Structure of Biological Materials
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1 ELEC ENG 3BA3: Structure of Biological Materials Notes for Lecture #7 Monday, September 24, 2012
2 3.2 Muscle biomechanics Organization: skeletal muscle is made up of muscle fibers each fiber is a single cell the contraction of a fiber is achieved by the motor proteins actin & myosin (from Guyton and Hall, 10 th Edition) 2
3 Fiber orientation: muscles that undergo large length changes or high velocities usually have long fibers running lengthwise muscles that undergo only small length changes but are required to produce large forces or stiffness have fibers arranged at an angle to the tendons to which they are attached 3
4 Muscle fiber innervation: 1. Motor neuron 2. Peripheral nerve 3. Neuromuscular junction 4. Muscle Motor unit: A motor unit is defined as an individual motor neuron plus all the muscle fibers that are innervated by that neuron. 4
5 Neuromuscular junction: 5
6 Steps in muscle fiber contraction 1. Motor neuron action potential 2. Action potential propagation along motor axon (myelinated fiber) 3. Transmission of acetylcholine (ACh) at neuromuscular junctions (synapses) 4. Action potential generation in muscle fiber 5. Release of Ca 2+ from sarcoplasmic reticulum initiates attractive forces between actin & myosin filaments, causing them to slide alongside each other ) muscle contraction 6. Return of Ca 2+ to sarcoplasmic reticulum, ending muscle contraction 6
7 Actin & myosin filament movement: (from Guyton and Hall, 10 th Edition) 7
8 Fiber types 1. Fast twitch large fibers, for greater contraction strength extensive sarcoplasmic reticulum for rapid release of Ca 2+ large amounts of glycolytic enzymes less extensive blood supply fewer mitochondria 8
9 2. Slow twitch smaller fibers innervated by smaller nerve fibers (axons) more extensive blood vessel system more mitochondria large amounts of myoglobin, speeding oxygen transport 9
10 Muscle fiber mechanics The main factors in determining muscle fiber contractile force are: 1. Velocity of contraction 2. Length of muscle fiber (relative to its resting length) 3. Neural activation 10
11 Force versus velocity: where F is the contractile force (N), v is the contractile velocity (lengths s -1 ), and F 0, a & b are constants. F 0 corresponds to the force when v = 0, i.e., during an isometric contraction. v max = bf 0 /a, when F = 0. 11
12 Force versus velocity (cont.): Often the stress value (P 0 = F 0 /A) is used instead of F 0, where A is the physiological cross sectional area obtained by dividing the muscle volume by its length. P 0 is generally between 100 and 300 kpa, and does not depend on the metabolic fiber type (fast or slow twitch). However, v max depends on the fiber type. 12
13 Force versus fiber length: 13
14 Force versus fiber length (cont.): (from Guyton and Hall, 10 th Edition) 14
15 Force versus activation: individual motor neuron action potentials produce a contractile force in a motor unit referred to as a twitch twitches begin to fuse as the action potential frequency increases above the fusion frequency the motor unit produces its maximum ( tetanic ) force 15
16 Force versus activation (cont.): The total muscle force is modulated by: the frequency of twitches in each of a muscle s motor units ) rate coding and the number of motor units being activated ) recruitment 16
17 3.3 Joint and limb biomechanics The movement of individual limbs or sets of limbs can be understood in terms of: translational forces and the resulting translational movements, and rotational moments and the resulting rotation around an axis (either a COM or a joint). 17
18 Free-body diagrams can be used to calculate the net translational force F acting on a limb: 18
19 The net moment M acting on a limb to cause rotation around a joint (or the COM) can also be found from the free-body diagram: 19
20 Newton s Equations of Motion: For the translational forces F i (acting through the axis of rotation), Newton s second law of motion gives the net force F resulting in the net translational acceleration a according to: 20
21 For the rotational moments M i (acting around the axis of rotation), the net moment M gives rise to an angular acceleration α according to: 21
22 An individual moment is the vector cross product of the lever arm vector r i and the force vector F i : The magnitude M i of the moment is given by: 22
23 The quantity sin(µ) r i is often referred to as the moment arm. This can be interpreted as the perpendicular distance from the line of the force to the axis of rotation. Alternatively, the quantity sin(µ) F i can be interpreted as the component of the force that is perpendicular to the lever arm. (Note: in some publications the definitions of the lever arm and moment arm are reversed, so be careful to check the definitions.) 23
24 Joint power: where M is the net joint moment (N m) and ω is the angular velocity (rad s -1 ). 24
25 Experimentally: joint kinematics are obtained using motioncapture techniques GRF moment arm is determined from a combination of the kinematic analysis and the force platform technique muscle moment arms are obtained from external measurements and/or medical imaging 25
26 Net joint moments during walking: 26
27 Net joint moments during running: 27
28 Net joint power during running: 28
29 29
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