1. Macro- to Micromechanics Tissue Mechanics – BME 615 Ray Vanderby University of Wisconsin

2. Why study micro-level phenomena when functional tissue behavior is usually at a meso- or macro-level? Consider Wolff’s Law (1892) as an example (Julius Wolff, Prof of Surgery and Anatomy, U of Berlin) –Trabeculae are sculpted to lie on axes of principal stress –Based on observation of cancellous bone architecture –Assumed that trabecular architecture could be predicted by a mathematical law related to principal stress of ECM

4. J Wolff proposed theory based on observations of normal and pathologically formed or loaded bones

5. Observations to support Wolff’s Law (besides Wolff’s evidence) Racquet-holding arm bones of tennis players become much stronger with thicker bones than those of the other arm. Astronauts who spend an extended time in space in microgravity return to Earth with significantly weaker (osteopenic) bones. Their bodies have resorbed some of calcified matrix that was previously their bones. Weightlifters often display increases in bone density in response to their training. Fighters punch or kick objects with increasing intensity (or of increasing hardness) to develop striking power. Often this produces an increases in bone density in the striking area. University of Wisconsin

6. Equilibrium Zone Signal Optimal Bone Loading Mechanobiology -bone remodeling Bone Remodeling Resorption Rate 1 Growth Rate 1 Bone Remodeling Signal Is often a function of: με - “apparent” microstrain magnitude N - # of repetitions + -

7. Algorithms can be formulated to model mechanically driven bone remodeling, but What is the “SIGNAL”???? Many mechanical parameters weakly correlate, e.g. for trabecular bone, R Bruce Martin suggests: where

8. Von Mises Stress Need single metric to predict density changes in bone --- SED? Von Mises Stress?

9. FEM Adaptation Theories

10. Huiskes et al. offer mech concept for tissue differentiation at bone-prosthesis interface

11. Weinans, Huiskes algorithm to model mechanically driven bone remodeling

12. Phenomenological mechanobiology to predict prosthesis-bone remodeling  At what level can a static, mechanically based model be predictive and useful?  How accurate can it be?  What about biology?  GF & soluble signals  Blood supply & nutrition  Cells  Etc, etc, etc.  “With 4 parameters I can fit an elephant, and with 5, I can make him wiggle his trunk.” John von Neumann “There’s no sense being precise when you don’t even know what you’re talking about.”

13. Some issues with biomechanical adaptation theories  Remodeling on neutral axis of turkey ulna in bending  Consideration for the number of loading cycles  Consideration for the rate of loading (rate reduces strain level for effect and high static load causes bone resorption)  Stress/strain is 2 nd order tensor – what directional info does one use?  What does the bone know about SED?  What does bone know about von Mises stress?  Why would a trabecular bone CELL care about apparent stress at all?  Trabecular struts forming circles will have tension AND compression AND no stress in close proximity to each other, what’s a bone to do?  What about marrow and fluids and CELLS?  What about hormones, nutrition, age, growth factors?  In vitro strain levels necessary for adaptive response do not correspond to in vivo bone strains.  Control with BMPs or bisphosphonates, etc. more dramatic. RAP  Peter Muir’s studies on neuro-system effects to contralateral limb??

14. Clint Rubin - his observations and conundrums After many years he found an osteogenic frequency 10-50Hz

15. Vibration increase bone density (and decreases fat – see Rubin papers) Sheep study 30 Hz at amplitude of ~5 με 20 min/day for 1 yr ↑ bone density by 32% Mouse study ↓ adipogenesis by 27% in 15 wks ↓fat production by 22% in 9 wks

16. Vibration increase bone density 30 Hz at amplitude of ~5 με 20 min/day for 1 year ↑ bone density by 32%

17. Repeal Wolff’s Law?? Steve Cowin now calls Wolff’s Law “A false premise..” and “the rigid mathematical form… is not valid” Cowin later used poroelasticity to describe remodeling with osteocytes in lacunae affected by fluid movement through canaliculi which is induced by deformation of surrounding solid matrix. Consider “law” to be philosophical statement synonymous with the phrase “functional adaptation” Applied to many tissues (e.g. ligament, vascular tissue, cortical bone, heart valves) Can be correlative in controlled settings – still useful! Since ECM stress (strain, SED, etc.) is not robustly predictive, most research has focused on cells Should investigate “mechanotransduction” at cell level!

18. Mechano-transduction How do cells sense load? How do they respond to load? First we need to learn about cells and how they work (e.g. CSK, focal adhesions, integrins, protein synthesis mechanisms, cell motility, molecular motors, etc.) Then we need to study the mechanisms of mechano-transduction. University of Wisconsin