A mathematical modeling framework for simulating stem cell

A mathematical modeling framework for simulating stem cell differentiation fates in cell populations By S. D. Harrevelt, in collaboration with F. J. Vermolen Challenge the future 1

Content • Introduction • Mathematics • Simulations • Conclussion • Discussion • Future work Challenge the future 2

Introduction problem A mathematical modeling framework for simulating stem cell differentiation fates in cell populations Challenge the future 3

Introduction problem • The goal: Given the novel model, investigate how certain parameter choices result in different cell compositions. Then, relate the choice of parameters and the cell composition to a real life situation. Challenge the future 4

Introduction problem Parameters Model Outcome Parameters Outcome Challenge the future 5

Mathematics Stem cell differentiation • Challenge the future 6

Mathematics Governing equations Cell maturation Challenge the future 7

Mathematics Governing equations Cell movement Challenge the future 8

Mathematics Governing equations Diffusion equation – source vector Mechanical balance equation – force vector Challenge the future 9

Mathematics Governing equations Force vector Challenge the future 10

Mathematics Governing equations Challenge the future 11

Simulations Simulation examples Challenge the future 12

Simulations Simulation examples Challenge the future 13

Conclussion We have a working model. . . But there is still a lot of work Challenge the future 14

Discussion For example: the bouncing in the previous film was wrong A good set of parameters will help a lot Challenge the future 15

Future work • Find suiting parameters • Introduce mechanical strain energy • Validation of solutions • Head-tail-muscle model • Add cell cyclus/death/regeneration Challenge the future 16

Questions? Questions? Questions? Questions? Challenge the future 17