Mechano-biological and bio-mechanical pathways in cutaneous wound healing.

Injuries to the skin heal through coordinated action of fibroblast-mediated extracellular matrix (ECM) deposition, ECM remodeling, and wound contraction. Defects involving the dermis result in fibrotic scars featuring increased stiffness and altered collagen content and organization. Although computational models are crucial to unravel the underlying biochemical and biophysical mechanisms, simulations of the evolving wound biomechanics are seldom benchmarked against measurements. Here, we leverage recent quantifications of local tissue stiffness in murine wounds to refine a previously-proposed systems-mechanobiological finite-element model. Fibroblasts are considered as the main cell type involved in ECM remodeling and wound contraction. Tissue rebuilding is coordinated by the release and diffusion of a cytokine wave, e.g. TGF-ß, itself developed in response to an earlier inflammatory signal triggered by platelet aggregation. We calibrate a model of the evolving wound biomechanics through a custom-developed hierarchical Bayesian inverse analysis procedure. Further calibration is based on published biochemical and morphological murine wound healing data over a 21-day healing period. The calibrated model recapitulates the temporal evolution of: inflammatory signal, fibroblast infiltration, collagen buildup, and wound contraction. Moreover, it enables in silico hypothesis testing, which we explore by: (i) quantifying the alteration of wound contraction profiles corresponding to the measured variability in local wound stiffness; (ii) proposing alternative constitutive links connecting the dynamics of the biochemical fields to the evolving mechanical properties; (iii) discussing the plausibility of a stretch- vs. stiffness-mediated mechanobiological coupling. Ultimately, our model challenges the current understanding of wound biomechanics and mechanobiology, beside offering a versatile tool to explore and eventually control scar fibrosis after injury.

Geometry of adipocyte packing in subcutaneous tissue contributes to nonlinear tissue properties captured through a Gaussian process surrogate model.

Subcutaneous tissue mechanical response is governed by the geometry and mechanical properties at the microscale and drives physiological and clinical processes such as drug delivery. Even though adipocyte packing is known to change with age, disease, and from one individual to another, the link between the geometry of the packing and the overall mechanical response of adipose tissue remains poorly understood. Here we create 1200 periodic representative volume elements (RVEs) that sample the possible space of Laguerre packings describing adipose tissue. RVE mechanics are modeled under tri-axial loading. Equilibrium configuration of RVEs is solved by minimizing an energetic potential that includes volume change contributions from adipocyte expansion, and area change contributions from collagen foam stretching. The resulting mechanical response across all RVE samples is interpolated with the aid of a Gaussian process (GP), revealing how the microscale geometry dictates the overall RVE mechanics. For example, increase in adipocyte size and increase in sphericity lead to adipose tissue softening. We showcase the use of the homogenized model in finite element simulations of drug injection by implementing a Blatz-Ko model, informed by the GP, as a custom material in the popular open-source package FEBio. These simulations show how microscale geometry can lead to vastly different injection dynamics even if the constituent parameters are held constant, highlighting the importance of characterizing individual's adipose tissue structure in the development of personalized therapies.

Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations.

We develop a fully data-driven model of anisotropic finite viscoelasticity using neural ordinary differential equations as building blocks. We replace the Helmholtz free energy function and the dissipation potential with data-driven functions that a priori satisfy physics-based constraints such as objectivity and the second law of thermodynamics. Our approach enables modeling viscoelastic behavior of materials under arbitrary loads in three-dimensions even with large deformations and large deviations from the thermodynamic equilibrium. The data-driven nature of the governing potentials endows the model with much needed flexibility in modeling the viscoelastic behavior of a wide class of materials. We train the model using stress-strain data from biological and synthetic materials including humain brain tissue, blood clots, natural rubber and human myocardium and show that the data-driven method outperforms traditional, closed-form models of viscoelasticity.

Multiscale mechanobiology: Coupling models of adhesion kinetics and nonlinear tissue mechanics.

The mechanical behavior of tissues at the macroscale is tightly coupled to cellular activity at the microscale. Dermal wound healing is a prominent example of a complex system in which multiscale mechanics regulate restoration of tissue form and function. In cutaneous wound healing, a fibrin matrix is populated by fibroblasts migrating in from a surrounding tissue made mostly out of collagen. Fibroblasts both respond to mechanical cues, such as fiber alignment and stiffness, as well as exert active stresses needed for wound closure. Here, we develop a multiscale model with a two-way coupling between a microscale cell adhesion model and a macroscale tissue mechanics model. Starting from the well-known model of adhesion kinetics proposed by Bell, we extend the formulation to account for nonlinear mechanics of fibrin and collagen and show how this nonlinear response naturally captures stretch-driven mechanosensing. We then embed the new nonlinear adhesion model into a custom finite element implementation of tissue mechanical equilibrium. Strains and stresses at the tissue level are coupled with the solution of the microscale adhesion model at each integration point of the finite element mesh. In addition, solution of the adhesion model is coupled with the active contractile stress of the cell population. The multiscale model successfully captures the mechanical response of biopolymer fibers and gels, contractile stresses generated by fibroblasts, and stress-strain contours observed during wound healing. We anticipate that this framework will not only increase our understanding of how mechanical cues guide cellular behavior in cutaneous wound healing, but will also be helpful in the study of mechanobiology, growth, and remodeling in other tissues.

Bayesian Inference With Gaussian Process Surrogates to Characterize Anisotropic Mechanical Properties of Skin From Suction Tests.

One of the intrinsic features of skin and other biological tissues is the high variation in the mechanical properties across individuals and different demographics. Mechanical characterization of skin is still a challenge because the need for subject-specific in vivo parameters prevents us from utilizing traditional methods, e.g., uniaxial tensile test. Suction devices have been suggested as the best candidate to acquire mechanical properties of skin noninvasively, but capturing anisotropic properties using a circular probe opening-which is the conventional suction device-is not possible. On the other hand, noncircular probe openings can drive different deformations with respect to fiber orientation and therefore could be used to characterize the anisotropic mechanics of skin noninvasively. We propose the use of elliptical probe openings and a methodology to solve the inverse problem of finding mechanical properties from suction measurements. The proposed probe is tested virtually by solving the forward problem of skin deformation by a finite element (FE) model. The forward problem is a function of the material parameters. In order to solve the inverse problem of determining skin properties from suction data, we use a Bayesian framework. The FE model is an expensive forward function, and is thus substituted with a Gaussian process metamodel to enable the Bayesian inference problem.

Multi-Fidelity Gaussian Process Surrogate Modeling of Pediatric Tissue Expansion.

Growth of skin in response to stretch is the basis for tissue expansion (TE), a procedure to gain new skin area for reconstruction of large defects. Unfortunately, complications and suboptimal outcomes persist because TE is planned and executed based on physician's experience and trial and error instead of predictive quantitative tools. Recently, we calibrated computational models of TE to a porcine animal model of tissue expansion, showing that skin growth is proportional to stretch with a characteristic time constant. Here, we use our calibrated model to predict skin growth in cases of pediatric reconstruction. Available from the clinical setting are the expander shapes and inflation protocols. We create low fidelity semi-analytical models and finite element models for each of the clinical cases. To account for uncertainty in the response expected from translating the models from the animal experiments to the pediatric population, we create multifidelity Gaussian process surrogates to propagate uncertainty in the mechanical properties and the biological response. Predictions with uncertainty for the clinical setting are essential to bridge our knowledge from the large animal experiments to guide and improve the treatment of pediatric patients. Future calibration of the model with patient-specific data-such as estimation of mechanical properties and area growth in the operating room-will change the standard for planning and execution of TE protocols.

High-Throughput Magnetic Actuation Platform for Evaluating the Effect of Mechanical Force on 3D Tumor Microenvironment.

Accurately replicating and analyzing cellular responses to mechanical cues is vital for exploring metastatic disease progression. However, many of the existing in vitro platforms for applying mechanical stimulation seed cells on synthetic substrates. To better recapitulate physiological conditions, a novel actuating platform is developed with the ability to apply tensile strain on cells at various amplitudes and frequencies in a high-throughput multi-well culture plate using a physiologically-relevant substrate. Suspending fibrillar fibronectin across the body of the magnetic actuator provides a matrix representative of early metastasis for 3D cell culture that is not reliant on a synthetic substrate. This platform enables the culturing and analysis of various cell types in an environment that mimics the dynamic stretching of lung tissue during normal respiration. Metabolic activity, YAP activation, and morphology of breast cancer cells are analyzed within one week of cyclic stretching or static culture. Further, matrix degradation is significantly reduced in breast cancer cell lines with metastatic potential after actuation. These new findings demonstrate a clear suppressive cellular response due to cyclic stretching that has implications for a mechanical role in the dormancy and reactivation of disseminated breast cancer cells to macrometastases.

The Geometry of Incompatibility in Growing Soft Tissues: Theory and Numerical Characterization.

Tissues in vivo are not stress-free. As we grow, our tissues adapt to different physiological and disease conditions through growth and remodeling. This adaptation occurs at the microscopic scale, where cells control the microstructure of their immediate extracellular environment to achieve homeostasis. The local and heterogeneous nature of this process is the source of residual stresses. At the macroscopic scale, growth and remodeling can be accurately captured with the finite volume growth framework within continuum mechanics, which is akin to plasticity. The multiplicative split of the deformation gradient into growth and elastic contributions brings about the notion of incompatibility as a plausible description for the origin of residual stress. Here we define the geometric features that characterize incompatibility in biological materials. We introduce the geometric incompatibility tensor for different growth types, showing that the constraints associated with growth lead to specific patterns of the incompatibility metrics. To numerically investigate the distribution of incompatibility measures, we implement the analysis within a finite element framework. Simple, illustrative examples are shown first to explain the main concepts. Then, numerical characterization of incompatibility and residual stress is performed on three biomedical applications: brain atrophy, skin expansion, and cortical folding. Our analysis provides new insights into the role of growth in the development of tissue defects and residual stresses. Thus, we anticipate that our work will further motivate additional research to characterize residual stresses in living tissue and their role in development, disease, and clinical intervention.

Personalized Computational Models of Tissue-Rearrangement in the Scalp Predict the Mechanical Stress Signature of Rotation Flaps.

OBJECTIVE: To elucidate the mechanics of scalp rotation flaps through 3D imaging and computational modeling. Excessive tension near a wound or sutured region can delay wound healing or trigger complications. Measuring tension in the operating room is challenging, instead, noninvasive methods to improve surgical planning are needed. DESIGN: Multi-view stereo allows creation of 3D patient-specific geometries based on a set of photographs. The patient-specific 3D geometry is imported into a finite element (FE) platform to perform a virtual procedure. The simulation is compared with the clinical outcome. Additional simulations quantify the effect of individual flap parameters on the resulting tension distribution. PARTICIPANTS: Rotation flaps for reconstruction of scalp defects following melanoma resection in 2 cases are presented. Rotation flaps were designed without preoperative FE preparation. MAIN OUTCOME MEASURE: Tension distribution over the operated region. RESULTS: The tension from FE shows peaks at the base and distal ends of the scalp rotation flap. The predicted geometry from the simulation aligns with postoperative photographs. Simulations exploring the flap design parameters show variation in the tension. Lower tensions were achieved when rotation was oriented with respect to skin tension lines (horizontal tissue fibers) and smaller rotation angles. CONCLUSIONS: Tension distribution following rotation of scalp flaps can be predicted through personalized FE simulations. Flaps can be designed to reduce tension using FE, which may greatly improve the reliability of scalp reconstruction in craniofacial surgery, critical in complex cases when scalp reconstruction is essential for coverage of hardware, implants, and/or bone graft.

Propagation of uncertainty in the mechanical and biological response of growing tissues using multi-fidelity Gaussian process regression.

A key feature of living tissues is their capacity to remodel and grow in response to environmental cues. Within continuum mechanics, this process can be captured with the multiplicative split of the deformation gradient into growth and elastic contributions. The mechanical and biological response during tissue adaptation is characterized by inherent variability. Accounting for this uncertainty is critical to better understand tissue mechanobiology, and, moreover, it is of practical importance if we aim to develop predictive models for clinical use. However, the current gold standard in computational models of growth and remodeling remains the use of deterministic finite element (FE) simulations. Here we focus on tissue expansion, a popular technique in which skin is stretched by a balloon-like device inducing its growth. We construct FE models of tissue expansion with various levels of detail, and show that a sufficiently broad set of FE simulations from these models can be used to train an accurate and efficient multi-fidelity Gaussian process (GP) surrogate. The approach is not limited to simulation data, rather, it can fuse different kinds of data, including from experiments. The main appeal of the framework relies on the common experience that highly detailed models (or experiments) are more accurate but also more costly, while simpler models (or experiments) can be easily evaluated but are bound to have some error. In these situations, doing uncertainty analysis tasks with the high fidelity models alone is not feasible and, conversely, relying solely on low fidelity approximations is also undesirable. We show that a multi-fidelity GP outperforms the high fidelity GP and low fidelity GP when tested against the most detailed FE model. In turn, having trained the multi-fidelity GP model, we showcase the propagation of uncertainty from the mechanical and biological response parameters to the spatio-temporal growth outcomes. We expect that the methods and applications in this paper will enable future research in parameter calibration under uncertainty and uncertainty propagation in real clinical scenarios involving tissue growth and remodeling.

Isogeometric Kirchhoff-Love shell formulations for biological membranes.

Computational modeling of thin biological membranes can aid the design of better medical devices. Remarkable biological membranes include skin, alveoli, blood vessels, and heart valves. Isogeometric analysis is ideally suited for biological membranes since it inherently satisfies the C1-requirement for Kirchhoff-Love kinematics. Yet, current isogeometric shell formulations are mainly focused on linear isotropic materials, while biological tissues are characterized by a nonlinear anisotropic stress-strain response. Here we present a thin shell formulation for thin biological membranes. We derive the equilibrium equations using curvilinear convective coordinates on NURBS tensor product surface patches. We linearize the weak form of the generic linear momentum balance without a particular choice of a constitutive law. We then incorporate the constitutive equations that have been designed specifically for collagenous tissues. We explore three common anisotropic material models: Mooney-Rivlin, May Newmann-Yin, and Gasser-Ogden-Holzapfel. Our work will allow scientists in biomechanics and mechanobiology to adopt the constitutive equations that have been developed for solid three-dimensional soft tissues within the framework of isogeometric thin shell analysis.

Computational modeling of skin: Using stress profiles as predictor for tissue necrosis in reconstructive surgery.

Local skin flaps have revolutionized reconstructive surgery. Mechanical loading is critical for flap survival: Excessive tissue tension reduces blood supply and induces tissue necrosis. However, skin flaps have never been analyzed mechanically. Here we explore the stress profiles of two common flap designs, direct advancement flaps and double back-cut flaps. Our simulations predict a direct correlation between regions of maximum stress and tissue necrosis. This suggests that elevated stress could serve as predictor for flap failure. Our model is a promising step towards computer-guided reconstructive surgery with the goal to minimize stress, accelerate healing, minimize scarring, and optimize tissue use.

Benchmarking physics-informed frameworks for data-driven hyperelasticity.

Data-driven methods have changed the way we understand and model materials. However, while providing unmatched flexibility, these methods have limitations such as reduced capacity to extrapolate, overfitting, and violation of physics constraints. Recently, frameworks that automatically satisfy these requirements have been proposed. Here we review, extend, and compare three promising data-driven methods: Constitutive Artificial Neural Networks (CANN), Input Convex Neural Networks (ICNN), and Neural Ordinary Differential Equations (NODE). Our formulation expands the strain energy potentials in terms of sums of convex non-decreasing functions of invariants and linear combinations of these. The expansion of the energy is shared across all three methods and guarantees the automatic satisfaction of objectivity, material symmetries, and polyconvexity, essential within the context of hyperelasticity. To benchmark the methods, we train them against rubber and skin stress-strain data. All three approaches capture the data almost perfectly, without overfitting, and have some capacity to extrapolate. This is in contrast to unconstrained neural networks which fail to make physically meaningful predictions outside the training range. Interestingly, the methods find different energy functions even though the prediction on the stress data is nearly identical. The most notable differences are observed in the second derivatives, which could impact performance of numerical solvers. On the rich data used in these benchmarks, the models show the anticipated trade-off between number of parameters and accuracy. Overall, CANN, ICNN and NODE retain the flexibility and accuracy of other data-driven methods without compromising on the physics. These methods are ideal options to model arbitrary hyperelastic material behavior.

A machine learning approach to predict in vivo skin growth.

Since their invention, tissue expanders, which are designed to trigger additional skin growth, have revolutionised many reconstructive surgeries. Currently, however, the sole quantitative method to assess skin growth requires skin excision. Thus, in the context of patient outcomes, a machine learning method which uses non-invasive measurements to predict in vivo skin growth and other skin properties, holds significant value. In this study, the finite element method was used to simulate a typical skin expansion protocol and to perform various simulated wave propagation experiments during the first few days of expansion on 1,000 individual virtual subjects. An artificial neural network trained on this dataset was shown to be capable of predicting the future skin growth at 7 days (avg. R2 = 0.9353) as well as the subject-specific shear modulus (R2 = 0.9801), growth rate (R2 = 0.8649), and natural pre-stretch (R2 = 0.9783) with a very high degree of accuracy. The method presented here has implications for the real-time prediction of patient-specific skin expansion outcomes and could facilitate the development of patient-specific protocols.

Optimizing autoinjector devices using physics-based simulations and Gaussian processes.

Autoinjectors are becoming a primary drug delivery option to the subcutaneous space. These devices need to work robustly and autonomously to maximize drug bio-availability. However, current designs ignore the coupling between autoinjector dynamics and tissue biomechanics. Here we present a Bayesian framework for optimization of autoinjector devices that can account for the coupled autoinjector-tissue biomechanics and uncertainty in tissue mechanical behavior. The framework relies on replacing the high fidelity model of tissue insertion with a Gaussian process (GP). The GP model is accurate yet computationally affordable, enabling a thorough sensitivity analysis that identified tissue properties, which are not part of the autoinjector design space, as important variables for the injection process. Higher fracture toughness decreases the crack depth, while tissue shear modulus has the opposite effect. The sensitivity analysis also shows that drug viscosity and spring force, which are part of the design space, affect the location and timing of drug delivery. Low viscosity could lead to premature delivery, but can be prevented with smaller spring forces, while higher viscosity could prevent premature delivery while demanding larger spring forces and increasing the time of injection. Increasing the spring force guarantees penetration to the desired depth, but it can result in undesirably high accelerations. The Bayesian optimization framework tackles the challenge of designing devices with performance metrics coupled to uncertain tissue properties. This work is important for the design of other medical devices for which optimization in the presence of material behavior uncertainty is needed.

Mechanical damage in porcine dermis: Micro-mechanical model and experimental characterization.

Skin is subjected to extreme mechanical loading during needle insertion and drug delivery to the subcutaneous space. There is a rich literature on the characterization of porcine skin biomechanics as the preeminent animal model for human skin, but the emphasis has been on the elastic response and specific anatomical locations such as the dorsal and the ventral regions. During drug delivery, however, energy dissipation in the form of damage, softening, and fracture, is expected. Similarly, reports on experimental characterization are complemented by modeling efforts, but with similar gaps in microstructure-driven modeling of dissipative mechanisms. Here we contribute to the bridging of these gaps by testing porcine skin from belly and breast regions, in two different orientation with respect to anatomical axes, and to progressively higher stretches in order to show damage accumulation and stiffness degradation. We complement the mechanical test with imaging of the collagen structure and a micro-mechanics modeling framework. We found that skin from the belly is stiffer with respect to the breast region when comparing the calf stiffness of the J-shaped stress-stretch response observed in most collagenous tissues. No significant direction dependent properties were found in either anatomical location. Both locations showed energy dissipation due to damage, evident though a softening of the stress-stretch response. The microstructure model was able to capture the elastic and damage progression with a small set of parameters, some of which were determined directly from imaging. We anticipate that data and model fits can help in predictive simulations for device design in situations where skin is subject to supra-physiological deformation such as in subcutaneous drug delivery.

Damage and Fracture Mechanics of Porcine Subcutaneous Tissue Under Tensile Loading.

Subcutaneous injection, which is a preferred delivery method for many drugs, causes deformation, damage, and fracture of the subcutaneous tissue. Yet, experimental data and constitutive modeling of these dissipation mechanisms in subcutaneous tissue remain limited. Here we show that subcutaneous tissue from the belly and breast anatomical regions in the swine show nonlinear stress-strain response with the characteristic J-shaped behavior of collagenous tissue. Additionally, subcutaneous tissue experiences damage, defined as a decrease in the strain energy capacity, as a function of the previously experienced maximum deformation. The elastic and damage response of the tissue are accurately described by a microstructure-driven constitutive model that relies on the convolution of a neo-Hookean material of individual fibers with a fiber orientation distribution and a fiber recruitment distribution. The model fit revealed that subcutaneous tissue can be treated as initially isotropic, and that changes in the fiber recruitment distribution with loading are enough to explain the dissipation of energy due to damage. When tested until failure, subcutaneous tissue that has undergone damage fails at the same peak stress as virgin samples, but at a much larger stretch, overall increasing the tissue toughness. Together with a finite element implementation, these data and constitutive model may enable improved drug delivery strategies and other applications for which subcutaneous tissue biomechanics are relevant.

Computational mechanobiology model evaluating healing of postoperative cavities following breast-conserving surgery.

Breast cancer is the most commonly diagnosed cancer type worldwide. Given high survivorship, increased focus has been placed on long-term treatment outcomes and patient quality of life. While breast-conserving surgery (BCS) is the preferred treatment strategy for early-stage breast cancer, anticipated healing and breast deformation (cosmetic) outcomes weigh heavily on surgeon and patient selection between BCS and more aggressive mastectomy procedures. Unfortunately, surgical outcomes following BCS are difficult to predict, owing to the complexity of the tissue repair process and significant patient-to-patient variability. To overcome this challenge, we developed a predictive computational mechanobiological model that simulates breast healing and deformation following BCS. The coupled biochemical-biomechanical model incorporates multi-scale cell and tissue mechanics, including collagen deposition and remodeling, collagen-dependent cell migration and contractility, and tissue plastic deformation. Available human clinical data evaluating cavity contraction and histopathological data from an experimental porcine lumpectomy study were used for model calibration. The computational model was successfully fit to data by optimizing biochemical and mechanobiological parameters through Gaussian process surrogates. The calibrated model was then applied to define key mechanobiological parameters and relationships influencing healing and breast deformation outcomes. Variability in patient characteristics including cavity-to-breast volume percentage and breast composition were further evaluated to determine effects on cavity contraction and breast cosmetic outcomes, with simulation outcomes aligning well with previously reported human studies. The proposed model has the potential to assist surgeons and their patients in developing and discussing individualized treatment plans that lead to more satisfying post-surgical outcomes and improved quality of life.

Stretching skin: The physiological limit and beyond.

The goal of this manuscript is to establish a novel computational model for skin to characterize its constitutive behavior when stretched within and beyond its physiological limits. Within the physiological regime, skin displays a reversible, highly nonlinear, stretch locking, and anisotropic behavior. We model these characteristics using a transversely isotropic chain network model composed of eight wormlike chains. Beyond the physiological limit, skin undergoes an irreversible area growth triggered through mechanical stretch. We model skin growth as a transversely isotropic process characterized through a single internal variable, the scalar-valued growth multiplier. To discretize the evolution of growth in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum algorithmic efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To illustrate the characteristic features of skin growth, we first compare the two simple model problems of displacement- and force-driven growth. Then, we model the process of stretch-induced skin growth during tissue expansion. In particular, we compare the spatio-temporal evolution of stress, strain, and area gain for four commonly available tissue expander geometries. We believe that the proposed model has the potential to open new avenues in reconstructive surgery and rationalize critical process parameters in tissue expansion, such as expander geometry, expander size, expander placement, and inflation timing.