Biomechanical modelling of tumor classification and growth

Open Access
Author:
Palocaren, Antony J
Graduate Program:
Engineering Mechanics
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
April 01, 2011
Committee Members:
  • Corina Stefania Drapaca, Thesis Advisor
Keywords:
  • tumor modelling
Abstract:
Palpation is an important clinical diagnostic practice which is based on the fact that tumors tend to be stiffer than the surrounding normal tissue. None of the modern, non-invasive, imaging modalities (such as CT scan, Magnetic Resonance Imaging, or Ultrasound) used today by radiologists to find and diagnose tumors provides the critical information about the stiffness of the imaged tissues. The work presented in this thesis is based on the clinical observation of palpation and focuses on testing the following hypothesis: the Young’s modulus of tissues helps differentiating not only between normal and abnormal tissues but, most importantly, between benign (not cancerous) and malignant (cancerous) tumors. We will show some preliminary results on tumor classification and growth with the help of biomechanical modeling. First, we propose a novel mechanical model of differentiating between benign and malignant tumors based on their corresponding Young’s moduli obtained using information about tissue microstructure provided by imaging mass spectrometry. Imaging mass spectrometry is a new technology that can provide a molecular assessment of tumor progression and treatment obtained from biopsies, with the potential to identify tumor subpopulations and predict patient survival that is not evident based on the cellular phenotype determined histologically. Our second biomechanical model shows how the mechanical properties of tumors affect their growth. By replacing the first order temporal derivative in this mechano-growth model with a fractional order derivative we are able to predict for the first time when a benign tumor turns into cancer. We used the Adomian method to find analytic solutions to the non-linear classic and fractional-order ordinary differential equation corresponding to our second model.