Modeling Fatigue Failure of Cartilage and Fibrous Biological Tissues Using Constrained Reactive Mixture Theory.

Fatigue failure in biological soft tissues plays a critical role in the etiology of chronic soft tissue injuries and diseases such as osteoarthritis. Understanding failure mechanisms is hindered by the decades-long timescales over which damage takes place. Analyzing the factors contributing to fatigue failure requires the help of validated computational models developed for soft tissues. This study presents a framework for fatigue failure of fibrous biological tissues based on reaction kinetics, where the composition of intact and fatigued material regions can evolve via degradation and breakage over time, in response to energy-based fatigue and damage criteria. Using reactive constrained mixture theory, material region mass fractions are governed by the axiom of mass balance. Progression of fatigue is controlled by an energy-based reaction rate, with user-selected probability functions defining the damage propensity of intact and fatigued material regions. Verification of this reactive theory, which is implemented in the open source FEBio finite element software, is provided in this study. Validation is also demonstrated against experimental data, showing that predicted damage can be linked to results from biochemical assays. The framework is also applied to study fatigue failure during frictional contact of cartilage. Simulating previous experiments suggests that frictional effects slightly increase fatigue progression, but the main driver is cyclic compressive contact loading. This study demonstrated the ability of theoretical models to complement and extend experimental findings, advancing our understanding of the time progression of fatigue in biological tissues.

The Problem With National Institute of Standards and Technology Thermodynamics Tables in Continuum Mechanics.

Thermodynamics is a fundamental topic of continuum mechanics and biomechanics, with a wide range of applications to physiological and biological processes. This study addresses two fundamental limitations of current thermodynamic treatments. First, thermodynamics tables distributed online by the U.S. National Institute of Standards and Technology (NIST) report properties of fluids as a function of absolute temperature T and absolute pressure P. These properties include mass density ρ, specific internal energy u, enthalpy h=u+P/ρ, and entropy s. However, formulations of jump conditions across phase boundaries derived from Newton's second law of motion and the first law of thermodynamics employ the gauge pressure p=P-Pr, where Pr is an arbitrarily selected referential absolute pressure. Interchanging p with P is not innocuous as it alters tabulated NIST values for u while keeping h and s unchanged. Using p for functions of state and governing equations solves the problem with using NIST entries for the specific internal energy u in standard thermodynamics tables and analyses of phase transformation in continuum mechanics. Second, constitutive models for the free energy of fluids, such as water and air, are not typically provided in standard thermodynamics treatments. This study proposes a set of constitutive models and validates them against suitably modified NIST data.

Continuum Growth Mechanics: Reconciling Two Common Frameworks.

The objective of this study was to investigate whether the two most common growth mechanics modeling frameworks, the constrained-mixture growth model and the kinematic growth model, could be reconciled mathematically. The purpose of this effort was to provide practical guidelines for potential users of these modeling frameworks. Results showed that the kinematic growth model is mathematically consistent with a special form of the constrained-mixture growth model, where only one generation of a growing solid exists at any given time, overturning its entire solid mass at each instant of growth in order to adopt the reference configuration dictated by the growth deformation. The thermodynamics of the kinematic growth model, along with the specialized constrained-mixture growth model, requires a cellular supply of chemical energy to allow deposition of solid mass under a stressed state. A back-of-the-envelope calculation shows that the amount of chemical energy required to sustain biological growth under these models is negligibly small, when compared to the amount of energy normally consumed daily by the human body. In conclusion, this study successfully reconciled the two most popular growth theories for biological growth and explained the special circumstances under which the constrained-mixture growth model reduces to the kinematic growth model.

Erratum: "A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity" [ASME J. Biomech Eng., 2023, 145(1), p. 011004; DOI: 10.1115/1.4054983].

In this erratum, we correct a mistake in a subcomponent of the numerical algorithm proposed in our recent study for modeling anisotropic reactive nonlinear viscoelasticity (doi:10.1115/1.4054983), for the special case where multiple weak bond families may be recruited with loading. This correction overcomes a nonphysical response noted under uni-axial cyclical loading.

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

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

Toward the Development of a Tissue Engineered Gradient Utilizing CRISPR-Guided Gene Modulation.

Cellular, compositional, and mechanical gradients are found throughout biological tissues, especially in transition zones between tissue types. Yet, strategies to engineer such gradients have proven difficult due to the complex nature of these tissues. Current strategies for tissue engineering complex gradients often utilize stem cells; however, these multipotent cells require direction from environmental cues, which can be difficult to control both in vitro and in vivo. In this study, we utilize clustered regularly-interspaced short palindromic repeats (CRISPR)-guided gene modulation to direct the differentiation of multipotent adipose-derived stem cells (ASCs) to demonstrate the effectiveness of CRISPR-engineered cells in tissue engineering applications. Specifically, we screen CRISPR-interference (CRISPRi) constructs targeting the promotors of selected osteogenic inhibitors and demonstrate that ASC osteogenic differentiation and mineral deposition can be regulated with CRISPRi targeting of Noggin without the use of exogenous growth factors in tissue engineered constructs. As a proof of concept, we combine three technologies developed out of our laboratories to demonstrate the controlled deposition of these engineered cells in a gradient with CRISPR-activation multiplex-engineered aggrecan/collagen type-II-chondrogenic ASCs on a high density anisotropic type I collagen construct to create a cell and tissue gradient similar to the fibrocartilage-to-mineralized-fibrocartilage gradient in the enthesis. Our results display the promise of CRISPR-engineered ASCs to produce tissue gradients, similar to what is observed in native tissue.

Early Resistance Rehabilitation Improves Functional Regeneration Following Segmental Bone Defect Injury.

Mechanical loading is integral to bone development and repair. The application of mechanical loads through rehabilitation are regularly prescribed as a clinical aide following severe bone injuries. However, current rehabilitation regimens typically involve long periods of non-loading and rely on subjective patient feedback, leading to muscle atrophy and soft tissue fibrosis. While many pre-clinical studies have focused on unloading, ambulatory loading, or direct mechanical compression, rehabilitation intensity and its impact on the local strain environment and subsequent bone healing have largely not been investigated. This study combines implantable strain sensors and subject-specific finite element models in a pre-clinical rodent model with a defect size on the cusp of critically-sized. Animals were enrolled in either high or low intensity rehabilitation one week post injury to investigate how rehabilitation intensity affects the local mechanical environment and subsequent functional bone regeneration. The high intensity rehabilitation animals were given free access to running wheels with resistance, which increased local strains within the regenerative niche by an average of 44% compared to the low intensity (no-resistance) group. Finite element modeling demonstrated that resistance rehabilitation significantly increased compressive strain by a factor of 2.0 at week 1 and 4.45 after 4 weeks of rehabilitation. The resistance rehabilitation group had significantly increased regenerated bone volume and higher bone bridging rates than its sedentary counterpart (bone volume: 22.00 mm3 ± 4.26 resistance rehabilitation vs 8.00 mm3 ± 2.27 sedentary; bridging rates: 90% resistance rehabilitation vs 50% sedentary). In addition, animals that underwent resistance running had femurs with improved mechanical properties compared to those left in sedentary conditions, with failure torque and torsional stiffness values matching their contralateral, intact femurs (stiffness: 0.036 Nm/deg ± 0.006 resistance rehabilitation vs 0.008 Nm/deg ± 0.006 sedentary). Running on a wheel with no resistance rehabilitation also increased bridging rates (100% no resistance rehabilitation vs 50% sedentary). Analysis of bone volume and von Frey suggest no-resistance rehabilitation may improve bone regeneration and hindlimb functionality. These results demonstrate the potential for early resistance rehabilitation as a rehabilitation regimen to improve bone regeneration and functional recovery.

Spatial Configurations of 3D Extracellular Matrix Collagen Density and Anisotropy Simultaneously Guide Angiogenesis.

Extracellular matrix (ECM) collagen density and fibril anisotropy are thought to affect the development of new vasculatures during pathologic and homeostatic angiogenesis. Computational simulation is emerging as a tool to investigate the role of matrix structural configurations on cell guidance. However, prior computational models have only considered the orientation of collagen as a model input. Recent experimental evidence indicates that cell guidance is simultaneously influenced by the direction and intensity of alignment (i.e., degree of anisotropy) as well as the local collagen density. The objective of this study was to explore the role of ECM collagen anisotropy and density during sprouting angiogenesis through simulation in the AngioFE and FEBio modeling frameworks. AngioFE is a plugin for FEBio (Finite Elements for Biomechanics) that simulates cell-matrix interactions during sprouting angiogenesis. We extended AngioFE to represent ECM collagen as deformable 3D ellipsoidal fibril distributions (EFDs). The rate and direction of microvessel growth were modified to depend simultaneously on the ECM collagen anisotropy (orientation and degree of anisotropy) and density. The sensitivity of growing neovessels to these stimuli was adjusted so that AngioFE could reproduce the growth and guidance observed in experiments where microvessels were cultured in collagen gels of varying anisotropy and density. We then compared outcomes from simulations using EFDs to simulations that used AngioFE's prior vector field representation of collagen anisotropy. We found that EFD simulations were more accurate than vector field simulations in predicting experimentally observed microvessel guidance. Predictive simulations demonstrated the ability of anisotropy gradients to recruit microvessels across short and long distances relevant to wound healing. Further, simulations predicted that collagen alignment could enable microvessels to overcome dense tissue interfaces such as tumor-associated collagen structures (TACS) found in desmoplasia and tumor-stroma interfaces. This approach can be generalized to other mechanobiological relationships during cell guidance phenomena in computational settings.

Dynamic Biophysical Cues Near the Tip Cell Microenvironment Provide Distinct Guidance Signals to Angiogenic Neovessels.

The formation of new vascular networks via angiogenesis is a crucial biological mechanism to balance tissue metabolic needs, yet the coordination of factors that influence the guidance of growing neovessels remain unclear. This study investigated the influence of extracellular cues within the immediate environment of sprouting tips over multiple hours and obtained quantitative relationships describing their effects on the growth trajectories of angiogenic neovessels. Three distinct microenvironmental cues-fibril tracks, ECM density, and the presence of nearby cell bodies-were extracted from 3D time series image data. The prominence of each cue was quantified along potential sprout trajectories to predict the response to multiple microenvironmental factors simultaneously. Sprout trajectories significantly correlated with the identified microenvironmental cues. Specifically, ECM density and nearby cellular bodies were the strongest predictors of the trajectories taken by neovessels (p < 0.001 and p = 0.016). Notwithstanding, direction changing trajectories, deviating from the initial neovessel orientation, were significantly correlated with fibril tracks (p = 0.003). Direction changes also occurred more frequently with strong microenvironmental cues. This provides evidence for the first time that local matrix fibril alignment influences changes in sprout trajectories but does not materially contribute to persistent sprouting. Together, our results suggest the microenvironmental cues significantly contribute to guidance of sprouting trajectories. Further, the presented methods quantitatively distinguish the influence of individual microenvironmental stimuli during guidance.

Modeling Inelastic Responses Using Constrained Reactive Mixtures.

This study reviews the progression of our research, from modeling growth theories for cartilage tissue engineering, to the formulation of constrained reactive mixture theories to model inelastic responses in any solid material, such as theories for damage mechanics, viscoelasticity, plasticity, and elasto-plastic damage. In this framework, multiple solid generations α can co-exist at any given time in the mixture. The oldest generation is denoted by α=s and is called the master generation, whose reference configuration Xs is observable. The solid generations α are all constrained to share the same velocity vs, but may have distinct reference configurations Xα. An important element of this formulation is that the time-invariant mapping Fαs=∂Xα/∂Xs between these reference configurations is a function of state, whose mathematical formulation is postulated by constitutive assumption. Thus, reference configurations Xα are not observable (α≠s). This formulation employs only observable state variables, such as the deformation gradient Fs of the master generation and the referential mass concentrations ρrα of each generation, in contrast to classical formulations of inelastic responses which rely on internal state variable theory, requiring evolution equations for those hidden variables. In constrained reactive mixtures, the evolution of the mass concentrations is governed by the axiom of mass balance, using constitutive models for the mass supply densities ρˆrα. Classical and constrained reactive mixture approaches share considerable mathematical analogies, as they both introduce a multiplicative decomposition of the deformation gradient, also requiring evolution equations to track some of the state variables. However, they also differ at a fundamental level, since one adopts only observable state variables while the other introduces hidden state variables. In summary, this review presents an alternative foundational approach to the modeling of inelastic responses in solids, grounded in the classical framework of mixture theory.

Finite Element Implementation of Computational Fluid Dynamics With Reactive Neutral and Charged Solute Transport in FEBio.

The objective of this study was to implement a novel fluid-solutes solver into the open-source finite element software FEBio, that extended available modeling capabilities for biological fluids and fluid-solute mixtures. Using a reactive mixture framework, this solver accommodates diffusion, convection, chemical reactions, electrical charge effects, and external body forces, without requiring stabilization methods that were deemed necessary in previous computational implementations of the convection-diffusion-reaction equation at high Peclet numbers. Verification and validation problems demonstrated the ability of this solver to produce solutions for Peclet numbers as high as 1011, spanning the range of physiological conditions for convection-dominated solute transport. This outcome was facilitated by the use of a formulation that accommodates realistic values for solvent compressibility, and by expressing the solute mass balance such that it properly captured convective transport by the solvent and produced a natural boundary condition of zero diffusive solute flux at outflow boundaries. Since this numerical scheme was not necessarily foolproof, guidelines were included to achieve better outcomes that minimize or eliminate the potential occurrence of numerical artifacts. The fluid-solutes solver presented in this study represents an important and novel advancement in the modeling capabilities for biomechanics and biophysics as it allows modeling of mechanobiological processes via the incorporation of chemical reactions involving neutral or charged solutes within dynamic fluid flow. The incorporation of charged solutes in a reactive framework represents a significant novelty of this solver. This framework also applies to a broader range of nonbiological applications.

The effects of leaflet material properties on the simulated function of regurgitant mitral valves.

Advances in three-dimensional imaging provide the ability to construct and analyze finite element (FE) models to evaluate the biomechanical behavior and function of atrioventricular valves. However, while obtaining patient-specific valve geometry is now possible, non-invasive measurement of patient-specific leaflet material properties remains nearly impossible. Both valve geometry and tissue properties play a significant role in governing valve dynamics, leading to the central question of whether clinically relevant insights can be attained from FE analysis of atrioventricular valves without precise knowledge of tissue properties. As such we investigated (1) the influence of tissue extensibility and (2) the effects of constitutive model parameters and leaflet thickness on simulated valve function and mechanics. We compared metrics of valve function (e.g., leaflet coaptation and regurgitant orifice area) and mechanics (e.g., stress and strain) across one normal and three regurgitant mitral valve (MV) models with common mechanisms of regurgitation (annular dilation, leaflet prolapse, leaflet tethering) of both moderate and severe degree. We developed a novel fully-automated approach to accurately quantify regurgitant orifice areas of complex valve geometries. We found that the relative ordering of the mechanical and functional metrics was maintained across a group of valves using material properties up to 15% softer than the representative adult mitral constitutive model. Our findings suggest that FE simulations can be used to qualitatively compare how differences and alterations in valve structure affect relative atrioventricular valve function even in populations where material properties are not precisely known.

Targeting damaged collagen for intra-articular delivery of therapeutics using collagen hybridizing peptides.

The objective of this study was to investigate the potential of collagen hybridizing peptides (CHPs), which bind to denatured collagen, to extend the retention time of near-infrared fluorophores (NIRF) following intra-articular (IA) injection in rat knee joints. CHPs were synthesized with a NIRF conjugated to the N-terminus. Male Sprague-Dawley rats were assigned to one of four experimental groups: healthy, CHP; osteoarthritis (OA), CHP; healthy, scrambled-sequence CHP (sCHP), which has no collagen binding affinity; or OA, sCHP. Animals in the OA groups received an IA injection of monosodium iodoacetate to induce OA. All animals then received the corresponding CHP injection. Animals were imaged repeatedly over 2 weeks using an in vivo fluorescence imaging system. Joint components were isolated and imaged to determine CHP binding distribution. Safranin-O and Fast Green histological staining was performed to confirm the development of OA. CHPs were found to be retained within the joint following IA injection in both healthy and OA animals for the full study period. In contrast, sCHP signal was negligible by 24-48 h. CHP signal was significantly greater (p < 0.05) in OA joints when compared to healthy joints. At the 2-week end point, multiple joint components retained CHPs, including cartilage, meniscus, and synovium. CHPs dramatically extended the retention time of NIRFs following IA injection in healthy and OA knee joints by binding to multiple collagenous tissues in the joint. These results support the pursuit of further research to develop CHP based therapeutics for IA treatment of OA.

The Effects of leaflet material properties on the simulated function of regurgitant mitral valves.

Advances in three-dimensional imaging provide the ability to construct and analyze finite element (FE) models to evaluate the biomechanical behavior and function of atrioventricular valves. However, while obtaining patient-specific valve geometry is now possible, non-invasive measurement of patient-specific leaflet material properties remains nearly impossible. Both valve geometry and tissue properties play a significant role in governing valve dynamics, leading to the central question of whether clinically relevant insights can be attained from FE analysis of atrioventricular valves without precise knowledge of tissue properties. As such we investigated 1) the influence of tissue extensibility and 2) the effects of constitutive model parameters and leaflet thickness on simulated valve function and mechanics. We compared metrics of valve function (e.g., leaflet coaptation and regurgitant orifice area) and mechanics (e.g., stress and strain) across one normal and three regurgitant mitral valve (MV) models with common mechanisms of regurgitation (annular dilation, leaflet prolapse, leaflet tethering) of both moderate and severe degree. We developed a novel fully-automated approach to accurately quantify regurgitant orifice areas of complex valve geometries. We found that the relative ordering of the mechanical and functional metrics was maintained across a group of valves using material properties up to 15% softer than the representative adult mitral constitutive model. Our findings suggest that FE simulations can be used to qualitatively compare how differences and alterations in valve structure affect relative atrioventricular valve function even in populations where material properties are not precisely known.

Collagen fibrils from both positional and energy-storing tendons exhibit increased amounts of denatured collagen when stretched beyond the yield point.

Collagen molecules are the base structural unit of tendons, which become denatured during mechanical overload. We recently demonstrated that during tendon stretch, collagen denaturation occurs at the yield point of the stress-strain curve in both positional and energy-storing tendons. We were interested in investigating how this load is transferred throughout the collagen hierarchy, and sought to determine the onset of collagen denaturation when collagen fibrils are stretched. Fibrils are one level above the collagen molecule in the collagen hierarchy, allowing more direct probing of the effect of strain on collagen molecules. We isolated collagen fibrils from both positional and energy-storing tendon types and stretched them using a microelectromechanical system device to various levels of strain. We stained the fibrils with fluorescently labeled collagen hybridizing peptides that specifically bind to denatured collagen, and examined whether samples stretched beyond the yield point of the stress-strain curve exhibited increased amounts of denatured collagen. We found that collagen denaturation in collagen fibrils from both tendon types occurs at the yield point. Greater amounts of denatured collagen were found in post-yield positional fibrils than in energy-storing fibrils. This is despite a greater yield strain and yield stress in fibrils from energy-storing tendons compared to positional tendons. Interestingly, the peak modulus of collagen fibrils from both tendon types was the same. These results are likely explained by the greater crosslink density found in energy-storing tendons compared to positional tendons. The insights gained from this study could help management of tendon and other musculoskeletal injuries by targeting collagen molecular damage at the fibril level. STATEMENT OF SIGNIFICANCE: When tendons are stretched or torn, this can lead to collagen denaturation (damage). Depending on their biomechanical function, tendons are considered positional or energy-storing with different crosslink profiles. By stretching collagen fibrils instead of fascicles from both tendon types, we can more directly examine the effect of tensile stretch on the collagen molecule in tendons. We found that regardless of tendon type, collagen denaturation in fibrils occurs when they are stretched beyond the yield point of the stress-strain curve. This provides insight into how load affects different tendon sub-structures during tendon injuries and failure, which will help clinicians and researchers understand mechanisms of injuries and potentially target collagen molecular damage as a treatment strategy, leading to improved clinical outcomes following injury.

A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity.

Reactive viscoelasticity is a theoretical framework based on the theory of reactive constrained mixtures that encompasses nonlinear viscoelastic responses. It models a viscoelastic solid as a mixture of strong and weak bonds that maintain the cohesiveness of the molecular constituents of the solid matter. Strong bonds impart the elastic response while weak bonds break and reform into a stress-free state in response to loading. The process of bonds breaking and reforming is modeled as a reaction where loaded bonds are the reactants and bonds reformed into a stress-free state are the products of a reaction. The reaction is triggered by the evolving state of loading. The state of stress in strong bonds is a function of the total strain in the material, whereas the state of stress in weak bonds is based on the state of strain relative to the time that these bonds were reformed. This study introduces two important practical contributions to the reactive nonlinear viscoelasticity framework: (1) normally, the evaluation of the stress tensor involves taking a summation over a continually increasing number of weak bond generations, which is poorly suited for a computational scheme. Therefore, this study presents an effective numerical scheme for evaluating the strain energy density, the Cauchy stress, and spatial elasticity tensors of reactive viscoelastic materials. (2) We provide the conditions for satisfying frame indifference for anisotropic nonlinear viscoelasticity, including for tension-bearing fiber models. Code verifications and model validations against experimental data provide evidence in support of this updated formulation.

Collagen Molecular Damage is a Hallmark of Early Atherosclerosis Development.

Remodeling of extracellular matrix proteins underlies the development of cardiovascular disease. Herein, we utilized a novel molecular probe, collagen hybridizing peptide (CHP), to target collagen molecular damage during atherogenesis. The thoracic aorta was dissected from ApoE-/- mice that had been on a high-fat diet for 0-18 weeks. Using an optimized protocol, tissues were stained with Cy3-CHP and digested to quantify CHP with a microplate assay. Results demonstrated collagen molecular damage, inferred from Cy3-CHP fluorescence, was a function of location and time on the high-fat diet. Tissue from the aortic arch showed a significant increase in collagen molecular damage after 18 weeks, while no change was observed in tissue from the descending aorta. No spatial differences in fluorescence were observed between the superior and inferior arch tissue. Our results provide insight into the early changes in collagen during atherogenesis and present a new opportunity in the subclinical diagnosis of atherosclerosis.

Damage Mechanics of Biological Tissues in Relation to Viscoelasticity.

This study examines the theoretical foundations for the damage mechanics of biological tissues in relation to viscoelasticity. Its primary goal is to provide a mechanistic understanding of well-known experimental observations in biomechanics, which show that the ultimate tensile strength of viscoelastic biological tissues typically increases with increasing strain rate. The basic premise of this framework is that tissue damage occurs when strong bonds, such as covalent bonds in the solid matrix of a biological tissue, break in response to loading. This type of failure is described as elastic damage, under the idealizing assumption that strong bonds behave elastically. Viscoelasticity arises from three types of dissipative mechanisms: (1) Friction between molecules of the same species, which is represented by the tissue viscosity. (2) Friction between fluid and solid constituents of a porous medium, which is represented by the tissue hydraulic permeability. (3) Dissipative reactions arising from weak bonds breaking in response to loading, and reforming in a stress-free state, such as hydrogen bonds and other weak electrostatic bonds. When a viscoelastic tissue is subjected to loading, some of that load may be temporarily supported by those frictional and weak bond forces, reducing the amount of load supported by elastic strong bonds and thus, the extent of elastic damage sustained by those bonds. This protective effect depends on the characteristic time response of viscoelastic mechanisms in relation to the loading history. This study formalizes these concepts by presenting general equations that can model the damage mechanics of viscoelastic tissues.

Mechanics of lung cancer: A finite element model shows strain amplification during early tumorigenesis.

Early lung cancer lesions develop within a unique microenvironment that undergoes constant cyclic stretch from respiration. While tumor stiffening is an established driver of tumor progression, the contribution of stress and strain to lung cancer is unknown. We developed tissue scale finite element models of lung tissue to test how early lesions alter respiration-induced strain. We found that an early tumor, represented as alveolar filling, amplified the strain experienced in the adjacent alveolar walls. Tumor stiffening further increased the amplitude of the strain in the adjacent alveolar walls and extended the strain amplification deeper into the normal lung. In contrast, the strain experienced in the tumor proper was less than the applied strain, although regions of amplification appeared at the tumor edge. Measurements of the alveolar wall thickness in clinical and mouse model samples of lung adenocarcinoma (LUAD) showed wall thickening adjacent to the tumors, consistent with cellular response to strain. Modeling alveolar wall thickening by encircling the tumor with thickened walls moved the strain amplification radially outward, to the next adjacent alveolus. Simulating iterative thickening in response to amplified strain produced tracks of thickened walls. We observed such tracks in early-stage clinical samples. The tracks were populated with invading tumor cells, suggesting that strain amplification in very early lung lesions could guide pro-invasive remodeling of the tumor microenvironment. The simulation results and tumor measurements suggest that cells at the edge of a lung tumor and in surrounding alveolar walls experience increased strain during respiration that could promote tumor progression.