Growth and Remodeling in Biological Tissue

This lecture deals with growth and remodeling in different kinds of biological tissue (like arterial soft tissue, bone, skin) and introduces students both into the physiological foundations and mathematical models in this field. Topics include:
(1) Mathematical foundations of surface growth
(2) Mathematical foundations of volumetric growth
(3) Load-dependent adaption processes
(4) Growth and remodeling in arterial soft tissue
(5) Growth and remodeling in bone (6) Growth and remodeling in skin
(7) Growth and remodling in plants
Theory-centered content will be supplemented with sample calculations.

Participation in "Growth and Remodeling in Biological Tissue" will allow students to acquire a thorough understanding of the physiological basis of growth and remodeling processes in biological tissue. In particular, the distinction between the surface growth and volumetric growth as well as the differences among various tissue types will be recognized and mastered. Thus, students will gain the ability to develop and apply mathematical models for growth and remodeling processes and subsequently use those models for both qualitative and (in so far as the current state of the art allows) quantitative computations and estimtaes. Notably, upon participation in the course, students will understand the significance of growth and remodeling processes for designing prostheses and implants in medical engineering and command the ability to apply said knowledge on practical applications.

Content conveyed via the lectures "Numerical methods for engineers", "Nonlinear Continuum Mechanics" as well as the introductory courses of higher mathematics are prequisites.

The course will be conducted in a lecture format. Central concepts will be displayed using a tablet PC such that students have the opportunity to compose notes. The tutorial aspects of the lecture will have example calculations done by the students on their own as well as in conjunction with the instructor.

Presentation using a tablet PC, learning materials and problem tasks on the online platform, computer-based tasks (both utilising student-owned notebooks as well as institute PCs)

Jay D. Humphrey, An Introduction to Biomechanics: Solids and Fluids, Analysis and Design. Springer Verlag, NY, 2004; Yuan-Cheng Fung, Biomechanics - Motion, Flow, Stress, and Growth. Springer Verlag, NY, 1990

Learning success will be tested by a written exam at the end of the semester. A written instead of an oral exam will ensure a sufficiently objective examination of the students' ability to develop and independently apply mathematical models. The only tools allowed during the examination are a writing implement and a non-programmable calculator, since the main educational objective is establishing a thorough understanding not reliant on students merely looking up relevant approaches, formulae and facts, but instead knowing them explicitly by heart. The exam poses mathematical problems as well as more general questions testing for knowledge. Questions are posed both in a free-form and a multiple choice format. The cumulative grade is comprised only of the exam at the end of term.