Model Of Biological Tissue Research Articles

Discovering 3D hidden elasticity in isotropic and transversely isotropic materials with physics-informed UNets

Three-dimensional variation in structural components or fiber alignments results in complex mechanical property distribution in tissues and biomaterials. In this paper, we use a physics-informed UNet-based neural network model (El-UNet) to discover the three-dimensional (3D) internal composition and space-dependent material properties of heterogeneous isotropic and transversely isotropic materials without a priori knowledge of the composition. We then show the capabilities of El-UNet by validating against data obtained from finite-element simulations of two soft tissues, namely, brain tissue and articular cartilage, under various loading conditions. We first simulated compressive loading of 3D brain tissue comprising of distinct white matter and gray matter mechanical properties undergoing small strains with isotropic linear elastic behavior, where El-UNet reached mean absolute relative errors under 1.5 % for elastic modulus and Poisson's ratio estimations across the 3D volume. We showed that the 3D solution achieved by El-UNet was superior to relative stiffness mapping by inverse of axial strain and two-dimensional plane stress/plane strain approximations. Additionally, we simulated a transversely isotropic articular cartilage with known fiber orientations undergoing compressive loading, and accurately estimated the spatial distribution of all five material parameters, with mean absolute relative errors under 5 %. Our work demonstrates the application of the computationally efficient physics-informed El-UNet in 3D elasticity imaging and provides methods for translation to experimental 3D characterization of soft tissues and other materials. The proposed El-UNet offers a powerful tool for both in vitro and ex vivo tissue analysis, with potential extensions to in vivo diagnostics. Statement of significanceElasticity imaging is a technique that reconstructs mechanical properties of tissue using deformation and force measurements. Given the complexity of this reconstruction, most existing methods have mostly focused on 2D problems. Our work is the first implementation of physics-informed UNets to reconstruct three-dimensional material parameter distributions for isotropic and transversely isotropic linear elastic materials by having deformation and force measurements. We comprehensively validate our model using synthetic data generated using finite element models of biological tissues with high bio-fidelity–the brain and articular cartilage. Our method can be implemented in elasticity imaging scenarios for in vitro and ex vivo mechanical characterization of biomaterials and biological tissues, with potential extensions to in vivo diagnostics.

Second harmonic generation microscopy, biaxial mechanical tests and fiber dispersion models in human skin biomechanics

Advanced numerical simulations of the mechanical behavior of human skin require thorough calibration of the material’s constitutive models based on experimental ex vivo mechanical tests along with images of tissue microstructure for a variety of biomedical applications. In this work, a total of 14 human healthy skin samples and 4 additional scarred skin samples were experimentally analyzed to gain deep insights into the biomechanics of human skin. In particular, second harmonic generation (SHG) microscopy was used to extract detailed images of the distribution of collagen fibers, which were subsequently processed using a three-dimensional Fourier transform-based method recently proposed by the authors to quantify the distribution of fiber orientations. Mechanical tests under both biaxial and uniaxial loading were performed to calibrate the relevant mechanical parameters of two widely used constitutive models of soft fiber-reinforced biological tissues that account for non-symmetrical fiber dispersion. The calibration of the models allowed us to identify correlations between the mechanical parameters of the constitutive models considered. Statement of significanceConstitutive models for soft collagenous tissues can accurately reproduce the complex nonlinear and anisotropic mechanical behavior of skin. However, a comprehensive analysis of both microstructural and mechanical parameters is still missing for human skin. In this study, these parameters are determined by combining biaxial mechanical tests and SHG stacks of collagen fibers on ex vivo healthy human skin samples. The constitutive parameters are provided for two widely used hyperelastic models and enable accurate characterization of skin mechanical behavior for advanced numerical simulations.

Экспериментальные исследования акустического поля поперечных волн в модели биологической ткани

Разработаны принципы проведения ультразвуковой диагностики при помощи технологии эластографии и представлена схема экспериментальной установки. Биологическая ткань смоделирована материалом силикон. Проведены исследования по определению продольной и поперечной составляющей скорости звука. Дальнейшие исследования позволят создать базу данных различных образцов патологических и здоровых тканей.

A computationally efficient gradient-enhanced healing model for soft biological tissues.

Soft biological tissues, such as arterial tissue, have the ability to grow and remodel in response to damage. Computational method plays a critical role in understanding the underlying mechanisms of tissue damage and healing. However, the existing healing model often requires huge computation time and it is inconvenient to implement finite element simulation. In this paper, we propose a computationally efficient gradient-enhanced healing model that combines the advantages of the gradient-enhanced damage model, the homeostatic-driven turnover remodeling model, and the damage-induced growth model. In the proposed model, the evolution of healing-related parameters can be solved explicitly. Additionally, an adaptive time increment method is used to further reduce computation time. The proposed model can be easily implemented in Abaqus, requiring only a user subroutine UMAT. The effectiveness of proposed model is verified through a semi-analytical example, and the influence of the variables in the proposed model is investigated using uniaxial tension and open-hole plate tests. Finally, the long-term development of aneurysms is simulated to demonstrate the potential applications of the proposed model in real biomechanical problems.

Biomechanical properties of nasal tissues

Introduction. Plastic rhinosurgery and augmentation rhinoplasty are very relevant today. Especially in relation to patients with congenital saddle deformity of the nasal dorsum, as well as patients with iatrogenic disorders of the nose shape, which dramatically reduce the quality of human life. There are violations of the function of the nose. The purpose of the work. Purpose. Within the framework of the necessity of performing silicone implantation rhinoplasty, the strength, elastic and hyperelastic properties of the soft tissues of the nasal fascia and periosteum were studied, the dynamic viscosity of the tissues of the nasal fascia and periosteum was evaluated, determining their relaxation properties using elastic, hyperelastic and rheological models. Methods. Linear, bilinear (with two Young modules), exponential, hyperelastic (neohookean, Mooney-Rivlin, Ogden, Yeoh, polynomial and Veronda-Westmann) and elastic-viscous (Maxwell) models of biological tissues were used. We used the Mathcad 15.0 computer algebra system and the universal package of interdisciplinary programs ANSYS Multiphysics Software (version 2022 R2). The accuracy of replacing the properties of real tissues with the results of calculations was calculated on the basis of indicators of descriptive statistics (standard deviation, maximum absolute error, maximum relative error and correlation coefficient). Results. It is proved that the bilinear model for the exact reproduction of the stress-strain curve assumes at the molecular level of tissues an initial linear reaction of elastin fibers, passing at ε=εcr into the final linear reaction of the collagen matrix. It was found that the properties of the periosteum (correlation coefficient R=0.9999) and nasal fascia (correlation coefficient R=0.9999) are described most adequately by the 5-parametric polynomial model of the 2nd order and the Yeoh model of the 3rd order (R=0.999 and R=1, respectively), the least accurately by the simple 1-parameter neohookean model (R=0.898 for the periosteum and R=0.905 for the fascia). Among elastic models, the exponential dependence characterizes the behavior of nasal materials quite well. Conclusion. Biomechanically verified that the periosteum is thicker, stronger and more rigid than the fascia. The established very high viscosity values indicate the slowness of relaxation processes in tissues. The periosteum relaxes tension more slowly, which improves the result of implant fixation. On the contrary, the relaxation time of the periosteum is higher than that of the fascia, from which it is concluded that it is preferable not to cut the periosteum during subcostal implantation.

Fourier transform-based method for quantifying the three-dimensional orientation distribution of fibrous units

Several materials and tissues are characterized by a microstructure composed of fibrous units embedded in a ground matrix. In this paper, a novel three-dimensional (3D) Fourier transform-based method for quantifying the distribution of fiber orientations is presented. The method allows for an accurate identification of individual fiber families, their in-plane and out-of-plane dispersion, and showed fast computation times. We validated the method using artificially generated 3D images, in terms of fiber dispersion by considering the error between the standard deviation of the reconstructed and the prescribed distributions of the artificial fibers. In addition, we considered the measured mean orientation angles of the fibers and validated the robustness using a measure of fiber density. Finally, the method is employed to reconstruct a full 3D view of the distribution of collagen fiber orientations based on in vitro second harmonic generation microscopy of collagen fibers in human and mouse skin. The dispersion parameters of the reconstructed fiber network can be used to inform mechanical models of soft fiber-reinforced materials and biological tissues that account for non-symmetrical fiber dispersion.

Differences in boundary behavior in the 3D vertex and Voronoi models.

An important open question in the modeling of biological tissues is how to identify the right scale for coarse-graining, or equivalently, the right number of degrees of freedom. For confluent biological tissues, both vertex and Voronoi models, which differ only in their representation of the degrees of freedom, have effectively been used to predict behavior, including fluid-solid transitions and cell tissue compartmentalization, which are important for biological function. However, recent work in 2D has hinted that there may be differences between the two models in systems with heterotypic interfaces between two tissue types, and there is a burgeoning interest in 3D tissue models. Therefore, we compare the geometric structure and dynamic sorting behavior in mixtures of two cell types in both 3D vertex and Voronoi models. We find that while the cell shape indices exhibit similar trends in both models, the registration between cell centers and cell orientation at the boundary are significantly different between the two models. We demonstrate that these macroscopic differences are caused by changes to the cusp-like restoring forces introduced by the different representations of the degrees of freedom at the boundary, and that the Voronoi model is more strongly constrained by forces that are an artifact of the way the degrees of freedom are represented. This suggests that vertex models may be more appropriate for 3D simulations of tissues with heterotypic contacts.

Nonlocal damage evaluation of a sigmoid-based damage model for fibrous biological soft tissues.

The comprehension and modeling of the mechanical behavior of soft biological tissues are essential due to their clinical applications. This knowledge is essential for predicting tissue responses accurately and enhancing our ability to compute the behavior of biological structures and bio-prosthetic devices under specific loading conditions. The current research is centered on modeling the initiation and progression of soft tissues damage, which typically exhibit intricate anisotropic and nonlinear elastic characteristics. For this purpose, the following study presents a comparative analysis of the computational performance of two distinct damage modeling techniques. The first technique employs a well-established damage model, based on a piece-wise exponential damage function as proposed by Calvo et al. (Int J Numer Methods Eng 69:2036-2057, 2007. https://doi.org/10.1002/nme.1825 ). The second approach adopts a sigmoid function, as proposed by López-Campos et al. (Comput Methods Biomech Biomed Eng 23(6):213-223. https://doi.org/10.1080/10255842.2019.1710742 ). The aim of this study is to verify the validity of the López-Campos sigmoid-based damage model to be used in finite element simulation, the implementation of which is unknown. For this proposal, both models were implemented within a commercial Finite Element software package, and their responses to local and non-local damage algorithms were assessed in depth through two standard benchmark tests: a plate with a hole and a ball burst. The results of this study indicate that, for a wide range of cases, such as in-plane stresses, out-plane stresses, stress concentration and contact, all over large displacement conditions, the López-Campos damage model shows a good response to non-local algorithms achieving mesh independence and convergence in all these cases. The results obtained are in line with those obtained for the Calvo's damage model, showing, in addition, larger deformations under in-plane stress and stress concentration conditions and a lower number of iterations under out-plane stress and contact conditions. Consequently, the López-Campos' damage model emerges as a valuable and useful tool in the field of mechanical damage research in biological systems.

Modified Moore–Gibson–Thompson Pennes’ bioheat transfer model for a finite biological tissue subjected to harmonic thermal loading

Modified Moore–Gibson–Thompson Pennes’ bioheat transfer model for a finite biological tissue subjected to harmonic thermal loading

One approach for selection of materials available for 3D printing of a dosimetry pelvic phantom: numerical simulation

Pelvic organ tumors are a serious problem in the field of oncology and account for one-third of the total number of the most common locations of neoplasms. Radiation therapy is often used to treat these types of cancer. A necessary procedure in the application of radiation therapy is the verification of the dosimetric plan to ensure maximum accuracy of radiation and minimize the negative effects of overexposure. To achieve these goals, dosimetry phantoms are used to mimic the structure and properties of biological tissues. Additive technologies can be an effective method for manufacturing such phantoms due to their high-precision ability to replicate both body geometry and anatomical structures. Today, the search and development of materials suitable for both additive technologies and assessing the interaction of ionizing radiation with matter is a relevant task. In this study, models of biological tissues and organs, as well as materials for 3D printing, were created. The features of Co-60 photon beam interaction with these materials were analyzed by numerical simulation. The calculated results demonstrated the suitability of plastic materials based on polylactide for simulating individual biological tissues and human organs from the point of view of interaction with ionizing radiation.

A data‐driven constitutive model for soft biological tissues

AbstractConstitutive modeling of soft biological tissues is crucial for biomedical simulations and a deep understanding of tissue mechanics. Classical constitutive models have a fixed mathematical expression, however, the microstructure and the corresponding macro‐mechanical response of different tissue types can vary significantly. A model that works for one tissue may not work for another kind of tissue, and choosing the right model may become challenging. To solve this issue, this study introduces a new data‐driven approach to creating a unified model for predicting the mechanical response of various tissue classes. The proposed model is based on B‐Spline approximations and assumes the strain energy function can be divided into volumetric, isotropic, and anisotropic components. The B‐Spline ansatz replaces partial derivatives of free energy energy function with respect to invariants with control points and polynomial degree, and allows the use of existing dispersion models. The model adapts its control point values to reduce the error between data and prediction until a threshold is reached, and is thermodynamically consistent through the use of optimization constraints. The model is demonstrated on various biological tissues, showing excellent fitting capabilities with a minimal number of control points. The outcome is a generic framework that can model any tissue given the data from experiments and imaging techniques.

Data-driven hyperelasticity, Part II: A canonical framework for anisotropic soft biological tissues

In this work, we present a novel anisotropic data-driven hyperelasticity framework for the constitutive modeling of soft biological tissues that allows direct incorporation of experimental data into the constitutive model, without requirement of a predetermined mathematical formula for the strain–energy density function. The data-driven framework is constructed through a dispersion-type anisotropic formulation based on a generalized structure tensor in the sense of Holzapfel et al. (2015) that take into account in- and out of plane dispersion. The partial derivatives of the strain energy density functions are replaced with appropriate B-spline interpolations where the control points are calibrated against experimental data obtained from uniaxial tension, triaxial shear, and (equi)biaxial tension deformations. The model calibration phase incorporates the normalization condition and the polyconvexity condition is enforced through the control points of the B-splines in order to ensure a stable constitutive response that allows unique solution in finite element analysis. The predictive capabilities of the proposed model are shown against linea alba, rectus sheath, aneurysmal abdominal aorta, and myocardium tissues. On the numerical side, the stress and moduli expressions of the model are derived and implemented into the finite element method. The performance of the model is demonstrated through representative boundary value problems.

Investigation of bio-thermo-mechanical responses based on nonlocal elasticity theory and fractional Pennes equation

A nonlocal fractional bio-thermo-mechanical model is developed in the context of modified fractional Pennes equation and nonlocal elasticity theory of Eringen. In the example analysis, a one-dimensional homogeneous and isotropic biological tissue model is assumed and the solutions of coupling fractional bio-thermo-mechanical equations are obtained by the method of Laplace transform. The heat conduction process and deformation in biological tissue under the action of a pulsing heat flux are investigated. The influences of fractional order parameter, pulsing heat flux characteristic time and nonlocal elastic parameter on the heat transfer, heat-induced deformation and thermal stress are analyzed.

Effect of matrix properties on transmission and reflectance mode division-of-focal-plane Stokes polarimetry.

Division-of-focal-plane Stokes polarimetry is emerging as a powerful tool for the microstructural characterization of soft tissues. How individual extracellular matrix (ECM) properties influence polarimetric signals in reflectance or transmission modes of quantitative polarized light imaging (QPLI) is not well understood. We aimed to investigate how ECM properties affect outcomes obtained from division-of-focal-plane polarimetric imaging in reflectance or transmission modes. Tunable collagen gel phantoms were used to modulate ECM properties of anisotropy, collagen density, crosslinking, and absorber density; the effects of degree of linear polarization (DoLP) and angle of polarization (AoP) on polarimetry outcomes were assessed. A model biological tissue (i.e., bovine tendon) was similarly imaged and evaluated using both reflectance and transmission modes. Reflectance QPLI resulted in decreased DoLP compared with transmission mode. A 90deg shift in AoP was observed between modes but yielded similar spatial patterns. Collagen density had the largest effect on outcomes besides anisotropy in both imaging modes. Both imaging modes were sufficiently sensitive to detect structural anisotropy differences in gels of varying fiber alignment. Conclusions drawn from phantom experiments should carry over when interpreting data from more complex tissues and can help provide context for interpretation of other Stokes polarimetry data.

Low-cost compact optical spectroscopy and novel spectroscopic algorithm for point-of-care real-time monitoring of nanoparticle delivery in biological tissue models.

Real-time monitoring of nanoparticle delivery in biological models is essential to optimize nanoparticle-mediated therapies. However, few techniques are available for convenient real-time monitoring of nanoparticle concentrations in tissue samples. This work reported novel optical spectroscopic approaches for low-cost point-of-care real-time quantification of nanoparticle concentrations in biological tissue samples. Fiber probe measured diffuse reflectance can be described with a simple analytical model by introducing an explicit dependence on the reduced scattering coefficient. Relying on this, the changes on the inverse of diffuse reflectance are proportional to absorption change when the scattering perturbation is negligible. We developed this model with proper wavelength pairs and implemented it with both a standard optical spectroscopy platform and a low-cost compact spectroscopy device for near real-time quantification of nanoparticle concentrations in biological tissue models. Both tissue-mimicking phantom and ex vivo tissue sample studies showed that our optical spectroscopic techniques could quantify nanoparticle concentrations in near real-time with high accuracies (less than 5% error) using only a pair of narrow wavelengths (530 nm and 630 nm). Novel low-cost point-of-care optical spectroscopic techniques were demonstrated for rapid accurate quantification of nanoparticle concentrations in tissue-mimicking medium and ex vivo tissue samples using optical signals measured at a pair of narrow wavelengths. Our methods will potentially facilitate real-time monitoring of nanoparticle delivery in biological models using low-cost point-of-care optical spectroscopy platforms, which will significantly advance nanomedicine in cancer research.

P‐2.16: Research on three‐dimensional reconstruction based on VTK

Three‐dimensional reconstruction of medical tomographic images is a technological way to provides a 3D model of biological tissue. As it not only provides a 3D model, but also shows the spatial location of this model, it received widespread attention. By human‐computer interaction, doctors can easily conduct disease analysis and surgical planning.This paper introduces a novel three‐dimensional reconstruction technology of magnetic resonance images, which deals with the brightness, contrast adjustment, and three‐dimensional reconstruction of Dicom images. This paper uses the Visualization Toolkit VTK to implement Dicom 3D image reconstruction. VTK has a large number of callable functions built in and encapsulates some common visualization algorithms. When visualizing medical data, VTK can directly call the related functions. VTK three‐dimensional reconstruction can help people intuitively see the contents of a 3D image. Displaying two‐ dimensional images is easy, but displaying 3D images is not. Previously, because of the limited technical means, even if the data of the 3D image is obtained, it can only be displayed as a slice of the 2D image, which is not intuitive. With the development of computer science and technology, the use of computer graphics technology to model and render 3D objects in real‐time has become the mainstream method of object display, while the past two‐dimensional display method has been gradually phased out.To describe the process of 3D modeling more accurately and intuitively, this paper focuses on a reconstruction technique, polygon drawing. Polygon drawing uses segmentation technology to perform contour recognition, extraction, and other operations on a series of two‐dimensional images, and ultimately restores the three‐dimensional model of the detected object and displays it as a surface.First, the original data is a discrete three‐dimensional spatial rule data field. The images generated by CT and MRI of tomography scanners belong to this data type, that is, the DICOM type image used in this paper. Second, the boundary between the content part and the background part in the three‐dimensional image is found in the unit of volume, and triangles are extracted to fit the boundary. Then, all the voxels are traversed to find out which triangles are finally assembled to form a triangular mesh of the surface of the real point in the image. Finally, a triangle mesh model is built to render the model, and the rendered model is put into the window to interact with users.

A continuous constraint satisfaction problem for the rigidity transition in confluent tissues

Models of confluent tissues are built out of tessellations of the space (both in two and three dimensions) in which the cost function is constructed in such a way that individual cells try to optimize their volume and surface in order to reach a target shape. At zero temperature, many of these models exhibit a rigidity transition that separates two phases: a liquid phase and a solid (glassy) phase. This phenomenology is now well established but the theoretical understanding is still not complete. In this work we consider an exactly soluble mean field model for the rigidity transition which is based on an abstract mapping. We replace volume and surface functions by random non-linear functions of a large number of degrees of freedom forced to be on a compact phase space. We then seek for a configuration of the degrees of freedom such that these random non-linear functions all attain the same value. This target value is a control parameter and plays the role of the target cell shape in biological tissue models. Therefore we map the microscopic models of cells to a random continuous constraint satisfaction problem with equality constraints. We argue that at zero temperature, the rigidity transition corresponds to the satisfiability transition of the problem. We also characterize both the satisfiable (SAT) and unsatisfiable (UNSAT) phase. In the SAT phase, before reaching the rigidity transition, the zero temperature SAT landscape undergoes an replica symmetry breaking (RSB)/ergodicity breaking transition of the same type as the Gardner transition in amorphous solids. By solving the RSB equations we compute the SAT/UNSAT threshold and the critical behavior around it. In the UNSAT phase we also compute the average shape index as a function of the target one and we compare the thermodynamical solution of the model with the results of the numerical greedy minimization of the corresponding cost function.

Phenotype switching in a global method for agent-based models of biological tissue.

Agent-based models (ABMs) are an increasingly important tool for understanding the complexities presented by phenotypic and spatial heterogeneity in biological tissue. The resolution a modeler can achieve in these regards is unrivaled by other approaches. However, this comes at a steep computational cost limiting either the scale of such models or the ability to explore, parameterize, analyze, and apply them. When the models involve molecular-level dynamics, especially cell-specific dynamics, the limitations are compounded. We have developed a global method for solving these computationally expensive dynamics significantly decreases the computational time without altering the behavior of the system. Here, we extend this method to the case where cells can switch phenotypes in response to signals in the microenvironment. We find that the global method in this context preserves the temporal population dynamics and the spatial arrangements of the cells while requiring markedly less simulation time. We thus add a tool for efficiently simulating ABMs that captures key facets of the molecular and cellular dynamics in heterogeneous tissue.

Finite elasticity of the vertex model and its role in rigidity of curved cellular tissues.

Using a mean field approach and simulations, we study the non-linear mechanical response of the vertex model (VM) of biological tissue to compression and dilation. The VM is known to exhibit a transition between solid and fluid-like, or floppy, states driven by geometric incompatibility. Target perimeter and area set a target shape which may not be geometrically achievable, thereby engendering frustration. Previously, an asymmetry in the linear elastic response was identified at the rigidity transition between compression and dilation. Here we show that the asymmetry extends away from the transition point for finite strains. Under finite compression, an initially solid VM can completely relax perimeter tension, resulting in a drop discontinuity in the mechanical response. Conversely, an initially floppy VM under dilation can rigidify and have a higher response. These observations imply that re-scaling of cell area shifts the transition between rigid and floppy states. Based on this insight, we calculate the re-scaling of cell area engendered by intrinsic curvature and write a prediction for the rigidity transition in the presence of curvature. The shift of the rigidity transition in the presence of curvature for the VM provides a new metric for predicting tissue rigidity from image data of curved tissues in a manner analogous to the flat case.

Identification of Constitutive Parameters for the Non-Local Damage Model of Soft Biological Tissues

Identification of Constitutive Parameters for the Non-Local Damage Model of Soft Biological Tissues