Modeling Interactions among Migration, Growth and Pressure in Tumor Dynamics

What are the biomechanical implications in the dynamics and evolution of a growing solid tumor? Although the analysis of some of the biochemical aspects related to the signaling pathways involved in the spread of tumors has advanced notably in recent times, their feedback with the mechanical aspects is a crucial challenge for a global understanding of the problem. The aim of this paper is to try to illustrate the role and the interaction between some evolutionary processes (growth, pressure, homeostasis, elasticity, or dispersion by flux-saturated and porous media) that lead to collective cell dynamics and defines a propagation front that is in agreement with the experimental data. The treatment of these topics is approached mainly from the point of view of the modeling and the numerical approach of the resulting system of partial differential equations, which can be placed in the context of the Hele-Shaw-type models. This study proves that local growth terms related to homeostatic pressure give rise to retrograde diffusion phenomena, which compete against migration through flux-saturated dispersion terms.

BDNF and NT-3 Increase Velocity of Activity Front Propagation in Unidimensional Hippocampal Cultures

Neurotrophins are known to promote synapse development as well as to regulate the efficacy of mature synapses. We have previously reported that in two-dimensional rat hippocampal cultures, brain-derived neurotrophic factor (BDNF) and neurotrophin-3 significantly increase the number of excitatory input connections. Here we measure the effect of these neurotrophic agents on propagating fronts that arise spontaneously in quasi-one-dimensional rat hippocampal cultures. We observe that chronic treatment with BDNF increased the velocity of the propagation front by about 30%. This change is attributed to an increase in the excitatory input connectivity. We analyze the experiment using the Feinerman–Golomb/Ermentrout–Jacobi/Moses–Osan model for the propagation of fronts in a one-dimensional neuronal network with synaptic delay and introduce the synaptic connection probability between adjacent neurons as a new parameter of the model. We conclude that BDNF increases the number of excitatory connections by favoring the probability to form connections between neurons, but without significantly modifying the range of the connections (connectivity footprint).

COMPUTER MODELS OF DEPOLARIZATION ALTERATIONS INDUCED BY MYOCARDIAL ISCHEMIA: THE EFFECT OF SUPERIMPOSED ISCHEMIC INHOMOGENEITIES ON PROPAGATION IN SPACE AND TIME-FREQUENCY DOMAINS

A two-dimensional modified Luo-Rudy model was created to represent a 40 mm by 40 mm slab of myocardial tissue. An inhomogeneity was introduced to simulate acute myocardial ischemia, with components of hyperkalemia, acidosis and anoxia. Simulations were carried out for various degrees of ischemia, to study both the interaction of the propagation front with the inhomogeneity, and the reconstructed signals. The simulations utilized a modified LR model, with a realistic anisotropy of myocardial tissue. Each cluster (.4 mm ×.4 mm) was given bulk electric properties, Rx and Ry (25Ω and 250Ω, respectively). The slab was stimulated and the 2D depolarization pattern was computed by numerical integration. To study ischemia, a circular inhomogeneity with concentric regions (ro=12.8 mm{border zone, BZ} , ri=11.2 mm{extreme zone, EZ} ) regions was introduced in the model. From the 2D simulations and the regional action potentials (AP), unipolar and bipolar lead potentials were reconstructed. Time-frequency decomposition was performed on the lead signals by wavelet analysis. Isochrone and (dV/dt) max maps were obtained to study depolarization. Our results indicate that spatial inhomogeneities yield dramatic spatial dispersion of the wavefront and are the origin of mid-frequency intra-QRS components in cardiac signals. Severe APD shortening and spatial distortion of the isochrone and upstroke maps are also observed.

Theoretical Analysis of Large Deformation Simultaneous Tearing and Peeling of Elastoplastic Materials

Simultaneous tearing and peeling of multiple strips is theoretically investigated using the large deflection theory of cantilevers made of elastoplastic material with linear strain hardening. The relationship between the fracture toughness and the curvature at the fracture propagation front is obtained for general cases. It is shown that for the moment loading case, the non-dimensional external moment, m1, during tearing and peeling along straight paths, is a constant and is independent of the initial beam length Lo. With concentrated force loading, the non-dimensional force f will reach a constant value f=fm during propagation. It is shown that fm is almost the same for both initially straight and pre-bent beams, and decreases with an increase in the external force loading angle φ. For initially straight beams, when the non-dimensional fracture toughness, D, is small, fm may be less than the initiation force f1 for fracture. Fm/H does not increase linearly with an increase in the beam width B0 and decreases at large B0 after it passes through a peak value. Comparison is made with experimental results for the tearing of ductile metal sheets along straight paths and the tearing fracture toughness value is found, including a method that uses propagation crack front curvature alone, without additional reference to the tearing force. However, the accuracy of the curvature at the crack propagation front has a large effect on the estimation of fracture toughness. High work-hardening and/or low toughness materials have no rapid change of curvature away from the crack front so that good estimates are possible and vice versa for low work-hardening solids.