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Vladimir G. Ivancevic
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The prediction and prevention of spinal injury is an important aspect of preventive health science. The spine, or vertebral column, represents a chain of 26 movable vertebral bodies, joint together by transversal viscoelastic intervertebral discs and longitudinal elastic tendons. This paper proposes a new locally-coupled loading-rate hypothesis}, which states that the main cause of both soft- and hard-tissue spinal injury is a localized Euclidean jolt, or SE(3)-jolt, an impulsive loading that strikes a localized spine in several coupled degrees-of-freedom simultaneously. To show this, based on the previously defined covariant force law, we formulate the coupled Newton-Euler dynamics of the local spinal motions and derive from it the corresponding coupled SE(3)-jolt dynamics. The SE(3)-jolt is the main cause of two basic forms of spinal injury: (i) hard-tissue injury of local translational dislocations; and (ii) soft-tissue injury of local rotational disclinations. Both the spinal dislocations and disclinations, as caused by the SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum model. Keywords: localized spinal injury, coupled loading-rate hypothesis, coupled Newton-Euler dynamics, Euclidean jolt dynamics, spinal dislocations and disclinations
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Prediction and prevention of musculo-skeletal injuries is an important aspect of preventive health science. Using as an example a human knee joint, this paper proposes a new coupled-loading-rate hypothesis, which states that a generic cause of any musculo-skeletal injury is a Euclidean jolt, or SE(3)-jolt, an impulsive loading that hits a joint in several coupled degrees-of-freedom simultaneously. Informally, it is a rate-of-change of joint acceleration in all 6-degrees-of-freedom simultaneously, times the corresponding portion of the body mass. In the case of a human knee, this happens when most of the body mass is on one leg with a semi-flexed knee -- and then, caused by some external shock, the knee suddenly `jerks; this can happen in running, skiing, sports games (e.g., soccer, rugby) and various crashes/impacts. To show this formally, based on the previously defined covariant force law and its application to traumatic brain injury (Ivancevic, 2008), we formulate the coupled Newton--Euler dynamics of human joint motions and derive from it the corresponding coupled SE(3)-jolt dynamics of the joint in case. The SE(3)-jolt is the main cause of two forms of discontinuous joint injury: (i) mild rotational disclinations and (ii) severe translational dislocations. Both the joint disclinations and dislocations, as caused by the SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum joint model. Keywords: musculo-skeletal injury, coupled-loading--rate hypothesis, coupled Newton-Euler dynamics, Euclidean jolt dynamics, joint dislocations and disclinations
The prediction and prevention of traumatic brain injury, spinal injury and general musculo-skeletal injury is a very important aspect of preventive medical science. Recently, in a series of papers, I have proposed a new coupled loading-rate hypothesis as a unique cause of all above injuries. This new hypothesis states that the main cause of all mechanical injuries is a Euclidean Jolt, which is an impulsive loading that strikes any part of the human body (head, spine or any bone/joint) - in several coupled degrees-of-freedom simultaneously. It never goes in a single direction only. Also, it is never a static force. It is always an impulsive translational and/or rotational force, coupled to some human mass eccentricity. Keywords: traumatic brain injury, spinal injury, musculo-skeletal injury, coupled loading-rate hypothesis, Euclidean jolt
The prediction and prevention of traumatic brain injury is a very important aspect of preventive medical science. This paper proposes a new coupled loading-rate hypothesis for the traumatic brain injury (TBI), which states that the main cause of the TBI is an external Euclidean jolt, or SE(3)-jolt, an impulsive loading that strikes the head in several coupled degrees-of-freedom simultaneously. To show this, based on the previously defined covariant force law, we formulate the coupled Newton-Euler dynamics of brains micro-motions within the cerebrospinal fluid and derive from it the coupled SE(3)-jolt dynamics. The SE(3)-jolt is a cause of the TBI in two forms of brains rapid discontinuous deformations: translational dislocations and rotational disclinations. Brains dislocations and disclinations, caused by the SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum brain model. Keywords: Traumatic brain injuries, coupled loading-rate hypothesis, Euclidean jolt, coupled Newton-Euler dynamics, brains dislocations and disclinations
In this paper we consider chemotherapy in a spatial model of tumor growth. The model, which is of reaction-diffusion type, takes into account the complex interactions between the tumor and surrounding stromal cells by including densities of endothelial cells and the extra-cellular matrix. When no treatment is applied the model reproduces the typical dynamics of early tumor growth. The initially avascular tumor reaches a diffusion limited size of the order of millimeters and initiates angiogenesis through the release of vascular endothelial growth factor (VEGF) secreted by hypoxic cells in the core of the tumor. This stimulates endothelial cells to migrate towards the tumor and establishes a nutrient supply sufficient for sustained invasion. To this model we apply cytostatic treatment in the form of a VEGF-inhibitor, which reduces the proliferation and chemotaxis of endothelial cells. This treatment has the capability to reduce tumor mass, but more importantly, we were able to determine that inhibition of endothelial cell proliferation is the more important of the two cellular functions targeted by the drug. Further, we considered the application of a cytotoxic drug that targets proliferating tumor cells. The drug was treated as a diffusible substance entering the tissue from the blood vessels. Our results show that depending on the characteristics of the drug it can either reduce the tumor mass significantly or in fact accelerate the growth rate of the tumor. This result seems to be due to complicated interplay between the stromal and tumor cell types and highlights the importance of considering chemotherapy in a spatial context.
Mathematical models of cardiac electrical excitation are increasingly complex, with multiscale models seeking to represent and bridge physiological behaviours across temporal and spatial scales. The increasing complexity of these models makes it computationally expensive to both evaluate long term (>60 seconds) behaviour and determine sensitivity of model outputs to inputs. This is particularly relevant in models of atrial fibrillation (AF), where individual episodes last from seconds to days, and inter-episode waiting times can be minutes to months. Potential mechanisms of transition between sinus rhythm and AF have been identified but are not well understood, and it is difficult to simulate AF for long periods of time using state-of-the-art models. In this study, we implemented a Moe-type cellular automaton on a novel, topologically correct surface geometry of the left atrium. We used the model to simulate stochastic initiation and spontaneous termination of AF, arising from bursts of spontaneous activation near pulmonary veins. The simplified representation of atrial electrical activity reduced computational cost, and so permitted us to investigate AF mechanisms in a probabilistic setting. We computed large numbers (~10^5) of sample paths of the model, to infer stochastic initiation and termination rates of AF episodes using different model parameters. By generating statistical distributions of model outputs, we demonstrated how to propagate uncertainties of inputs within our microscopic level model up to a macroscopic level. Lastly, we investigated spontaneous termination in the model and found a complex dependence on its past AF trajectory, the mechanism of which merits future investigation.
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