Finite Element Analysis and Biological Growth Realization using Robot Swarms

Our understanding of growth and remodeling of biological systems has increased in the past two decades; however, this knowledge has not yet been used in human-designed systems or engineering applications. This project studies designing and building a network of robots that mimics the biological behavior of growth driven by cell-cell communication and control networks. The objective of this research is to harness the principles that govern tissue adaptation and morphogenesis, where peer-to-peer local communication determines global properties, to create human-made engineering systems with life-like capabilities. We used Arduino microcontrollers to control an individual robot in an expandable 3d-printed cuboid shell. Each individual cuboid robot will be able to communicate with up to 6 robots, one connected to each of its faces. Through local data communication, and enlarging and shrinking of individual robots, one would be able to model growth and other biological systems using a large assembly of these identical robots. Additionally, we expect (through additional research) to be able to physically demonstrate biological simulations of processes such as growth or morphogenesis to other researchers/laypersons, allowing quicker and deeper understanding of these complex processes to a large audience

A Parametric Study of the Mechanics of Different Skin Flap Techniques

In modern day plastic and reconstructive surgeries numerous skin flap designs have been developed and are used to close open wounds. Skin flaps are developed with the intention of imposing minimal tension in skin closure. Excessive tension can lead to poor blood flow that result in post-surgery complications such as necrosis. Currently there is no standard in choosing a skin flap design and a surgeon\u27s choice is based personal experience. A comparison of the mechanical loading in these various designs has not yet been done. We have developed a parametric study, using finite element analysis, of two advancement skin flaps designs. The study focuses on the stress in the design as the defect size is increased. The defect size is increased by scaled by scaling the overall boundary condition to size. From this study, we have found that the stresses of a skin flap on a planar surface are dependent on the defect size. In addition, the choice of skin flap can significantly impact the stresses

Characterization and Quantification of Fibrin Gel Mechanics with Fibroblast Invasion

Cutaneous wounds undergo an intricate healing process stimulated by a variety of local mechanical and biological stimuli that lead to patterns of growth and remodeling. Despite significant research in dermal wound healing, pathological scarring is still common particularly in wounds closed under mechanical stress, or large wounds left to heal by secondary intention. The purpose of this study is to utilize previously established wound healing models using fibrin gels and fibroblasts to better understand the functional relationships of the biological processes of normal compared to abnormal wound healing. Increases in uni-axial strain and transforming growth factor beta-1 concentration have been shown to have an increased effect on fibroblast action, leading to increased collagen deposition and overall gel stiffness. This in vitro model will help in the construction of a computational model to be used in future research

Generative Hyperelasticity with Physics-Informed Probabilistic Diffusion Fields

Many natural materials exhibit highly complex, nonlinear, anisotropic, and heterogeneous mechanical properties. Recently, it has been demonstrated that data-driven strain energy functions possess the flexibility to capture the behavior of these complex materials with high accuracy while satisfying physics-based constraints. However, most of these approaches disregard the uncertainty in the estimates and the spatial heterogeneity of these materials. In this work, we leverage recent advances in generative models to address these issues. We use as building block neural ordinary equations (NODE) that -- by construction -- create polyconvex strain energy functions, a key property of realistic hyperelastic material models. We combine this approach with probabilistic diffusion models to generate new samples of strain energy functions. This technique allows us to sample a vector of Gaussian white noise and translate it to NODE parameters thereby representing plausible strain energy functions. We extend our approach to spatially correlated diffusion resulting in heterogeneous material properties for arbitrary geometries. We extensively test our method with synthetic and experimental data on biological tissues and run finite element simulations with various degrees of spatial heterogeneity. We believe this approach is a major step forward including uncertainty in predictive, data-driven models of hyperelasticityComment: 22 pages, 11 figure

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, concentrationdriven, 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

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, classical machine learning techniques often ignore the fundamental laws of physics and 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 data sets from different sources and different levels of resolution. We show how machine learning and multiscale modeling can complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces. We critically 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

In vivo measurement of skin surface strain and sub-surface layer deformation induced by natural tissue stretching.

Stratum corneum and epidermal layers change in terms of thickness and roughness with gender, age and anatomical site. Knowledge of the mechanical and tribological properties of skin associated with these structural changes are needed to aid in the design of exoskeletons, prostheses, orthotics, body mounted sensors used for kinematics measurements and in optimum use of wearable on-body devices. In this case study, optical coherence tomography (OCT) and digital image correlation (DIC) were combined to determine skin surface strain and sub-surface deformation behaviour of the volar forearm due to natural tissue stretching. The thickness of the epidermis together with geometry changes of the dermal-epidermal junction boundary were calculated during change in the arm angle, from flexion (90°) to full extension (180°). This posture change caused an increase in skin surface Lagrange strain, typically by 25% which induced considerable morphological changes in the upper skin layers evidenced by reduction of epidermal layer thickness (20%), flattening of the dermal-epidermal junction undulation (45-50% reduction of flatness being expressed as Ra and Rz roughness profile height change) and reduction of skin surface roughness Ra and Rz (40-50%). The newly developed method, DIC combined with OCT imaging, is a powerful, fast and non-invasive methodology to study structural skin changes in real time and the tissue response provoked by mechanical loading or stretching

Virtual testing of advanced composites, cellular materials and biomaterials: A review

This paper documents the emergence of virtual testing frameworks for prediction of the constitutive responses of engineering materials. A detailed study is presented, of the philosophy underpinning virtual testing schemes: highlighting the structure, challenges and opportunities posed by a virtual testing strategy compared with traditional laboratory experiments. The virtual testing process has been discussed from atomistic to macrostructural length scales of analyses. Several implementations of virtual testing frameworks for diverse categories of materials are also presented, with particular emphasis on composites, cellular materials and biomaterials (collectively described as heterogeneous systems, in this context). The robustness of virtual frameworks for prediction of the constitutive behaviour of these materials is discussed. The paper also considers the current thinking on developing virtual laboratories in relation to availability of computational resources as well as the development of multi-scale material model algorithms. In conclusion, the paper highlights the challenges facing developments of future virtual testing frameworks. This review represents a comprehensive documentation of the state of knowledge on virtual testing from microscale to macroscale length scales for heterogeneous materials across constitutive responses from elastic to damage regimes