Fundamentals of Biomedical Engineering

INTRODUCTION

1.The upper and lower limbs were evolved basically for bearing the weight of the body and for locomotion as it is seen in quadrupeds (eg. cows and dogs). Therefore the two pairs of limbs are formed on the similar basic pattern. The evident similarities of upper and lower limbs are :

2.Due to the evolution of erect posture in man, the function of weight bearing was taken over entirely by the lower limbs. As a result of this removal of function of load bearing, the upper limbs (specially the hands) became free. Hands were gradually evolved into the organs having greater manipulative skill. The upper limbs started performing different functions. Hence the apparent difference between the upper and lower limbs is as a result of the difference of functions.

Evolution

Change of Posture

The division of the upper limbs with bones and joints are:

3.The forces involved on various joints can be classified as (1) internal forces (2) external forces. Internal forces are developed in muscles and joint reactions. External forces are gravitational force and mechanical applied forces. To apply the principles of statics to analyze the mechanics of human joints, following assumptions are made :

(a) Only one muscle groups controls the movement of joint

(b) Muscle attachment is at a joint which is known

(c) The line of action of muscle tension is known

(d) Proper point of joint at which joint can rotate is known

(e) Segmental weight of the parts of body with their centre of gravity are known

(f) Frictional forces at joints are small & negligible

(g) All forces acting on a joint are coplanar

(h) Deformation is small and negligible in muscles, bones and tendons etc

(k) Dynamic effect is ignored

MECHANICS OF THE SHOULDER

1.Shoulder joint: It is also called glenohumeral joint between hemispherical humeral head (ball) and the shallowly concave glenoid fossa (socket) of the scapula bone. Hence it is a ball and socket joint which permits variety of movements to the arm. The movements allowed are flexion and extension, abduction and adduction, outward rotation and inward rotation. The configuration of the articular surfaces of this joint makes the joint more susceptible to instability. The stability of the joint is due to the presence of ligaments and muscles. Ligaments are glenohumeral and coracohumeral while the major muscles of the joint are :

2.The shoulder girdle consists of the clavicle (collarbone) and scapula (shoulder blade). The acromioclavicular joint gives small synovial articulation between acromion of the scapula and the distal clavicle. Coracoclavicular ligaments join these two bones. The sternoclavicular joint is a saddle synovial joint and it gives articulation between sternum and clavicle. Costoclavicle ligaments join these bones and provide stability. Both these joints of clavicle with sternum and scapula have layers of cartilage (called menisci) interposed in between the joints. There are six types of movement possible as shown in the figure. There are 6

muscles that control and coordinate these movements viz. trape = 145, levator scapulae, rhomboid pectoralis minor, serratus anterior and subclavius.

Sternoclavicular and Acromioclavicular Joints

3.The shoulder joint is very susceptible to injuries like dislocation of the joint & the fracture of the humerus bone. As the head of humerus is relativity free to rotate about the articulating surface of the glenoid fossa the freedom of movement is gained by

reduced joint stability. The humeral head is likely to be displaced if external loading is more than the strength of the muscles and ligaments.

ANALYSIS OF FORCE ON THE SHOULDER JOINTS

1.Case study 1: Let us take a typical case of

arm stretched fully & holding a weight (Wb) as shown in the figure. Free body diagram of the arm is also shown. The shoulder joint is at point A, deltoid muscle is attached at point B; center of gravity of the arm is at point C and weight in hand is acting at point D. The force F is developed by deltoid muscle at point B which makes an angle α

with horizontal. The reaction R acts at the joint which makes an angle β with horizontal. The weight of the arm (W) acts vertically downwards at point C. The weight held in hand also acts vertically downwards at point D. The mechanical model of the arm is also shown. The distances of point B, C, & D from point A are a, b, and c respectively. Now we have a coplanar force system in equilibrium which gives us three equations

of equilibrium i.e. Σ Px = O, Σ PY = 0 & Σ M = O.

M uscle

Shoulder Joint

w b

Arm Abducted Horizontally

Free Body Diagram of Arm

a

b

c

Mechanical Model of Arm

Σ Py = 0, – R sin β + F sin α – W– Wb = 0

Σ MA = 0, – F sin a × a + W × b + Wb × c = 0

... (iii)

If we have been given the value of a = 20, b = 40, c = 60, α = 12°, m = 4 Kg

(W = 4× g = 4 × 10 = 40 N), mb= 5 Kg (Wb = 5 ×10 = 50 N) then substituting these

values in equations (i), (ii) and (iii)

From eqn (vii) and (viii) tan β = 0.123

β = 7

=1056.5

2.Case study 2: Consider an athlete is strengthening his shoulder joint by lowering and raising a bar bell with arms straight while lying down as shown in figure below. The weight of the bar bell is Wb at a distance

‘b’ from the shoulder joint (point D) and Wa is weight of the arms acting at a distance ‘a’ from the shoulder joint. Now we can analyse the force system, when the arm is making an angle θ with horizontal.

M0 = Wa × a cos θ + Wb × b cos θ.

If we take, a = 30 cm, b = 60 cm, Wa = 60 N and Wb = 300 N

M0 = 60× 0.30 cos θ + 300×0.60 cos θ

=(18 +18) cos θ

=36 cos θ

The moment at the shoulder joint varies as per the angle θ. It is maximum when θ = 0 (arm is horizontal) and zero when θ = 90 (arm is vertical).

b

W b

Free Body and Mechanical Model of Arm

MECHANICS OF THE ELBOW

1.The elbow joint has three bones viz humerus, radius and ulna. Humerus lies in upper arm while radius & ulna lie in forearm. At the distal (far from root) humerus has capitulum (rounded head) and spool shaped trochlea. The humeroulnar joint is a huge joint formed by humerus (distal) and ulna having concave trochlear fossa (cavity) at proximal (root). The joint can make only uniaxial rotation which permits flexion and extension. The humeroradial joint is formed

MECHANICS OF UPPER LIMBS

by the capitulum of the distal humerus and head of the radius. It is a also a hinge joint. The third joint in this region is the proximal radioulnar joint which is a pivot joint formed by the head of the radius and the radial notch of the proximal ulna. The joint permits the radius and ulna to make relative rotation about the longitudinal axis of either of the bones. The movement by the joint from the palm-up to the palm down is called pronation while the movement by the joint from the palm down to palm up is called supination.

Bones of the Elbow

Flexion

Extension

Movements of the Elbow

Supernation Pronation

Movements of the Forearm

2.The muscles coordinating & controlling the movement of the elbow joint are:

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(a) Bicep brachii: It is the most powerful flexor of the elbow joint, specially when the joint is in supinated position. On the distal side, the biceps is attached to the tuberosity of the radius and on the proximal side, it has attachments at the top of the coracoid process and upper lip of the glenoid fossa.

(b) Brachialis muscle: This flexor has attachments at the lower half of the anterior portion of the humerus & the coronoid process of the ulna.

(c) Triceps brachii: The muscle controls the extension movements of the elbow. It has attachments of the lower head of the glenoid cavity of the scapula, the upper half of the posterior surface of humerus, the lower two thirds of the posterior surfaces of the humerus and the olecranon process of the ulna.

Triceps

Brachialis

Brachio

Radialis

Pronator Teres

ANTERIOR

Tricep

Brachii

Anconeus

Supinator

POSTERIOR

Muscles of the Elbow

(d) Pronator teres and supinator muscles:

The pronator teres is attached to the lower part of the inner condyloid ridge of the humerus, the medial side of the ulna and the middle third of the humerus, the medial side of the ulna and middle third of the outer surface of the radius. As the name suggests, it performs pronation. The supination muscle has attachments at the outer condyloid ridge of the humerus, the

Biceps in

Triceps resting phase in resting

phase

Forearm

at rest

Biceps Triceps contracts relaxes

Forearm half raised

Forearm

fully raised

Raising of Forearm

neighboring part of the ulna and the outer third of the radius. The muscle controls supination. The coordinated relaxation and contraction of the opposing muscles enables to control movement of the limbs. To raise the forearm, the biceps (two rooted muscle) contracts and shortens while triceps (three rooted muscles) relaxes. To lower the forearm, the reverse occurs.

Biceps Triceps replaces contracts

Forearm half lower

Forearm

back rest

Lowering of Forearm

MECHANICS OF UPPER LIMBS

3.The elbow joint : The elbow joint is a synovial joint of the hinge variety. A ligamentous capsule encloses an articular cavity filled with synovial fluid. The synovial fluid is a thick and viscous substance. The primary function of synovial fluid is to provide lubrication to the articulating surfaces which reduces coefficient of friction, thereby frictional forces acting against movements are reduced considerably. The synovial fluid also nourishes the articulating cartilages . Besides above two functions, the synovial fluid helps in distributing the forces acting on the joint to a large area. All forces acting on the fluid are transferred to the fluid as liquid pressure which is uniform in all directions. The components of the fluid pressure along the

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horizontal get cancelled and the vertical components get added up, resulting into a vertical force on the joint. The elbow joint is continuous with the superior radioulnar joint. The humeroradial, the humeroulnar and the superior radioulnar joints together are known as cubital articulations. The long axis of the arm makes an angle of about 170° with the long axis of the forearm when the forearm is extended and supinated. The elbow joint is susceptible to fractures and dislocations. Fractures occurs at the epicondyles of the humerus and coronoid process of ulna. Another elbow injury that happens frequently is tennis elbow, which occurs due to repeated and forceful pronation and supination movement of the elbow.