Anomalous glassy dynamics in simple models of dense biological tissue

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.

Understanding the structural dynamics of many-particle glassy systems remains a key challenge in statistical physics. Over the last decade, glassy dynamics has also been reported in biological tissues, but is far from being understood. It was recently shown that vertex models of dense biological tissue exhibit very atypical, sub-Arrhenius dynamics, and here we ask whether such atypical structural dynamics of vertex models are related to unusual elastic properties. It is known that at zero temperature these models have an elasticity controlled by their underconstrained or isostatic nature, but little is known about how their elasticity varies with temperature. To address this question we investigate the 2D Voronoi model and measure the temperature dependence of the intermediate-time plateau shear modulus and the bulk modulus. We find that unlike in conventional glass formers, these moduli increase monotonically with temperature until the system fluidizes. We further show that the structural relaxation time can be quantitatively linked to the plateau shear modulus G_{p}, i.e. G_{p} modulates the typical energy barrier scale for cell rearrangements. This suggests that the anomalous, structural dynamics of the 2D Voronoi model originates in its unusual elastic properties. Based on our results, we hypothesize that underconstrained systems might more generally give rise to a new class of "ultrastrong" glass formers.

The suppression of density fluctuations at different length scales is the hallmark of hyperuniformity. Here, we explore the presence of this hidden order in a manybody interacting model of biological tissue, known to exhibit a transition, or sharp crossover, from a solid to a fluid like phase. We show that the density fluctuations in the rigid phase are only suppressed up to a finite lengthscale. This length scale monotonically increases and grows rapidly as we approach the fluid phase reminiscent to divergent behavior at a critical point, such that the system is effectively hyperuniform in the fluid phase. Furthermore, complementary behavior of the structure factor across the critical point also indicates that hyperuniformity found in the fluid phase is stealthy.

Precise cutting of biological tissue is possible with the Er:YAG laser because of the strong absorption of radiation exhibited by water containing media at 2.94 micrometers wavelength. To achieve control over the thermal damage caused to the tissue and over the extent of the coagulation zone, a thorough knowledge of the local temperature distribution arising near the impact zone is necessary. Calculations are possible in some simple cases, whereas in others, where liquified tissue material acts as a secondary heat source long after the pulse, a time resolved direct measurement of the temperature distributions with microscopical spatial resolution would be desirable. We have developed a method for measuring two-dimensional temperature distributions in optically transparent media with a high time resolution (up to 4 ns) and with microscopical spatial resolution by imaging the temperature dependent fluorescence distribution of 2 micrometers thin films positioned inside the target. With this method we have measured the temperature distributions at different times after the impact of single pulses from an Er:YAG laser at various fluences in gelatin targets, which we use as model for biological tissue. The results are compared with the thermal damage inflicted in vitro to different types of animal tissue. A strong dependence of the temperature distributions and their dynamical behavior on pulse fluence and water content of the target is observed, in congruence with the coagulation zones observed biological tissue.

An essential property of soft biological tissues is the ability to adapt according to respective loading conditions, e.g. by means of fibre reorientation (remodelling). In particular with regard to arterial tissue, an externally unloaded state of the material is generally associated with residual stresses. In this contribution a three‐dimensional micro‐sphere‐based constitutive model for anisotropic soft biological tissue is presented, which includes fibre‐reorientation‐related remodelling as well as residual stress‐effects. As a key aspect of this contribution, time‐dependent remodelling effects are incorporated by introducing evolution equations for the integration directions of the micro‐sphere scheme, which thereby characterize the material's anisotropic properties. An appropriate remodelling approach for the orthotropic case is discussed, whereas the effect of residual stresses is additionally included in the model by means of a multiplicative decomposition of the deformation gradient tensor. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

It is desirable for the non-and-mini traumatic laser surgical procedures to remove tissue accurately with the minimal thermal damage to the adjacent non-irradiated tissues. Photo-thermal interactions between laser rays and biological tissues have various thermal effects such as coagulation, vaporization and carbonization. The energy of laser continuously accumulates and diffuses in biological tissues, so that different extent thermal effects and thermal damage of biological tissues have been induced. In this paper, the thermal conduction model and optical parameters of biological tissues are discussed, the relevant thermal effects calculation equations are deduced, the instantaneous temperature distribution of biological tissue irradiated by high power laser is simulated, the thermal damage depth is numerically predicted and the relationship curve between time and the thermal penetraction depth is described. The study is of significance in revealing the mechanisms of laser thermal interaction with biological tissue, as well as developing clinical application of laser medicine.

A computational multilayer model to simulate hollow needle insertion into biological porcine liver tissue

Vertex models have become essential tools for understanding tissue morphogenesis by simulating the mechanical and geometric properties of cells in various biological systems. These models represent cells as polygons or polyhedra, capturing cellular interactions such as adhesion, tension, and force generation. This review explores the ongoing evolution of computational vertex models, highlighting their application to complex tissue dynamics, including organoid development, wound healing, and cancer metastasis. We examine different energy formulations used in vertex models, which account for mechanical forces such as surface tension, volume conservation, and intercellular adhesion. Additionally, this review discusses the challenges of expanding traditional 2D models to 3D structures, which require the inclusion of factors like mechanical polarisation and topological transitions. We also introduce recent advancements in modelling techniques that allow for more flexible and dynamic cell shapes, addressing limitations in earlier frameworks. Mechanochemical feedback and its role in tissue behaviour are explored, along with cutting-edge approaches like self-propelled Voronoi models. Finally, the review highlights the importance of parameter inference in these models, particularly through Bayesian methods, to improve accuracy and predictive power. By integrating these new insights, vertex models continue to provide powerful frameworks for exploring the complexities of tissue morphogenesis.

This paper presents new results on a novel coupled-physics modality called magneto-acousto-electrical tomography (MAET). With static magnetic field, a beam of ultrasound is applied to the sample to be imaged; the ultrasonic vibration can lead to the separation of the charges due to the Lorentz force and produces the current distributed in the object. In this paper, simulations were conducted on biological tissue model, and the electrical properties were reconstructed, which could reflect the state of physiological or pathological. We also conducted experiments to detect the voltage signal of microvolt level by the electrodes placed around the sample. The series of experiments were conducted on low-conductivity (0.2 S/m) animal gelatin phantom and real biological tissue, successively placed in a 260 mT magnetic field and sonicated with a plane ultrasonic transducer of central frequency 2.25 MHz. In this paper, we obtained axis resolution of 1 mm, much more significant improvement than the previous reports. More importantly, the experimental result does also demonstrate the feasibility of MAET to image the electrical properties of biological tissue.

In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the cell-centered model, and the cellular Potts model. So far, in any case, pressures have not neatly been dealt with and the curvatures of the cell boundaries have been even omitted through their approximations. We focus on these quantities and formulate them in the vertex model. Thus, a model with the curvatures is constructed, and its algorithm for simulation is provided. The possible extensions and applications of this model are also discussed.

Soft materials such as polymers and biological tissues have several engineering and biomechanical applications. These materials exhibit complex mechanical behavior, characterized by large strains, hysteresis, rate sensitivity, stress softening (Mullins effect), and deviatoric and volumetric plasticity. The need to accurately predict the behavior of such materials has been a tremendous challenge for scientists and engineers. This thesis presents a seamless, fully variational constitutive model capable of capturing all of the above complex characteristics. Also, this work describes a fitting procedure based on the use of Genetic Algorithms, which proves to be necessary for the multi-modal, non-convex optimization required to identify fitting material parameters. The capabilities of the presented model are demonstrated via several fits of experimental tests on a wide range of materials. These tests involve monotonic and cyclic loading of polyurea, high-density polyethylene, and brain tissue, and also involve cyclic hysteresis, softening, rate effects, shear, and cavitation plasticity. Application to ballistic impact on a polyurea retrofitted DH36 steel plate is simulated and validated, utilizing the soft material model presented in this thesis for the polymer and a porous plasticity model for the metal. Localization elements are also included in this application to capture adiabatic shear bands. Moreover, computational capability for assessing the blast performance of metal/elastomer composite shells utilizing the soft material model for the elastomer is also presented. Another implemented application is in the area of traumatic brain injuries under impact/acceleration loading. Clinically observed brain damage is reproduced utilizing the model presented in this work and a predictive capability of the distribution, intensity, and reversibility/irreversibility of brain tissue damage is demonstrated.

Magnetic induction tomography (MIT) is a new medical functional imaging technique. This paper proposes a multi-layer model of the biological tissue. And a new reconstruction method of magnetic induction tomography based on the improved genetic algorithm(GA) was introduced. The GA was improved from the following aspects: the generation of the initial population, selection, crossover and mutation operation. The simulation results indicate that the method can reflect local and large-area bleeding in the shallow of biological tissue, and construct a base for the future clinical brain disease monitoring.

During the recent years the number of the wounded and killed due to firearms use both in Ukraine and in the majority of the world countries has increased. Therefore, examination of gunshot injuries is rather topical issue now in forensic medicine, and it is a considerable comprehensive question.Transience of incidences with the use of firearms in the majority of cases does not enable to find a real picture of circumstances when these incidences occur. Therefore, the issues of traumatic factor identification in these cases, especially with perforating and tangential injuries, are very important in forensic medicine, but remain elucidated insufficiently.
 At the same time, a dynamic development of upto-date computer technologies enables to increase the level of visualization, forensic diagnostics of injuries and substantiation of expert conclusions in case of gunshot injuries.
 Purpose of the study. To study diagnostic possibilities of three-dimensional spatial reconstruction method for forensic identification of the main traumatic factor in case of gunshot injuries.
 Materials and methods. Ballistic plasticine and gel, fragments of pig skin with subcutaneous fat, fragments of biological tissues with gunshot injuries were used as the material for the study. The obtained experimental gunshot injuries (45 cases) and cases of injuries from the expert practice (30 cases) were subjected to photogrammetric with possibility to obtain a three-dimensional spatial model of every injury by means of the computer program Agisoft Photoscan.
 Results. The studies conducted differ from the existing ones by their novelty, higher inventive and scientific-practical level. Three-dimensional spatial digital models of the injured biological tissues and their imitators will be designed, examined and analyzed for the first time, and the diagnostic criteria for forensic identification of the main traumatic factor of gunshot body injuries will be developed. The obtained textured models of gunshot injuries in «Obj» format can be imported into the program 3dsMax, which enables to examine linear sizes of every fragment of a wound canal with higher accuracy (to 0,001 cm) in comparison with classical methods of examination.
 The results obtained while conducting the study enable not only to develop computer threedimensional digital models of gunshot body injuries, but examine their character and morphologic peculiarities in forensic practice on an up-to-date scientific level. All the mentioned above enables to formulate and substantiate new, more accurate forensic diagnostic identification criteria of the main traumatic factor of gunshot body injuries.
 Conclusion. Introduction of up-to date computer technologies into the practice of forensic medicine will enable to determine identifying peculiarities of the main traumatic factor in case of gunshot injuries with a higher accuracy.

Numerical solutions to the basic heat flow equation: K{∇2T−1κ∂T∂t}=Q(t)(1) are presented, where Q (t) represents a specified average power density level delivered from a laser source to a target comprised of biological tissue. The model employed assumes such tissue to be homogeneous and characterized by an average thermal diffusivity, κ; an average thermal conductivity, K; and an average density, ρ. We show how computer-generated temperature profiles may be made, and how information extracted from such profiles may be consolidated into plots of surface temperature rise and depth of penetration of a given temperature with respect to exposure time at specified power density levels. Furthermore, we show that computer numerical simulation can predict heat flow characteristics of biological tissue in much the same manner as in previous laser material process modelling, provided limitations and simplifying assumptions of the technique are clearly understood.

Most tissue optical spectroscopy platforms use a fiber probe for light delivery and collection, while the inconsistent probe-sample contact could induce significant distortions in the measured optical signals, which consequently bring analysis errors. Moreover, it will be practically difficult to use a fiber probe for measurements in some cases such as oral cancer investigations using small animal models. To address the critical challenge, we report a portable, lens-based, optical spectroscopy device capable of quantifying key vascular and metabolic parameters in vivo without probe-sample contact. We combined lenses based diffuse reflectance and fluorescence spectroscopy into one portable platform to enable multi-parametric functional characterizations of orthotopic tongue cancer models in vivo. We also implemented easy-to-use spectroscopic algorithms with the system for rapid quantification of the key metabolic and vascular parameters on biological tissue models. We then demonstrated our non-contact optical spectroscopy on tissue-mimicking phantoms and in vivo mouse tongue tumor models. Our phantom and in vivo animal studies showed that our non-contact optical spectroscopy, along with spectroscopic algorithms, could quantify the major metabolic and vascular parameters on in vivo tongue tumors with high accuracy. We also captured the diverse metabolic and vascular phenotypes of tongue tumors with different radiation sensitivity. Our new optical spectroscopy implemented with easy-to-use spectroscopic algorithms will provide a non-contact way for rapid and systematic characterizations of biological tissue metabolism and vascular microenvironment in vivo, which may significantly advance head and neck cancer research in the future.