Internal Biomechanics: Tissue and Muscle Mechanics Flashcards

Internal Biomechanics: Tissue and Muscle Mechanics

Overview of Internal Biomechanics

Core Topics: * Tissue mechanics. * Muscle mechanics (including eccentric and concentric actions). * Interaction with the environment. * Effect of internal and external forces.

Forces, Deformation, and Injury Loading

Experimental Context: Rubber Band Groups (G1 and G2): * Group 1 (G1): Consists of 1 rubber band. * Group 2 (G2): Consists of 5 rubber bands.
Loading Scenario A: Applying Equal Force: * When the same amount of force is applied to both groups separately, it results in unequal deformation ( $\Delta\text{ length}$ ). * Result: G1 (1 rubber band) is easy to break and exhibits greater deformation. G2 (5 rubber bands) is harder to break and exhibits smaller deformation.
Loading Scenario B: Applying Equal Deformation: * When G1 and G2 are lengthened to the same distance separately, it results from unequal forces. * Result: It requires significantly more force to lengthen G2 to the same distance as G1.
Key Principle: Force and deformation outcomes depend on the angle of application and the amount of force applied.

Stress: Standardizing the Loading

Definition of Stress ( $\sigma$ ): * Stress is a normalized loading to the analysis plane. * Verbatim Definition: "The intensity of the distributed force, F, distributed over an area, A." * Formula: $\sigma = \frac{F}{A}$ * Units: $N/m^2$ (Newtons per square meter) or Pascals ( $Pa$ ). * Variables: * $F$ : Internal force. * $A$ : Internal area (analysis plane).
Conceptual Explanation: Stress represents how much force is applied to a specific amount of area.

Anatomical Directions, Planes, and Motion

Anatomical Position Definitions: * Anterior: Forward (e.g., Patella is anterior to the knee joint). * Posterior: Backward. * Superior: Upward (e.g., Humerus is superior to the elbow joint). * Inferior: Downward (e.g., Tibia is inferior to the knee joint). * Medial: Toward the middle/midline (e.g., Ulnar is medial to the radius). * Lateral: Toward the sides (e.g., Radius is lateral to the ulnar).
Cardinal Planes of the Body: 1. Sagittal Plane: A vertical plane dividing the body into right and left parts. 2. Frontal (Coronal) Plane: Divides the body into anterior and posterior parts. 3. Transverse (Horizontal) Plane: Divides the body into superior and inferior parts.
Joint Motion Principles: * All segments rotate about a joint center. * Joint motions are defined based on anatomical positions, planes, and axes. * Examples: The lower leg rotates about the knee joint; the foot rotates about the ankle joint.

Types of Loading (Hsieh, Chapter 8)

1. Tensile Loading (Pull/Stretch): * Mechanism: Loading applied along the longitudinal axis of the body and perpendicular to the analysis plane. * Action: Forces pull apart, causing the body to lengthen. * Example: Tensed muscles such as a bicep curl; longitudinal pull/stretch of a ligament.
2. Compressive Loading: * Mechanism: Forces push into the tissue/body, "squishing" it toward the middle. * Direction: Along the longitudinal axis and perpendicular to the analysis plane (transverse/frontal/sagittal). * Action: Causes the body to shorten or deform. * Example: Body weight pushing down on bone tissue.
3. Shear Loading: * Mechanism: Forces act parallel to each other but in opposite directions (material sliding past each other). * Direction: Loading is applied medially-laterally; acts parallel to the analysis plane (perpendicular to frontal/sagittal, parallel to transverse). * Example: The tibia sliding forward or backward relative to the femur.
4. Torsion Loading: * Mechanism: Due to torque applied on the longitudinal axis of the body at each end. * Action: A rotational form of shear stress; twisting along the longitudinal line. * Example: spine torsion when landing and upper body rotates while feet are fixed; walking creates torsion in the leg.
5. Bending (Complex Loading): * Mechanism: A combination of tensile and compressive stress within the same internal structure. * Stress Profile: One side of the material experiences compression while the opposite side experiences tension. * Real-world Example: Standing on a single leg puts 60% of body weight pushing down on the femoral head. Because the femur is stabilized, bending occurs on the neck of the femur.
6. Combination Loading: * A single bone may experience weight-bearing (compression), twisting (torsion), and muscle action (tension) simultaneously.

Stress and Strain Relationship

Strain ( $\epsilon$ ): * Definition: The measurement of deformation from the original length, often expressed as a percentage. * Conceptual Distinction: Stress is the cause (load); strain is the effect (deformation). * Formula: $\epsilon = \frac{l_f - l_i}{l_i} = \frac{\Delta l}{l_i}$ \text{% Strain} = \frac{\Delta l}{l_i} \times 100 * Units: Dimensionless (ratio), but often expressed as decimal or percentage.
Stiffness and Young's Modulus: * The slope of the stress-strain curve represents the stiffness of the material. * Young's Modulus ( $E$ ): $E = \frac{\Delta \sigma}{\Delta \epsilon}$ * Interpretation: A steeper slope indicates a stiffer material (higher Young's Modulus). For example, it requires more stress to lengthen 10 rubber bands than one single band to the same distance; therefore, 10 bands have greater stiffness.

Stress-Strain Regions and Landmarks

Elastic Region: The area where the material deforms under stress but returns (recoils) to its original shape/length when the stress is removed.
Yield Point: The end of the linear elastic region. Stress beyond this point leads to the plastic region.
Plastic Region: The area where further stress results in permanent deformation. Even after stress is removed, the material will not return to its original length; it has a new shape.
Landmarks: * Yield Strength: The stress level at the yield point; identifies the transition from elastic to plastic behavior. * Ultimate Strength: The maximum stress a material is capable of withstanding before starting to fail. * Failure Strength: The stress level at which the material ruptures or breaks (total rupture).
Toe Region: Seen in muscle-tendon units; a period of easy stretch where tissue is relaxed and does not require high levels of stress initially.

Toughness and Mechanical Energy

Definition: Toughness is the material's ability to absorb mechanical energy before breaking.
Measurement: Represented by the total area under the stress-strain curve (Combination of stress and strain capacity).
Verbatim Principles: * Toughness is the capacity to do work ( $W = F \times d$ ). * Brittle Materials: Can handle high stress but show minimal strain (deformation) before failure (e.g., dry bone, a sliding glass door). These are "strong but fragile" or not tough. * Tough Materials: Can handle both high stress and high strain before failure (e.g., live bone vs. dry bone).

Composition of Connective Tissues

Constituents: Cell, Collagen, Elastin, Ground Substance, Mineral, Water.
Water Content by Tissue Type: * Bone: 20% to 30% water (contains 45% mineral). * Cartilage: 20% to 70% water. * Tendon and Ligament: 25% to 70% water.

Viscoelasticity

Definition: Biological tissues are viscoelastic, meaning stress and strain behaviors depend on the rate and type of loading. Behaviors include: * Creep: Under a constant compressive stress, strain increases over time as water is squeezed out of the tissue until strain reaches a maximum. * Stress Relaxation: Under a constant compressive strain, stress initially increases as water is squeezed out, reaches a maximum, and then decreases (relaxes) to a lower value. * Hysteresis: The phenomenon where the loading and unloading paths on a stress-strain curve are different. Energy is lost (usually as heat) during the cycle.
Mechanical properties across directions: * Isotropic: Same mechanical properties in every direction. * Anisotropic: Different mechanical properties in different directions (typical of biological tissues).

Specific Tissue Mechanics: Bone and Cartilage

Bone Categories: * Cortical Bone: "Compact" bone; stiff; sustains roughly 2% of maximum strain before failure. * Cancellous Bone: "Spongy" or trabecular bone; handles more deformation than cortical bone before breaking but has less overall strength. * Ultimate Strength of Bone (Loading Modes): * Compression: $200\,MPa$ * Tension: $125\,MPa$ * Shear: $65\,MPa$ * Mechanical Reference: $1\,MPa = 145\,lb/in^2$ (Transcript note suggests a variant of $125\,lb/in$ as well).
Cartilage Structure: * Composed of 70% water and 20% collagen fiber. * Collagen Fiber Arrangement: * Surface: Parallel to the surface. * Middle: Randomly arranged. * Deep (near bone): Perpendicular to the surface.

Tendon and Ligament Mechanics

Functional Goal: Ligaments connect bone-to-bone to stabilize the joint.
Typical Maximum Strain: Approximately 8-10%.
Stress-Strain Regions for Tendons/Ligaments: 1. Toe Region (Region 1): Physiological loading; slack is taken up. 2. Linear Region (Region 2): Consistent elastic behavior. 3. Partial Rupture (Region 3): Microfailures occur. 4. Complete Rupture (Region 4): Total failure/injury.

Practice Problems and Calculations

Ligament Strain Calculation: * Given: Initial length ( $l_i$ ) = $1\,cm$ ; Final length ( $l_f$ ) after loading = $1.001\,cm$ . * Calculation: $\epsilon = \frac{1.001 - 1.0}{1.0} \times 100 = 0.1\%$
Achilles Tendon Elongation: * Given: Initial length = $10\,cm$ ; Strain = $6\%$ . * Calculation: $\Delta l = 10\,cm \times 0.06 = 0.6\,cm$ $l_f = 10.6\,cm$
Young's Modulus Calculation (from Graph Data): * Given points: $(X_1, Y_1) = (0.01, 20)$ , $(X_2, Y_2) = (0.02, 40)$ . * Formula: $E = \frac{40 - 20}{0.02 - 0.01} = \frac{20}{0.01} = 2000\,kN/m/m$