Exploring uncertainty in hyper-viscoelastic properties of scalp skin through patient-specific finite element models for reconstructive surgery.

Understanding skin responses to external forces is crucial for post-cutaneous flap wound healing. However, the in vivo viscoelastic behavior of scalp skin remains poorly understood. Personalized virtual surgery simulations offer a way to study tissue responses in relevant 3D geometries. Yet, anticipating wound risk remains challenging due to limited data on skin viscoelasticity, which hinders our ability to determine the interplay between wound size and stress levels. To bridge this gap, we reexamine three clinical cases involving scalp reconstruction using patient-specific geometric models and employ uncertainty quantification through a Monte Carlo simulation approach to study the effect of skin viscoelasticity on the final stress levels from reconstructive surgery. Utilizing the generalized Maxwell model via the Prony series, we can parameterize and efficiently sample a realistic range of viscoelastic response and thus shed light on the influence of viscoelastic material uncertainty in surgical scenarios. Our analysis identifies regions at risk of wound complications based on reported threshold stress values from the literature and highlights the significance of focusing on long-term responses rather than short-term ones.

Islet-on-chip: promotion of islet health and function via encapsulation within a polymerizable fibrillar collagen scaffold.

The protection and interrogation of pancreatic ß-cell health and function ex vivo is a fundamental aspect of diabetes research, including mechanistic studies, evaluation of ß-cell health modulators, and development and quality control of replacement ß-cell populations. However, present-day islet culture formats, including traditional suspension culture as well as many recently developed microfluidic devices, suspend islets in a liquid microenvironment, disrupting mechanochemical signaling normally found in vivo and limiting ß-cell viability and function in vitro. Herein, we present a novel three-dimensional (3D) microphysiological system (MPS) to extend islet health and function ex vivo by incorporating a polymerizable collagen scaffold to restore biophysical support and islet-collagen mechanobiological cues. Informed by computational models of gas and molecular transport relevant to ß-cell physiology, a MPS configuration was down-selected based on simulated oxygen and nutrient delivery to collagen-encapsulated islets, and 3D-printing was applied as a readily accessible, low-cost rapid prototyping method. Recreating critical aspects of the in vivo microenvironment within the MPS via perfusion and islet-collagen interactions mitigated post-isolation ischemia and apoptosis in mouse islets over a 5-day period. In contrast, islets maintained in traditional suspension formats exhibited progressive hypoxic and apoptotic cores. Finally, dynamic glucose-stimulated insulin secretion measurements were performed on collagen-encapsulated mouse islets in the absence and presence of well-known chemical stressor thapsigargin using the MPS platform and compared to conventional protocols involving commercial perifusion machines. Overall, the MPS described here provides a user-friendly islet culture platform that not only supports long-term ß-cell health and function but also enables multiparametric evaluations.

Impact of Indenter Size and Microrelief Anisotropy on the Tribological Behavior of Human Skin.

Everyday, we interact with screens, sensors, and many other devices through contact with the skin. Experimental efforts have increased our knowledge of skin tribology but are challenged by the fact that skin has a complex structure, undergoes finite deformations, has nonlinear material response, and has properties that vary with anatomical location, age, sex, and environmental conditions. Computational models are powerful tools to dissect the individual contribution of these variables to the overall frictional response. Here, we present a three-dimensional high-fidelity multilayer skin computational model including a detailed surface topography or skin microrelief. Four variables are explored: local coefficient of friction (COF), indenter size, mechanical properties of the stratum corneum, and displacement direction. The results indicate that the global COF depends nonlinearly on the local COF, implying a role for skin deformation on the friction response. The global COF is also influenced by the ratio of the indenter size to the microrelief features, with larger indenters smoothing out the role of skin topography. Changes in stiffness of the uppermost layer of skin associated with humidity have a substantial effect on both the contact area and the reaction forces, but the overall changes in the COF are small. Finally, for the microrelief tested, the response can be considered isotropic. We anticipate that this model and results will enable the design of materials and devices for a desired interaction against skin.

Multiscale mechanical characterization and computational modeling of fibrin gels.

Fibrin is a naturally occurring protein network that forms a temporary structure to enable remodeling during wound healing. It is also a common tissue engineering scaffold because the structural properties can be controlled. However, to fully characterize the wound healing process and improve the design of regenerative scaffolds, understanding fibrin mechanics at multiple scales is necessary. Here, we present a strategy to quantify both the macroscale (1-10 mm) stress-strain response and the deformation of the mesoscale (10-1000 µm) network structure during unidirectional tensile tests. The experimental data were then used to inform a computational model to accurately capture the mechanical response of fibrin gels. Simultaneous mechanical testing and confocal microscopy imaging of fluorophore-conjugated fibrin gels revealed up to an 88% decrease in volume coupled with increase in volume fraction in deformed gels, and non-affine fiber alignment in the direction of deformation. Combination of the computational model with finite element analysis enabled us to predict the strain fields that were observed experimentally within heterogenous fibrin gels with spatial variations in material properties. These strategies can be expanded to characterize and predict the macroscale mechanics and mesoscale network organization of other heterogeneous biological tissues and matrices. STATEMENT OF SIGNIFICANCE: Fibrin is a naturally-occurring scaffold that supports cellular growth and assembly of de novo tissue and has tunable material properties. Characterization of meso- and macro-scale mechanics of fibrin gel networks can advance understanding of the wound healing process and impact future tissue engineering approaches. Using structural and mechanical characteristics of fibrin gels, a theoretical and computational model that can predict multiscale fibrin network mechanics was developed. These data and model can be used to design gels with tunable properties.

Lymphatic uptake of biotherapeutics through a 3D hybrid discrete-continuum vessel network in the skin tissue.

Subcutaneous administration is a common approach for the delivery of biotherapeutics, which is achieved mainly through the absorption across lymphatic vessels. In this paper, the drug transport and lymphatic uptake through a three-dimensional hybrid discrete-continuum vessel network in the skin tissue are investigated through high-fidelity numerical simulations. We find that the local lymphatic uptake through the explicit vessels significantly affects macroscopic drug absorption. The diffusion of drug solute through the explicit vessel network affects the lymphatic uptake after the injection. This effect, however, cannot be captured using previously developed continuum models. The lymphatic uptake is dominated by the convection due to lymphatic drainage driven by the pressure difference, which is rarely studied in experiments and simulations. Furthermore, the effects of injection volume and depth on the lymphatic uptake are investigated in a multi-layered domain. We find that the injection volume significantly affects the rate of lymphatic uptake through the heterogeneous vessel network, while the injection depth has little influence, which is consistent with the experimental results. At last, the binding and metabolism of drug molecules are studied to bridge the simulations to the drug clearance experients. We provide a new approach to study the diffusion and convection of drug molecules into the lymphatic system through the hybrid vessel network.

Mechanobiological wound model for improved design and evaluation of collagen dermal replacement scaffolds.

Skin wounds are among the most common and costly medical problems experienced. Despite the myriad of treatment options, such wounds continue to lead to displeasing cosmetic outcomes and also carry a high burden of loss-of-function, scarring, contraction, or nonhealing. As a result, the need exists for new therapeutic options that rapidly and reliably restore skin cosmesis and function. Here we present a new mechanobiological computational model to further the design and evaluation of next-generation regenerative dermal scaffolds fabricated from polymerizable collagen. A Bayesian framework, along with microstructure and mechanical property data from engineered dermal scaffolds and autograft skin, were used to calibrate constitutive models for collagen density, fiber alignment and dispersion, and stiffness. A chemo-bio-mechanical finite element model including collagen, cells, and representative cytokine signaling was adapted to simulate no-fill, dermal scaffold, and autograft skin outcomes observed in a preclinical animal model of full-thickness skin wounds, with a focus on permanent contraction, collagen realignment, and cellularization. Finite element model simulations demonstrated wound cellularization and contraction behavior that was similar to that observed experimentally. A sensitivity analysis suggested collagen fiber stiffness and density are important scaffold design features for predictably controlling wound contraction. Finally, prospective simulations indicated that scaffolds with increased fiber dispersion (isotropy) exhibited reduced and more uniform wound contraction while supporting cell infiltration. By capturing the link between multi-scale scaffold biomechanics and cell-scaffold mechanochemical interactions, simulated healing outcomes aligned well with preclinical animal model data. STATEMENT OF SIGNIFICANCE: Skin wounds continue to be a significant burden to patients, physicians, and the healthcare system. Advancing the mechanistic understanding of the wound healing process, including multi-scale mechanobiological interactions amongst cells, the collagen scaffolding, and signaling molecules, will aide in the design of new skin restoration therapies. This work represents the first step towards integrating mechanobiology-based computational tools with in vitro and in vivo preclinical testing data for improving the design and evaluation of custom-fabricated collagen scaffolds for dermal replacement. Such an approach has potential to expedite development of new and more effective skin restoration therapies as well as improve patient-centered wound treatment.

Acceleration of PDE-Based Biological Simulation Through the Development of Neural Network Metamodels.

PURPOSE OF REVIEW: Partial differential equation (PDE) mathematical models of biological systems and the simulation approaches used to solve them are widely used to test hypotheses and infer regulatory interactions based on optimization of the PDE model against the observed data. In this review, we discuss the ability of powerful machine learning methods to accelerate the parametric screening of biophysical informed- PDE systems. RECENT FINDINGS: A major shortcoming in more broad adaptation of PDE-based models is the high computational complexity required to solve and optimize the models and it requires many simulations to traverse the very high-dimensional parameter spaces during model calibration and inference tasks. For instance, when scaling up to tens of millions of simulations for optimization and sensitivity analysis of the PDE models, compute times quickly extend from months to years for sufficient coverage to solve the problems. For many systems, this brute-force approach is simply not feasible. Recently, neural network metamodels have been shown to be an efficient way to accelerate PDE model calibration and here we look at the benefits and limitations in extending the PDE acceleration methods to improve optimization and sensitivity analysis. SUMMARY: We use an example simulation to quantitatively and qualitatively show how neural network metamodels can be accurate and fast and demonstrate their potential for optimization of complex spatiotemporal problems in biology. We expect these approaches will be broadly applied to speed up scientific research and discovery in biology and other systems that can be described by complex PDE systems.

Integrating machine learning and multiscale modeling-perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences.

Fueled by breakthrough technology developments, the biological, biomedical, and behavioral sciences are now collecting more data than ever before. There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. However, machine learning alone ignores the fundamental laws of physics and can result in ill-posed problems or non-physical solutions. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. However, multiscale modeling alone often fails to efficiently combine large datasets from different sources and different levels of resolution. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces. We review the current literature, highlight applications and opportunities, address open questions, and discuss potential challenges and limitations in four overarching topical areas: ordinary differential equations, partial differential equations, data-driven approaches, and theory-driven approaches. Towards these goals, we leverage expertise in applied mathematics, computer science, computational biology, biophysics, biomechanics, engineering mechanics, experimentation, and medicine. Our multidisciplinary perspective suggests that integrating machine learning and multiscale modeling can provide new insights into disease mechanisms, help identify new targets and treatment strategies, and inform decision making for the benefit of human health.

Propagation of material behavior uncertainty in a nonlinear finite element model of reconstructive surgery.

Excessive mechanical stress following surgery can lead to delayed healing, hypertrophic scars, and even skin necrosis. Measuring stress directly in the operating room over large skin areas is not feasible, and nonlinear finite element simulations have become an appealing alternative to predict stress contours on arbitrary geometries. However, this approach has been limited to generic cases, when in reality each patient geometry and procedure are unique, and material properties change from one person to another. In this manuscript, we use multi-view stereo to capture the patient-specific geometry of a 7-year-old female undergoing cranioplasty and complex tissue rearrangement. The geometry is used to setup a nonlinear finite element simulation of the reconstructive procedure. A key contribution of this work is incorporation of material behavior uncertainty. The finite element simulation is computationally expensive, and it is not suitable for uncertainty propagation which would require many such simulations. Instead, we run only a few expensive simulations in order to build a surrogate model by Gaussian process regression of the principal components of the stress fields computed with these few samples. The inexpensive surrogate is then used to compute the statistics of the stress distribution in this patient-specific scenario.

Digital analysis yields more reliable and accurate measures of dermal and epidermal thickness in histologically processed specimens compared to traditional methods.

Changes in the thickness of the dermis and epidermis have been described in the scenario of tissue expansion as well as inflammatory skin processes (psoriasis, contact hypersensitivity and so on). These changes have previously been quantified using ocular micrometers to obtain and then average a limited number of spot measurements, leading to suboptimal accuracy. We describe a rapid method of using freely available ImageJ software to analyze digitized images of fixed skin specimens. By determining the cross-sectional area and surface length of a skin layer, a simple calculation produces more accurate and reproducible measurements of its thickness compared to historical methods, with excellent inter-rater reliability.

Determining the Differential Effects of Stretch and Growth in Tissue-Expanded Skin: Combining Isogeometric Analysis and Continuum Mechanics in a Porcine Model.

BACKGROUND: The relative effects of skin growth and stretch during tissue expansion have not been studied. The authors use novel analytic techniques that allow calculation of these factors at any point of a skin patch. OBJECTIVE: The authors sought to determine how stretch and growth change with different expansion rates and to correlate these values with histologic and cellular changes in skin. MATERIALS AND METHODS: Two minipigs were implanted with a total of 5 tissue expanders under tattooed skin grids. One pig was expanded over 35 days and the second over 15 days. Isogeometric analysis allowed calculation of growth and stretch. Expanders with similar total deformation were compared between protocols. Regression analysis determined predictive effects of stretch and growth on histologic data from the second animal. RESULTS: Deformation was more attributable to stretch in rapid than in slow expansion (1.40 vs1.12, p < .001). Growth was higher in slow expansion than in rapid (1.52 vs 1.07, p < .001). Both growth and stretch predicted epidermal thickness, dermal thinning, and keratinocyte proliferation. Growth predicted vascularity. CONCLUSION: Isogeometric analysis allows determination of precise surface area changes for correlation to microscopic-level data. Using the model, the authors identified that skin deformation in rapid expansion is more attributable to stretch.

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics.

Tissue expansion is a popular technique in plastic and reconstructive surgery that grows skin in vivo for correction of large defects such as burns and giant congenital nevi. Despite its widespread use, planning and executing an expansion protocol is challenging due to the difficulty in measuring the deformation imposed at each inflation step and over the length of the procedure. Quantifying the deformation fields is crucial, as the distribution of stretch over time determines the rate and amount of skin grown at the end of the treatment. In this manuscript, we present a method to study tissue expansion in order to gain quantitative knowledge of the deformations induced during an expansion process. This experimental protocol incorporates multi-view stereo and isogeometric kinematic analysis in a porcine model of tissue expansion. Multi-view stereo allows three-dimensional geometric reconstruction from uncalibrated sequences of images. The isogeometric kinematic analysis uses splines to describe the regional deformations between smooth surfaces with few mesh points. Our protocol has the potential to bridge the gap between basic scientific inquiry regarding the mechanics of skin expansion and the clinical setting. Eventually, we expect that the knowledge gained with our methodology will enable treatment planning using computational simulations of skin deformation in a personalized manner.

A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth.

The purpose of this manuscript is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. We combine the theories of volumetric growth and mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid/fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To illustrate the capabilities of this model, several example finite element test problems are considered using model geometry and material parameters based on experimental data from a porcine coronary artery. Multiple growth laws are considered, including time-driven, concentration-driven, and stress-driven growth. Time-driven growth is compared against an exact analytical solution to validate the model. For concentration-dependent growth, changing the diffusivity (representing a change in drug) fundamentally changes growth behavior. We further demonstrate that for stress-dependent, solid-only growth of an artery, growth of an MPHETS model results in a more uniform hoop stress than growth in a hyperelastic model for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To our knowledge, this manuscript provides the first full description of an MPHETS model with growth. The developed computational framework can be used in concert with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues.

Multi-view stereo analysis reveals anisotropy of prestrain, deformation, and growth in living skin.

Skin expansion delivers newly grown skin that maintains histological and mechanical features of the original tissue. Although it is the gold standard for cutaneous defect correction today, the underlying mechanisms remain poorly understood. Here we present a novel technique to quantify anisotropic prestrain, deformation, and growth in a porcine skin expansion model. Building on our recently proposed method, we combine two novel technologies, multi-view stereo and isogeometric analysis, to characterize skin kinematics: Upon explantation, a unit square retracts ex vivo to a square of average dimensions of [Formula: see text]. Upon expansion, the unit square deforms in vivo into a rectangle of average dimensions of [Formula: see text]. Deformations are larger parallel than perpendicular to the dorsal midline suggesting that skin responds anisotropically with smaller deformations along the skin tension lines. Upon expansion, the patch grows in vivo by [Formula: see text] with respect to the explanted, unexpanded state. Growth is larger parallel than perpendicular to the midline, suggesting that elevated stretch activates mechanotransduction pathways to stimulate tissue growth. The proposed method provides a powerful tool to characterize the kinematics of living skin. Our results shed light on the mechanobiology of skin and help us to better understand and optimize clinically relevant procedures in plastic and reconstructive surgery.

Application of finite element modeling to optimize flap design with tissue expansion.

BACKGROUND: Tissue expansion is a widely used technique to create skin flaps for the correction of sizable defects in reconstructive plastic surgery. Major complications following the inset of expanded flaps include breakdown and uncontrolled scarring secondary to excessive tissue tension. Although it is recognized that mechanical forces may significantly impact the success of defect repair with tissue expansion, a mechanical analysis of tissue stresses has not previously been attempted. Such analyses have the potential to optimize flap design preoperatively. METHODS: The authors establish computer-aided design as a tool with which to explore stress profiles for two commonly used flap designs, the direct advancement flap and the double back-cut flap. The authors advanced both flaps parallel and perpendicular to the relaxed skin tension lines to quantify the impact of tissue anisotropy on stress distribution profiles. RESULTS: Stress profiles were highly sensitive to flap design and orientation of relaxed skin tension lines, with stress minimized when flaps were advanced perpendicular to relaxed skin tension lines. Maximum stresses in advancement flaps occurred at the distal end of the flap, followed by the base. The double back-cut design increased stress at the lateral edges of the flap. CONCLUSIONS: The authors conclude that finite element modeling may be used to effectively predict areas of increased flap tension. Performed preoperatively, such modeling can allow for the optimization of flap design and a potential reduction in complications such as flap dehiscence and hypertrophic scarring.

Systems-based approaches toward wound healing.

Wound healing in the pediatric patient is of utmost clinical and social importance because hypertrophic scarring can have aesthetic and psychological sequelae, from early childhood to late adolescence. Wound healing is a well-orchestrated reparative response affecting the damaged tissue at the cellular, tissue, organ, and system scales. Although tremendous progress has been made toward understanding wound healing at the individual temporal and spatial scales, its effects across the scales remain severely understudied and poorly understood. Here, we discuss the critical need for systems-based computational modeling of wound healing across the scales, from short-term to long-term and from small to large. We illustrate the state of the art in systems modeling by means of three key signaling mechanisms: oxygen tension-regulating angiogenesis and revascularization; transforming growth factor-ß (TGF-ß) kinetics controlling collagen deposition; and mechanical stretch stimulating cellular mitosis and extracellular matrix (ECM) remodeling. The complex network of biochemical and biomechanical signaling mechanisms and the multiscale character of the healing process make systems modeling an integral tool in exploring personalized strategies for wound repair. A better mechanistic understanding of wound healing in the pediatric patient could open new avenues in treating children with skin disorders such as birth defects, skin cancer, wounds, and burn injuries.

On the biomechanics and mechanobiology of growing skin.

Skin displays an impressive functional plasticity, which allows it to adapt gradually to environmental changes. Tissue expansion takes advantage of this adaptation, and induces a controlled in situ skin growth for defect correction in plastic and reconstructive surgery. Stretches beyond the skin's physiological limit invoke several mechanotransduction pathways, which increase mitotic activity and collagen synthesis, ultimately resulting in a net gain in skin surface area. However, the interplay between mechanics and biology during tissue expansion remains unquantified. Here, we present a continuum model for skin growth that summarizes the underlying mechanotransduction pathways collectively in a single phenomenological variable, the strain-driven area growth. We illustrate the governing equations for growing biological membranes, and demonstrate their computational solution within a nonlinear finite element setting. In displacement-controlled equi-biaxial extension tests, the model accurately predicts the experimentally observed histological, mechanical, and structural features of growing skin, both qualitatively and quantitatively. Acute and chronic elastic uniaxial stretches are 25% and 10%, compared to 36% and 10% reported in the literature. Acute and chronic thickness changes are -28% and -12%, compared to -22% and -7% reported in the literature. Chronic fractional weight gain is 3.3, compared to 2.7 for wet weight and 3.3 for dry weight reported in the literature. In two clinical cases of skin expansion in pediatric forehead reconstruction, the model captures the clinically observed mechanical and structural responses, both acutely and chronically. Our results demonstrate that the field theories of continuum mechanics can reliably predict the mechanical manipulation of thin biological membranes by controlling their mechanotransduction pathways through mechanical overstretch. We anticipate that the proposed skin growth model can be generalized to arbitrary biological membranes, and that it can serve as a valuable tool to virtually manipulate living tissues, simply by means of changes in the mechanical environment.

Growing skin: tissue expansion in pediatric forehead reconstruction.

Tissue expansion is a common surgical procedure to grow extra skin through controlled mechanical over-stretch. It creates skin that matches the color, texture, and thickness of the surrounding tissue, while minimizing scars and risk of rejection. Despite intense research in tissue expansion and skin growth, there is a clear knowledge gap between heuristic observation and mechanistic understanding of the key phenomena that drive the growth process. Here, we show that a continuum mechanics approach, embedded in a custom-designed finite element model, informed by medical imaging, provides valuable insight into the biomechanics of skin growth. In particular, we model skin growth using the concept of an incompatible growth configuration. We characterize its evolution in time using a second-order growth tensor parameterized in terms of a scalar-valued internal variable, the in-plane area growth. When stretched beyond the physiological level, new skin is created, and the in-plane area growth increases. For the first time, we simulate tissue expansion on a patient-specific geometric model, and predict stress, strain, and area gain at three expanded locations in a pediatric skull: in the scalp, in the forehead, and in the cheek. Our results may help the surgeon to prevent tissue over-stretch and make informed decisions about expander geometry, size, placement, and inflation. We anticipate our study to open new avenues in reconstructive surgery and enhance treatment for patients with birth defects, burn injuries, or breast tumor removal.