Design of a Tri-Phasic Biomechanical Model Describing Healthy and Cancerous Tissue

Open Access
Barber, Kathryn Irene
Area of Honors:
Engineering Science
Bachelor of Science
Document Type:
Thesis Supervisors:
  • Corina Stefania Drapaca, Thesis Supervisor
  • Judith A Todd, Honors Advisor
  • Patrick James Drew, Faculty Reader
  • computational modeling
  • tri-phasic model
  • cancer
  • brain tissue
  • magnetic resonance elastography
  • non-invasive diagnostic procedures
The ever-growing field of non-invasive diagnostic technologies is continually providing new insights into in vivo biological processes, requiring joint efforts among researchers in medicine, science, and engineering. One of these emerging technologies, Magnetic Resonance Elastography (MRE), uses an imaging technique to measure the elasticity of biological tissues subject to mechanical stresses. The resulting strains are measured using Magnetic Resonance Imaging (MRI) and the related elastic modulus is computed from models of tissues mechanics. The elastic modulus contains important information about the pathology of the imaged tissues. For example, fibrotic tissue in the liver is much less elastic than healthy tissue, and malignant tumors are more elastic than benign tumors. Thus, MRE can help in tumor detection, determination of characteristics of disease, and in assessment of rehabilitation. The biomechanical models used so far in MRE are classic macroscopic models which do not incorporate any relevant information about the electro-chemical processes that take place in the microstructure of the tissue. A novel multiscale model is presented that may differentiate not only between healthy and diseased tissues but also between benign and malignant tumors. The tissue is modeled as a triphasic material of porous, viscoelastic solid filled with interstitial fluid and dissolved ions. A recently-developed homogenization technique for materials with evolving microstructure was used to approximate a periodic microscopic structure.