Fundamentals of Biomedical Engineering

MECHANICS OF THE KNEE

1.The knee is the largest joint in the body. It is also a most complex joint. The complexity is the result of fusion of three joints in one. It is formed by fusion of the lateral femorotibial, medial femorotibial and femoropatellar joints. It is a compound synovial joint, incorporating two condylar joints between the condyles of femur (thigh bone) and tibia (leg bone) and one saddle joint between the femur and the patella. The femorotibial has two distinct articulations between the medial and lateral condyles of

the femur and the tibia. These articulations are separated by layers of cartilage, called menisci (fibrocartilaginous discs). The lateral and medial menisci prevent bone to bone contact between the articulating surfaces of the femur and the tibia and they also work as shock absorbers. The femoropatellar joint is the articulation between the anterior end of the femoral condyles and the patella which is a floating bone kept in position by the quadriceps tendon and the patellar ligaments. The patella also protects the knee from impact related injuries and enhances the pulling effect of

quadriceps muscles on the tibia through patellar tendon. The stability of the knee joint is provided by (1) ligaments (2) menisci (3) muscles crossing the joint. Flexion and extension are chief movements. These movements take place in the upper compartment of the joint above the menisci. They differ from the ordinary hinge movement in two ways (1) The transverse axis around which these movements take place is not fixed. During extension, the axis moves forward and upwards and in the reverse direction during flexion, (2) These movements are invariably accompanied by rotations. Rotatory movements at the knee are of a small range. Rotations take place around a vertical axis and are permitted in the lower compartment of the joint, below the menisci. Muscles producing movements at the knee joints are:

2.The knee is a weak joint because the articular surfaces are not congruent. The tibial condyles are too small and shallow to hold the large and convex femoral condyles in place. The femoropatellar articulation is also quite insecure because of the shallow articular surfaces and the outward articulation between the long axis of the

thigh and of the leg. The stability of the joint is maintained by cruciate and collateral ligaments and muscles crossing the joint. The leg may be abnormally abducted (genu valgum or knock knee) or abnormally adducted (genu varus or bow knee). Common injuries are (1) injury to menisci

(2) injury to cruciate ligaments (3) injury to collateral ligaments.

3.Another leg bone on the outerside of tibia is known as fibula. It acts as support to the tibia but does not take any part in the knee joint formation. The front portion of the knee joint is formed by patella which articulates with the lower part of the femur and upper part of the tibia. The patella moves up and down with contraction and relaxation of the thigh muscle while straightening and bending the joint. The movements of the joint are smooth and painless as long as there is no trauma or irregularity in their articular surfaces. Any physical or nutritional trauma may cause degeneration of the articular surfaces or loose body formation. These changes are associated with pain and irregular movements at the joint and further degeneration of the joint.

4.Case study 1: To determine muscle force

‘F’ acting in patellar tendon, reactions Raxial and Rshear on the tibial plateau when a man weighing 1000 N is slowly climbing the stairs as shown in the figure. Let θ is angle made by the tibia with horizontal, t = distance between patellar tendon from the patello femoral joint, S = horizontal distance between ground reaction and the patello femoral joint. Assume the weight of the lower leg and any effect of fibula are negligible. We have now a system of

coplanar force system and we get three equations of equilibrium i.e. ΣMj = 0, ΣPx = 0, ΣPy = 0, ΣMj = 0, F × t – 1000 × S = 0

Free Body Diagram of Lower Leg

S or F = 1000 × t

ΣPx = 0 (along the long axis of the tibia)

Raxial = 1000 cos θ + F

Σ PY = 0, Rshear = 1000 sin θ

If we take t = 60 mm, s = 200 mm and θ = 60°, then

200

F = 1000 × 60 = 3333.3 N

1

Raxial = 1000 × 2 + 3333.3 = 3833.3 N

3

Rshear = 1000 × 2 = 866 N

5.Case study 2: A man is wearing a heavy boot and doing lower leg flexion and

MECHANICS OF LOWER LIMBS

extension exercise from a sitting position as shown in the figure. We draw the free body diagram of lower leg as well as mechanical model of the leg. F is the magnitude of force exerted by the quadriceps muscle on the tibia through the patellar tendon.

R is the reaction on the tibiofemoral joint at point 0. The patellar tendon is attached to the tibia bone at point A. The CG of the lower leg is located at point B. The CG of the boot is located at C. The distance of point AB and C from point O are a,b and c respectively. The tibia makes an angle of α with horizontal and the muscle force makes angle of β with the long axis of the tibia. We resolve the forces along the tibia axis (x- axis) and vertical to the tibia axis (y-axis)

Fx = F cos β

Fy = F sin β

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Wbx = Wb sin α Wby = Wb cos α Wlx = Wl sin α Wly = W1 cos α

Taking moment about point 'O' which is ΣMO = 0

F sin β × a – Wl cos α × Wb cos α × c = 0

R cos θ – F cos β+ Wb sin α+ Wl sin α = 0 Now, ΣPy = 0

R sin θ = F sin β – (Wb + Wl) cos α.

R2 =[F cosα – (wb − wb ) sin]2 +

[F sin β + (Wb +Wb ) cosα]2

w b

R2 = F 2 + (Wb + Wl )2

–2F(Wb +Wl ) sin (α + β)

6.It can be seen that normal component of F (quadricep muscle force = F sin β) tries to rotate the tibia about the knee joint while its tangential component (= F cos β) along the tibia axis tends to move the tibia towards the tibiofemoral joint. If θ is small, F cos θ is more and more muscle force is wasted to compress the knee joint. If θ is large, F sin θ is large and a larger portion of the muscle tension is used to rotate the tibia or lower leg about the knee joint.

7.It can be seen that the patella bone provides anterior displacement of the quadriceps and patellar tendons thus lengthening the moment arm of the muscular force by increasing the angle β. As shown in the figure, muscular

force F make angle β1 when patella is present and angle β2 when patella is absent. The moment arm is AB sin β1 with patella > AB sin β2 without patella as β1> β2. Decreasing of moment arm results into the quadriceps muscle to exert more force than normal to rotate the lower leg about the knee joint.

Functions of Patella

8.It can be seen that quadriceps muscle goes over the patella while getting connected to the femur and the tibia. The patella and the muscle form a rope pulley arrangement. The larger is the tension in the muscle, the larger is the compressive force or pressure, the patella exerts on the femoropatella joint.

Now we have three forces F , F and R which are concurrent at point 0 with angles of the forces are α, β and v respectively with the horizontal. We can apply Lami’s theorem for finding a solution.

F β

R v

MECHANICS OF LOWER LIMBS

MECHANICS OFTHE ANKLE

1.The ankle joint consists of a deep socket formed by the lower ends of the tibia and fibula into which is fitted the upper part of the body of the talus. The talus is able to move on a transverse axis in a hinge like manner. The shape of the bone and the strength of the ligaments and the surrounding tendons make this joint strong and stable.

2.The ankle joint complex consists of three joints i e. tibiotalar, fibulotalar and tibiofibular. The tibiotalar joint (ankle joint) is a synovial joint of the hinge variety. The articulation is between the spool like convex surface of the trochlea (structure serving as pulley) of the talus and the concave distal end of the tibia. The tibiotalar joint is the articulation between the external malleolus (rounded bony) of the tibula and the medial and lateral surfaces of the trochlea of the talus. The distal tibiofibular joint is the articulation between the internal malleolus of the tibia and the external malleolus of the fibula. The ankle permits flexion and extension in sagittal plane, inversion and eversion, inward and outward rotation, and pronation and supination movements are possible about the foot joints such as the subtalar and transverse joints between the talus and calcaneus.

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3.Case study: Consider a man standing on tiptoe of the foot as shown in the figure. The ground reaction equal to weight of the man is acting vertically unwards at point ‘A’ F is the magnitude of the force exerted by the archilles tendon and it makes angle α with the horizontal at point B. R is the magnitude of reaction exerted by the tibia on the talus at the ankle joint (point ‘C’).

Ankle Joint

It makes an angle β with the horizontal. Now we have three force system and these forces have to be concurrent during equilibrium. We can apply Lami’s theorem to find the solution.

Fill up the gaps

1.The hip bone is made of ______ elements (a) two (b) three

2.There are ______ hip bones (a) two (b) three

3.The thigh bone is ___________

(a) Tibia (b) femur

4.Lower limbs and upper limbs have a _____

by which they are attained to axial skeleton (a) girdle (b) joint

5.Tibia and ______ are leg bones (a) femur (b) fibula

6.The hip joint is formed by the femoral head fitting well into the deep socket of the

_______(a) acetabulum (b) sacrum

7.The _______ of the leg does not take part in the formation of knee joint (a) tibia (b) fibula

8.Patella is also known as ______ (a) knee cap (b) force deflector

9.Patella is a large _______ bone developed in the tendon of quadriceps femoris

(a) sesamoid (b) irregular

10.Acetabulum has a shape of ______

(a) cup (b) plane

11.In varus deformity, the femoral neck bends or twists ______ (a) inward (b) outward

12.In valgus deformity, the femoral neck bends or twists (a) inward (b) outward

13.The angle of femur neck with vertical is greats than 125° for ______ and less than 125° for ______ (a) valgus, varus (b) varus, valgus

14.The femoral neck is ______ susceptible to fracture in varus deformity (a) more (b) less

15.A man with weak hip abductor muscle or painful hip joint usually lean ______ the weaker side (a) toward (b) away

16.Leaning towards the painful side while walking is called _______ (a) abductor gait (b) crippled gait

17.The largest joint in the body is ______

(a) knee (b) hip

18.The most complex joint in the body is _____

a) knee (b) hip

19.The knee joint is a complex joint formed by the thigh bone, leg bones and _____

(a) patella (b ) talus

20.The ankle joint formed by the tibia and fibula as they form socket into which is fitted upper part of the _____(a) calcaneous

(b) talus

21.Patella also ________ the moment arm of the muscular force during extension

(a) shortens (b) lengthens

22.The knock knee is an abnormality of the knee joint when the leg is abnormally -----

(a) adducted (b) abducted

23.The bow knee is an abnormality of the knee joint if the leg is abnormally ---------

(a) adducted (b) abducted

24.Cane is held -----side of the painful hip joint to reduce the abductor muscle force

(a) same (b) opposite

INTRODUCTION

1.The blood has carriers of fuel supply. The blood has ability to transport waste materials to predestined destinations. The blood also contains a mechanism for repairing small system punctures and a method for rejecting foreign elements from the system. Man is able to sustain life because the blood is supplied to all systems of the body. The circulating blood supplies oxygen and nutrients to the cells of the body. The heart is a very important organ in the body which acts as a pump to circulate the blood in the body. The failure of heart is the cause of many deaths. There are many techniques and instruments to measure functioning of heart and to diagnose any of its malfunctioning for treatment so as to avoid its failure. The cardiovascular system consists of heart, distribution system (arteries and arterioles), diffusing system (capillaries in contact with cells) and collecting systems (veins), The cardiovascular system is a closed hydraulic system. Blood pressure,

flow and volume are measured by using engineering techniques.

WORKING PRINCIPLE OF CARDIOVASCULAR SYSTEM

1.The cardiovascular system or the blood vascular system is a closed hydraulic system. The blood consists of plasma and corpuscles. The red corpuscles, white corpuscles and thrombocytes are suspended in the plasma. There are about 4.5 to 5.5 million red blood cells per cubic millimeter of blood. There is about 3.5 to 5 litres/min blood circulating in normal adult at rest. The blood circulating system consists of:

(a) Heart: The circulation of blood is maintained within the blood vessels by the rhythmic pressure in the trunk vessels exerted by the contraction and expansion of the heart. The heart acts as a pump whose elastic muscular walls contract rhythmically to develop pressure to push the blood through the vascular system. The heart contracts

Right Lung

O2

Coronary sinus

CO 2

Inferior

Vena Cava

Vena Cava

continuously and rhythmically, without rest, about 1,00,000 times per day. The average heart rate is 75 beats per min i.e., each cycle of beat is completed in 0.8 seconds.

(b) Distribution system: The blood is supplied to all cells of the body through distribution system which consists of arteries, arterioles and capillaries. Each artery bifurcates to smaller arteries until smaller type (arterioles) is reached. The arterioles feed into the capillaries where oxygen is supplied to the cells and carbon dioxide is removed from the cells. The oxygen depleted blood moves to venules.

(c) Diffusing system: It consists of fine capillaries which are in contact with the cells of the body. Capillaries take blood

from arterioles and transference of oxygen to cells and carbon dioxide to the blood takes place through capillaries. The oxygen depleted blood from capillaries moves to vein. Tissue metabolism is the process by which cells take oxygen from blood and give out carbon dioxide to blood.

(d) Collecting system: It consists of veins. It collects blood which is depleted of oxygen and which contains waste products of metabolic processes from various organs. The blood is taken back to heart which sends it to lungs for reoxygenation and then the recirculation of oxygenated blood to all systems of the body. The veins differ from arteries in having valves to control the direction of flow towards the heart.

2.The organs which are supplementing the functioning of cardiovascular system are:

(a) Lungs: The blood with carbon dioxide and air intake reach lungs which provide a region of interface for the transfer of oxygen to the blood from air and removal of carbon dioxide from the blood to the air.

(b) Kidney/liver and spleen: These organs help in the removal of waste products

and in maintaining the chemical quality of the blood.

THE HEART: WORKING AND

STRUCTURE

1.The heart can be considered as a pair of two stage pumps working in series with each stage of the pumps arranged physically in parallel. However the circulating blood passes through from first stage to second