Longitudinal nonlinear wave propagation through soft tissue

On shockwave propagation and attenuation in poly(ethylene glycol) diacrylate hydrogels

An analytical model is developed to predict shockwave propagation and attenuation in hydrogels by combining the classical method of shock characteristics and a solution for the shock front structure. To guide the development of the model, molecular dynamics (MD) simulations are performed. Specifically, a one-dimensional shock pulse in poly(ethylene glycol) diacrylate (PEGDA) hydrogels is simulated with the nonequilibrium MD method. The role of polymer concentration on the shock response is evaluated by constructing hydrogels with 20, 35, and 50 wt% PEGDA concentrations in an idealized crosslinked network. Steady-state pressure-density and shock-particle velocity relationships are established using the Murnaghan equation of state. Shock front structure is characterized by a power-law equation that relates the shock front thickness with shock pressure. These results are used as critical input for the shock propagation and attenuation model. The model is then evaluated via comparison with the classical method of characteristics. It shows significant improvement in accuracy and successfully captures salient features of shockwave attenuation, including the shock pressure amplitude, the velocities of the shock and release waves, and the attenuation timeline. Hydrogels with higher polymer concentrations exhibit a shorter attenuation time at all particle velocities studied. This behavior is attributed to differences in bulk properties and shock front structure in hydrogels with different polymer/water concentrations.

Toward a Reasoned Classification of Diseases Using Physico-Chemical Based Phenotypes

Background: Diseases and health conditions have been classified according to anatomical site, etiological, and clinical criteria. Physico-chemical mechanisms underlying the biology of diseases, such as the flow of energy through cells and tissues, have been often overlooked in classification systems.

Objective: We propose a conceptual framework toward the development of an energy-oriented classification of diseases, based on the principles of physical chemistry.

Methods: A review of literature on the physical chemistry of biological interactions in a number of diseases is traced from the point of view of the fluid and solid mechanics, electricity, and chemistry.

Results: We found consistent evidence in literature of decreased and/or increased physical and chemical forces intertwined with biological processes of numerous diseases, which allowed the identification of mechanical, electric and chemical phenotypes of diseases.

Discussion: Biological mechanisms of diseases need to be evaluated and integrated into more comprehensive theories that should account with principles of physics and chemistry. A hypothetical model is proposed relating the natural history of diseases to mechanical stress, electric field, and chemical equilibria (ATP) changes. The present perspective toward an innovative disease classification may improve drug-repurposing strategies in the future.

One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes

The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures.

Mechanical response of brain tissue under blast loading

In this study, a framework for understanding the propagation of stress waves in brain tissue under blast loading has been developed. It was shown that tissue nonlinearity and rate dependence are the key parameters in predicting the mechanical behavior under such loadings, as they determine whether traveling waves could become steeper and eventually evolve into shock discontinuities. To investigate this phenomenon, in the present study, brain tissue has been characterized as a quasi-linear viscoelastic (QLV) material and a nonlinear constitutive model has been developed for the tissue that spans from medium loading rates up to blast rates. It was shown that development of shock waves is possible inside the head in response to high rate compressive pressure waves. Finally, it was argued that injury to the nervous tissue at the microstructural level could be partly attributed to the high stress gradients with high rates generated at the shock front and this was proposed as a mechanism of injury in brain tissue.

A micromechanical procedure for viscoelastic characterization of the axons and ECM of the brainstem

In this study, the optimal viscoelastic material parameters of axon and extracellular matrix (ECM) in porcine brain white matter were identified using a genetic algorithm (GA) optimization procedure. The procedure was combined with micromechanical finite element analysis (FEA) of brain tissue and experimental stress relaxation tests on brainstem specimens to find the optimal material coefficients of axon and ECM. The stress relaxation tests were performed in tension on 10 brainstem specimens at 3% strain level. The axonal volume fraction in brainstem was measured from the Scanning Electron Microscopy images of the brain tissue. A square periodic volume element was selected to represent the microscale homogenized brainstem tissue. Periodic boundary conditions were applied on the square volume element to mimics the repetitive nature of the volume element. Linear viscoelastic material properties were assumed for the brain tissue constituents under small deformation. The constitutive behavior was expressed in terms of Prony series. The GA procedure searched for the optimal material parameters by fitting the time-dependent tissue stresses of brain tissue FEA to the stresses of relaxation tests under the same loading conditions. The optimization procedure converged after 60 iterations. The initial elastic modulus of axon was found to be 12.86kPa, three times larger than that of ECM. The long-term elastic modulus of axon was 3.7kPa, while for ECM this value was 1.03kPa. The concordance correlation coefficient between FEA estimated elastic modulus of brainstem tissue using the optimal material properties and the experimental elastic modulus of brainstem specimens was 0.952, showing a strong agreement. The optimal material properties of brain tissue constituents can find applications in micromechanical analysis of brain tissue to gain insight into diffuse axonal injures (DAIs).