In the literature different computational models for predicting tumor initiation and proliferation have been proposed in recent years [Araujo and McElwain 2009, Quaranta et al. 2005, Roose et al. 2007, Lowengrub et al. 2010]. Here, a novel mathematical approach based on the Thermodynamically Constrained Averaging Theory (TCAT) is presented and applied to either tumor initiation prediction or diabetic ulcer initiation. The common aspects in the respective models at continuum level are the balance equations governing the phenomena and some of the constitutive equations; in this work, similarities and dissimilarities between the two models are analyzed. TCAT [Gray et al 2005, Gray et al 2012] is a framework recently established for the analysis of continuum and porous media, which is consistent over multiple scales. It provides a rigorous yet flexible method for developing multiphase, continuum models at any scale of interest. TCAT uses averaging theorems to formally and consistently convert microscale equations to the larger macroscale. These averaging theorems convert averages of microscale derivatives into derivatives of macroscale averages and share some features of the well-known transport and divergence theorems. Tumor growth in the avascular stage results from cells resisting death, evading growth suppressors and from sustaining proliferative signaling while diabetic foot ulcers result from the simultaneous action of multiple contributing causes [Lavery et al. 1998, Armstrong et al. 1998]; the major are peripheral neuropathy and ischemia from peripheral vascular disease. Neuropathy in diabetic patients is manifested in the motor, autonomic, and sensory components of the nervous system [Bowering et al. 2001]. Peripheral arterial disease affects the tibial and peroneal arteries: endothelial cell dysfunction leads to constriction and the increased thromboxane A2 leads to an increased risk for plasma hypercoagulability. There is also the potential for alterations in the vascular extracellular matrix leading to stenosis of the arterial lumen [Paraskevas et al. 2008]. Cumulatively, this leads to occlusive arterial disease that results in ischemia [Boulton et al 2008, Paraskevas et al 2008, Zochodone et al. 1999]. The diabetic foot biological-tissue model considered herein consists of three phases: one solid and two fluids. The cells maintain tissue integrity by cell to cell contact, and the extracellular matrix (ECM) acts as a scaffolding system to give the tissue more structure and rigidity. In our model the ECM components of a tissue will be treated as a single solid phase. The governing equations will be solved by the finite element method. To solve displacements properly for the solid phase, we need appropriate boundary conditions. These are obtained by embedding the ulcer model in a higher order one, i.e. the foot biomechanics model. The whole formulation is multiscale and multiphysics and will be solved with a staggered approach.

Application of a Computational Tumor Growth Model to Diabetic Foot Ulcer Prevention

GUIOTTO, ANNAMARIA;SAWACHA, ZIMI;AVOGARO, ANGELO;BOSO, DANIELA;SCHREFLER, BERNHARD;COBELLI, CLAUDIO
2012

Abstract

In the literature different computational models for predicting tumor initiation and proliferation have been proposed in recent years [Araujo and McElwain 2009, Quaranta et al. 2005, Roose et al. 2007, Lowengrub et al. 2010]. Here, a novel mathematical approach based on the Thermodynamically Constrained Averaging Theory (TCAT) is presented and applied to either tumor initiation prediction or diabetic ulcer initiation. The common aspects in the respective models at continuum level are the balance equations governing the phenomena and some of the constitutive equations; in this work, similarities and dissimilarities between the two models are analyzed. TCAT [Gray et al 2005, Gray et al 2012] is a framework recently established for the analysis of continuum and porous media, which is consistent over multiple scales. It provides a rigorous yet flexible method for developing multiphase, continuum models at any scale of interest. TCAT uses averaging theorems to formally and consistently convert microscale equations to the larger macroscale. These averaging theorems convert averages of microscale derivatives into derivatives of macroscale averages and share some features of the well-known transport and divergence theorems. Tumor growth in the avascular stage results from cells resisting death, evading growth suppressors and from sustaining proliferative signaling while diabetic foot ulcers result from the simultaneous action of multiple contributing causes [Lavery et al. 1998, Armstrong et al. 1998]; the major are peripheral neuropathy and ischemia from peripheral vascular disease. Neuropathy in diabetic patients is manifested in the motor, autonomic, and sensory components of the nervous system [Bowering et al. 2001]. Peripheral arterial disease affects the tibial and peroneal arteries: endothelial cell dysfunction leads to constriction and the increased thromboxane A2 leads to an increased risk for plasma hypercoagulability. There is also the potential for alterations in the vascular extracellular matrix leading to stenosis of the arterial lumen [Paraskevas et al. 2008]. Cumulatively, this leads to occlusive arterial disease that results in ischemia [Boulton et al 2008, Paraskevas et al 2008, Zochodone et al. 1999]. The diabetic foot biological-tissue model considered herein consists of three phases: one solid and two fluids. The cells maintain tissue integrity by cell to cell contact, and the extracellular matrix (ECM) acts as a scaffolding system to give the tissue more structure and rigidity. In our model the ECM components of a tissue will be treated as a single solid phase. The governing equations will be solved by the finite element method. To solve displacements properly for the solid phase, we need appropriate boundary conditions. These are obtained by embedding the ulcer model in a higher order one, i.e. the foot biomechanics model. The whole formulation is multiscale and multiphysics and will be solved with a staggered approach.
2012
Proceedings of the First NEMB Venice Workshop on "CANCER NANOTECHNOLOGY"
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2532955
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