Biomechanics Study Guide

📖 Core Concepts Biomechanics – Study of structure, function, and motion of biological systems using mechanics; spans from whole organisms to proteins. Continuum assumption – Treats tissue/fluid as a continuous material; breaks down when length scales approach micro‑structural features. Linear elasticity – Appropriate for hard tissues (bone, shell, wood) where deformations are small. Finite‑strain theory – Required for soft tissues (skin, tendon, muscle, cartilage) that experience large deformations. Navier–Stokes equations – Governing equations for incompressible Newtonian flow (e.g., blood in large vessels). Fahraeus–Lindquist effect – In vessels only slightly larger than a red blood cell, apparent viscosity drops, lowering wall shear stress. Inverse Fahraeus–Lindquist effect – In vessels smaller than a red blood cell, cells travel single‑file, raising wall shear stress. Biotribology – Mechanics of friction, wear, and lubrication in biological joints (hip, knee). Finite Element Method (FEM) – Numerical technique to solve complex biomechanical boundary‑value problems (stress, heat, mass, electricity). --- 📌 Must Remember Blood flow in major arteries ≈ incompressible Newtonian → use Navier–Stokes. Wall shear stress (τₛ) decreases with Fahraeus–Lindquist effect, increases with inverse effect. Hard tissue modeling → linear elasticity (stress ∝ strain). Soft tissue modeling → finite‑strain (non‑linear stress‑strain). Wolff’s law – Bone remodels in response to mechanical loading patterns. Biomechanical hierarchy – Molecular → cellular → tissue → organ → whole‑body. Key tools – Force platforms, motion capture, EMG, strain gauges, optical tweezers, acoustic force spectroscopy. --- 🔄 Key Processes Modeling Blood Flow Identify vessel size → decide Newtonian vs. particulate model. Apply Navier–Stokes: $$\rho\left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v}\cdot\nabla\mathbf{v}\right) = -\nabla p + \mu\nabla^2\mathbf{v} + \mathbf{f}$$ Adjust wall shear stress based on Fahraeus–Lindquist (large) or inverse (tiny) effect. Finite Element Analysis Workflow Define geometry → mesh (elements). Assign material model (linear elastic for bone, hyper‑elastic for cartilage). Apply boundary conditions (forces, displacements, pressures). Solve → post‑process stresses/strains. Joint Wear Assessment (Biotribology) Measure contact pressure & sliding velocity. Determine lubrication regime (boundary, mixed, fluid film). Calculate wear volume using Archard’s law: $$V = k \frac{F \, s}{H}$$ where k = wear coefficient, F = normal load, s = sliding distance, H = hardness. Neuromechanical Experiment Record motion capture → joint kinematics. Simultaneously acquire neural signals (EMG, cortical recordings). Correlate activation patterns with joint torques to infer motor‑unit recruitment. --- 🔍 Key Comparisons Newtonian vs. Non‑Newtonian blood models Newtonian: constant viscosity → valid in large vessels. Non‑Newtonian: viscosity varies with shear rate → needed in arterioles, capillaries. Hard tissue vs. Soft tissue modeling Hard: linear elasticity, small strains. Soft: finite‑strain (hyper‑elastic), large strains. Fahraeus–Lindquist vs. Inverse Fahraeus–Lindquist F‑L: vessel ≈ RBC size → ↓ viscosity → ↓ wall shear stress. Inverse: vessel < RBC size → single‑file flow → ↑ wall shear stress. Biotribology (joint) vs. Biotribology (tissue‑engineered cartilage) Joint: natural lubrication (synovial fluid). Engineered: often dry or artificial lubricants; focus on subsurface damage. --- ⚠️ Common Misunderstandings “Blood is always Newtonian.” – Only true in large arteries; microcirculation exhibits significant non‑Newtonian behavior. “All tissues can be modeled with linear elasticity.” – Soft tissues undergo large deformations; linear models underestimate stresses. “FEM gives exact answers.” – Results depend on mesh quality, material model, and boundary condition fidelity. “Higher shear stress always damages vessels.” – Physiological shear stress can be protective; pathological levels (very high or low) are harmful. --- 🧠 Mental Models / Intuition “Scale determines physics.” – When the characteristic length > cell size → continuum, Newtonian fluid; when comparable → discrete cell effects dominate (Fahraeus–Lindquist). “Stiffness hierarchy.” – Think of bone as a steel beam (linear), tendon as a rubber band (non‑linear). “Joint as a lubricated hinge.” – Low friction when fluid film is thick; wear spikes when film thins (boundary lubrication). --- 🚩 Exceptions & Edge Cases Microvascular flow – RBCs dominate rheology; classic Navier–Stokes fails. Highly anisotropic tissues (e.g., myocardium) – Require direction‑dependent material models, not isotropic linear elasticity. Very high strain‑rate impacts (e.g., blast injury) – Viscoplastic or rate‑dependent models needed. --- 📍 When to Use Which Navier–Stokes → Large vessels, steady or pulsatile flow, Newtonian assumption acceptable. Particle‑based or Casson model → Arterioles, capillaries, where cell‑cell interactions matter. Linear elasticity → Bone, shell, wood, any material with small deformations (<5%). Finite‑strain (hyper‑elastic) → Skin, tendon, muscle, cartilage, large deformation problems. FEM vs. analytical solution → Use FEM when geometry, loading, or material behavior is complex; analytical only for simple, idealized cases. --- 👀 Patterns to Recognize “Diameter ≈ RBC size → Fahraeus–Lindquist” – Look for wording about “slightly larger than a red blood cell.” “Non‑linear stress‑strain curve → soft tissue” – Presence of large strain percentages. “Wear + lubrication regime → joint health” – Any mention of synovial fluid, cartilage, or implant wear. “Computational prediction → experimental design” – Statements about using FEM to plan or interpret experiments. --- 🗂️ Exam Traps Distractor: “Blood is always modeled as incompressible Newtonian.” – Wrong for micro‑circulation; expect a nuance about vessel size. Distractor: “All soft tissues can be approximated with linear springs.” – Soft tissues need finite‑strain theory; linear springs oversimplify. Distractor: “Higher wall shear stress always improves vascular health.” – Only physiological ranges are beneficial; extremes are pathological. Distractor: “Finite element analysis eliminates the need for experimental validation.” – FEM complements, not replaces, experiments. ---