroblasts can exhibit contact guidance in aligned fibril networks by sensing anisotropy of network mechanical resistance.

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

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.

Swelling of Collagen-Hyaluronic Acid Co-Gels: An In Vitro Residual Stress Model.

Tissue-equivalents (TEs), simple model tissues with tunable properties, have been used to explore many features of biological soft tissues. Absent in most formulations however, is the residual stress that arises due to interactions among components with different unloaded levels of stress, which has an important functional role in many biological tissues. To create a pre-stressed model system, co-gels were fabricated from a combination of hyaluronic acid (HA) and reconstituted Type-I collagen (Col). When placed in solutions of varying osmolarity, HA-Col co-gels swell as the HA imbibes water, which in turn stretches (and stresses) the collagen network. In this way, co-gels with residual stress (i.e., collagen fibers in tension and HA in compression) were fabricated. When the three gel types tested here were immersed in hypotonic solutions, pure HA gels swelled the most, followed by HA-Col co-gels; no swelling was observed in pure collagen gels. The greatest swelling rates and swelling ratios occurred in the lowest salt concentration solutions. Tension on the collagen component of HA-Col co-gels was calculated from a stress balance and increased nonlinearly as swelling increased. The swelling experiment results were in good agreement with the stress predicted by a fibril network + non-fibrillar interstitial matrix computational model.

Multiscale Mechanical Model of the Pacinian Corpuscle Shows Depth and Anisotropy Contribute to the Receptor's Characteristic Response to Indentation.

Cutaneous mechanoreceptors transduce different tactile stimuli into neural signals that produce distinct sensations of touch. The Pacinian corpuscle (PC), a cutaneous mechanoreceptor located deep within the dermis of the skin, detects high frequency vibrations that occur within its large receptive field. The PC is comprised of lamellae that surround the nerve fiber at its core. We hypothesized that a layered, anisotropic structure, embedded deep within the skin, would produce the nonlinear strain transmission and low spatial sensitivity characteristic of the PC. A multiscale finite-element model was used to model the equilibrium response of the PC to indentation. The first simulation considered an isolated PC with fiber networks aligned with the PC's surface. The PC was subjected to a 10 µm indentation by a 250 µm diameter indenter. The multiscale model captured the nonlinear strain transmission through the PC, predicting decreased compressive strain with proximity to the receptor's core, as seen experimentally by others. The second set of simulations considered a single PC embedded epidermally (shallow) or dermally (deep) to model the PC's location within the skin. The embedded models were subjected to 10 µm indentations at a series of locations on the surface of the skin. Strain along the long axis of the PC was calculated after indentation to simulate stretch along the nerve fiber at the center of the PC. Receptive fields for the epidermis and dermis models were constructed by mapping the long-axis strain after indentation at each point on the surface of the skin mesh. The dermis model resulted in a larger receptive field, as the calculated strain showed less indenter location dependence than in the epidermis model.

A multiscale approach to modeling the passive mechanical contribution of cells in tissues.

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.

A coupled fiber-matrix model demonstrates highly inhomogeneous microstructural interactions in soft tissues under tensile load.

A soft tissue's macroscopic behavior is largely determined by its microstructural components (often a collagen fiber network surrounded by a nonfibrillar matrix (NFM)). In the present study, a coupled fiber-matrix model was developed to fully quantify the internal stress field within such a tissue and to explore interactions between the collagen fiber network and nonfibrillar matrix (NFM). Voronoi tessellations (representing collagen networks) were embedded in a continuous three-dimensional NFM. Fibers were represented as one-dimensional nonlinear springs and the NFM, meshed via tetrahedra, was modeled as a compressible neo-Hookean solid. Multidimensional finite element modeling was employed in order to couple the two tissue components and uniaxial tension was applied to the composite representative volume element (RVE). In terms of the overall RVE response (average stress, fiber orientation, and Poisson's ratio), the coupled fiber-matrix model yielded results consistent with those obtained using a previously developed parallel model based upon superposition. The detailed stress field in the composite RVE demonstrated the high degree of inhomogeneity in NFM mechanics, which cannot be addressed by a parallel model. Distributions of maximum/minimum principal stresses in the NFM showed a transition from fiber-dominated to matrix-dominated behavior as the matrix shear modulus increased. The matrix-dominated behavior also included a shift in the fiber kinematics toward the affine limit. We conclude that if only gross averaged parameters are of interest, parallel-type models are suitable. If, however, one is concerned with phenomena, such as individual cell-fiber interactions or tissue failure that could be altered by local variations in the stress field, then the detailed model is necessary in spite of its higher computational cost.

Microstructural and mechanical differences between digested collagen-fibrin co-gels and pure collagen and fibrin gels.

Collagen and fibrin are important extracellular matrix (ECM) components in the body, providing structural integrity to various tissues. These biopolymers are also common scaffolds used in tissue engineering. This study investigated how co-gelation of collagen and fibrin affected the properties of each individual protein network. Collagen-fibrin co-gels were cast and subsequently digested using either plasmin or collagenase; the microstructure and mechanical behavior of the resulting networks were then compared with the respective pure collagen or fibrin gels of the same protein concentration. The morphologies of the collagen networks were further analyzed via three-dimensional network reconstruction from confocal image z-stacks. Both collagen and fibrin exhibited a decrease in mean fiber diameter when formed in co-gels compared with the pure gels. This microstructural change was accompanied by an increased failure strain and decreased tangent modulus for both collagen and fibrin following selective digestion of the co-gels. In addition, analysis of the reconstructed collagen networks indicated the presence of very long fibers and the clustering of fibrils, resulting in very high connectivities for collagen networks formed in co-gels.

Mechanics of a fiber network within a non-fibrillar matrix: model and comparison with collagen-agarose co-gels.

While collagen is recognized as the predominant mechanical component of soft connective tissues, the role of the non-fibrillar matrix (NFM) is less well understood. Even model systems, such as the collagen-agarose co-gel, can exhibit complex behavior, making it difficult to identify relative contributions of specific tissue constituents. In the present study, we developed a two-component microscale model of collagen-agarose tissue analogs and used it to elucidate the interaction between collagen and NFM in uniaxial tension. Collagen fibers were represented with Voronoi networks, and the NFM was modeled as a neo-Hookean solid. Model predictions of total normal stress and Poisson's ratio matched experimental observations well (including high Poisson's values of ~3), and the addition of NFM led to composition-dependent decreases in volume change and increases in fiber stretch. Because the NFM was more resistant to volume change than the fiber network, extension of the composite led to pressurization of the NFM. Within a specific range of parameter values (low shear modulus and moderate Poisson's ratio), the magnitude of the reaction force decreased relative to this pressurization component resulting in a negative (compressive) NFM stress in the loading direction, even though the composite tissue was in tension.

Mechanical behavior of collagen-fibrin co-gels reflects transition from series to parallel interactions with increasing collagen content.

Fibrin and collagen, biopolymers occurring naturally in the body, are biomaterials commonly-used as scaffolds for tissue engineering. How collagen and fibrin interact to confer macroscopic mechanical properties in collagen-fibrin composite systems remains poorly understood. In this study, we formulated collagen-fibrin co-gels at different collagen-to-fibrin ratios to observe changes in the overall mechanical behavior and microstructure. A modeling framework of a two-network system was developed by modifying our micro-scale model, considering two forms of interaction between the networks: (a) two interpenetrating but noninteracting networks ("parallel"), and (b) a single network consisting of randomly alternating collagen and fibrin fibrils ("series"). Mechanical testing of our gels show that collagen-fibrin co-gels exhibit intermediate properties (UTS, strain at failure, tangent modulus) compared to those of pure collagen and fibrin. The comparison with model predictions show that the parallel and series model cases provide upper and lower bounds, respectively, for the experimental data, suggesting that a combination of such interactions exists between the collagen and fibrin in co-gels. A transition from the series model to the parallel model occurs with increasing collagen content, with the series model best describing predominantly fibrin co-gels, and the parallel model best describing predominantly collagen co-gels.