2BiomechanicsEN.pptx

[Audio] Medical Physics II Asst. Prof. Goran Kolarevic, specialist of medical physics 2024/25.

[Audio] 2. Biomechanics Leonardo da Vinci (1452-1519) made detailed observations of animal motions and muscle functions. Our present concepts of mechanics were formulated by Isaac Newton (UK, 1643-1727), whose major work on mechanics, Principia Mathematica, was published in 1687. The locomotor system enables humans to move. It consist of: Passive elements (bones and joints) and Active elements (muscles). Bone's function (walking-movement, protection of vital organs, .........). Bones are composed of collagen and minerals. Loss of minerals reduces bone strength (osteoporosis). Bone structure: compact and spongy..

[Audio] Joints Immobile and Movable (can rotate around): a) 1 axis (elbow, knee, fingers) b) 2 axles (ankle of the foot) c) 3 and more axes (shoulder and hip joint) Muscles - during their contraction, forces are generated at their ends. Tendons connect muscles to bones. The skeletal muscles producing skeletal movements consist of many thousands of parallel fibers wrapped in a flexible sheath that narrows at both ends into tendons. Some muscles end in two or three tendons; these muscles are called, biceps and triceps. Leonardo da Vinci, wrote "The muscles always begin and end in the bones that touch one another, and they never begin and end on the same bone…" "It is the function of the muscles to pull (contract) ..... Contraction force = number of contr. muscle fibers.

[Audio] Rigid body-under the influence of external forces during movement, the mutual position of the points of the body does not change. They do not deform under the influence of force (does not exist in nature - bone). Under the influence of an external force, it can move translationally or rotationally. Balance of the Body Translation - under the influence of an external force, all points of the body travel the same distance and have the same speed (v) and acceleration (a) ( m - body mass) The condition for the translational equilibrium of the body is the vector sum of all forces acting on the body is equal to zero: Example: the weight of the body Q is equal to the forces which the pad works on the left and right leg: Fr + Fr - Q = 0.

[Audio] Body rotation - points do not cross the same path lengths. They move in circles whose centers lie on a straight line - axis of rotation. If a force F acts on the point (A) in a plane normal to the axis of rotation, its effect is manifested by the moment of the force M defined as the vector product of the radius vector (r) and the force (F). The vector of the moment of force lies along the axis of rotation, the direction is determined by the right-hand rule, and the intensity (magnitude) of the moment of force is M = r F sinφ d = r sinφ M = F d where d is the normal distance from the direction of force action to the axis of rotation..

[Audio] Levers and lever systems - a model of the functioning of the locomotor system We can get a basic idea of the locomotor system functioning if we consider bones as levers. Bones-levers are physically rigid bodies, i.e., bodies that do not deform under the influence of force. Levers A lever is a rigid bar free to rotate about a fixed point called the fulcrum. The position of the fulcrum is fixed so that it is not free to move with respect to the bar. Levers are used to lift loads in an advantageous way. A locomotor force F (effort−muscle) acts on one end, and a load Q on the other. The normal distance from the fulcrum to the attack line of the force is called the force arm a, while the normal distance from the fulcrum to the attack line of the load is the load arm b. Two equal moments of force act on the lever at the same time, so the equation of equilibrium of the lever is: F ⋅ a = Q ⋅ b k = Q / F = a / b is the lever transfer coefficient a) if k > 1 it is a force lever b) if k < 1 then it is a speed lever.

[Audio] Archimedes (287–212 BC) understood the power of applying the right force at the right place. He was so confident in ideas he said: Give me a place to stand on, and I will move the Earth. Based on the similarity of the triangles: L1/L2 = a/b ie v1/v2 = a/b.

[Audio] 1st class lever - a two-armed lever where the support−fulcrum is located between the attack points of the forces acting on the lever. If the arms of the lever are different, the lever is called multi-armed, and if they are equal, the lever is equal-armed. As an example, we can observe the head whose support O is on the first vertebra of the spinal column, at one end is the force of the neck muscles Fm, which maintains the head in an upright position, and at the other end is the load force Q which pulls the head forward. Otherwise, levers of the first class are rarely found in the human body. An example is a human head in an upright position. We have the weight of the head Q, the point of support O at the junction of the skull and the first cervical vertebra. Equilibrium is maintained by the force F exerted by the neck muscle on the skull. F b k = Q / F = a / b (k > 1).

[Audio] Example: The effect of the human head on the first cervical vertebra. For a person to keep his head in a vertical position, the force of the neck muscle FM maintains the balance of the weight of the head Q. The size of this force should be calculated for the case when the mass of the head is m = 3 kg, as well as the reaction force of the first cervical vertebra FC. The distance from the point of attack of the weight of the head (center of gravity) to the point of support on the first cervical vertebra is 3 cm, while the distance from the point of support to the point of attack of the force of the neck muscles is 5 cm. Q = m g = 30 N It follows from the equilibrium condition of the lever: a) Translational equilibrium condition FM + Q = Fc b) Rotational equilibrium condition FM × 5 cm = Q × 3 cm FM = (3/5) × Q = 18 N Fc = 18 N + 30 N = 48 N If the surface of the first spine on which the head lies down is 5 cm2, the stress (pressure) that the spine suffers will be: σ = Fc / S = 9.6 N/cm2.

[Audio] 2nd class lever one-armed lever where the point of attack of the load is located between the fulcrum and the point of attack of the muscle force (active force). (k>1) As an example, you can take a human foot that is supported on the toes. This lever is acted upon by the force of the muscle (m. soleus) F and the load force Q whose line of attack passes through the tibia and the ankle joint. The arm of the muscle force F is greater than the arm of the load force Q, which can be taken to be equal to half the weight of a person. From the leverage transfer coefficients and the ratio of the force arms, a relatively weaker muscle can lift the entire body..

[Audio] 3rd class lever - one-armed lever where the point of attack of the active force F is located between the support and the point of attack of the load Q. The force arm is smaller than the load arm, so these are always speed levers, and the transfer coefficient is always less than 1. The forearm can be taken as an example. The support is in the center of the elbow joint, the active force Fb comes from the contraction of the biceps muscle, while the resistance Q can represent the weight of the object in the hand. Since a << b (Q/F = a/b) the force of the biceps must be large, especially if an object of great mass is held in the hand. The mandible (lower jaw) is a type 3rd class lever..

[Audio] Leverage systems To study the human locomotor system, knowledge of lever system functioning is necessary. A system of levers is represented by two or more levers of any kind, interconnected so that the movement of one of them affects the movement of the entire system. Such a system of levers represents a model of mutually articulated bones in the locomotor system, whose unique functioning is realized with the help of muscles that are attached to them. The relationship between force and load will depend not only on the characteristics of individual levers, but also on the angle that the levers, or bones, overlap with each other. Hand model. The dependence of the muscles on the mutual position of the bones can be demonstrated by the example of a hand with a load Q . We will consider two cases: a) the angle between the forearm and upper arm bone is 90 , b) the angle between the forearm and upper arm bone is 180 ..

[Audio] A comparative analysis of the two mentioned cases shows that the forces required to maintain balance in the case of a body of the same weight in a hand differ by more than three times. The average value of the weight of the forearm is Qp = 15 N, the whole hand is Qr = 60 N, and the weight of the ball is Q = 30 N. The attack points of the forces Qp and Qr are in the centers of the forearm and the hand, respectively. In the first case, the balance of the forearm and body weight is maintained by the force of the biceps Fb. When the arm is extended, there is no action of the biceps, which now has no conditions for contraction. The function is taken over by the deltoid muscle of greater mass and stronger contraction, which can generate a force Fd several tens of times greater than the weight of the body in the hand. The force must be large because it acts at a small angle (of α = 16 ) in relation to the lever, which means that there is an active effect of only its component Fd sinα..

[Audio] Example, the leg model - the analysis of the dependence of muscle force on the relative position of the leg bones can be performed using a physical model. In the process of moving a person from a squatting position to a standing position, the leg, which was bent at the knee, is straightened thanks to the contraction of the thigh muscle. For angle values 0 <θ<160 coefficient k<1, which means that the lever acts as a speed lever, so the force (F) must be significantly greater than the load (Q/2). Above 160 , the lever acts as a force lever which means that the force is less than the load. It is known from practice that the initial phase of standing up from a squat is significantly slower than the final phase..

[Audio] Example. Hip-the picture shows the hip joint and its simplified lever representation. The hip is stabilized by a group of muscles, on which the resultant force (Fm) acts. The weight of the leg is represented by (Qn), which is up to 20 % of the total body mass, i.e. Qn = 0.2 Q. If a person stands upright on one leg as in a light walk, and has a mass of 70 (kg), Q ≅ 700 (N), then Fm ≅ 1.59 · Q = 1113 (N). Limping-people with an injured hip, limp by leaning towards the injured side while walking (picture). As a result, the center of mass moves to a position directly above the hip joint, reducing the force on the injured area. In this case, Fm = 0.47 · Q = 329 (N), which is a significant reduction compared to the forces applied during the normal leg position..

[Audio] Example, when the body trunk is bent forward at an angle of 60° to the vertical with the arms freely falling. The point of rotation (A) is the fifth lumbar vertebra. We can represent the back as a lever arm (AB). The weight of the trunk is represented by the force Q1. The weight of the head and arms is represented by the force Q2. The erector spinalis muscle maintains the position of the back. For a man of mass 70 (kg), Q1 and Q2 are 320 (N) and 160 (N), respectively. It is shown that in order to support body weight, the muscle must exert a force of 2000 (N), and the compression force of the fifth lumbar vertebra is 2230 (N). If, in addition, a person holds a weight of 20 (kg) in his hand, the force on the muscle is 3220 (N), and the compression of the vertebra is 3490 (N). This example shows that the fifth lumbar vertebra is subjected to large forces. It is not surprising that back pain most often occurs in this region..

[Audio] Real systems Elasticity and elastic deformations We looked at bones as levers that do not deform under the forces influence. There is always a degree of deformation under the influence of external forces. Then there are internal forces that tend to return the body to its original shape. These are elastic forces. Their size depends on the forces between the molecules that make them up. The nature of intermolecular forces The effect of intermolecular forces is felt at a distance that is up to ten times greater than the dimensions of the molecule (10−10 m) and has an electrostatic and quantum nature. Molecules have (+) and (−) charges, so we have attractive Fp and repulsive Fo forces (a and b are proportionality coefficients). ro is the equilibrium state Fp = Fo, where is also the minimum of potential energy (Ep). F is the resultant force between 2 molecules..

[Audio] Elasticity and plasticity In the absence of external forces, molecules maintain an equilibrium state ro. The effect of external forces changes this distance, and as a reaction, it grows repulsive (during compression) or attractive (during stretching). These are elastic forces, which are also called restitution forces because they tend to re-establish the initial state of equilibrium between the molecules (elastic deformation). If the external forces are large enough to move the molecules away from the sphere of their action, elastic forces will not occur and their bonds will break (plastic deformation). Elastic deformation There are several types of deformations (stretching, compression, shearing, twisting,...) and they occur on the human locomotor system (bones, muscles, tendons). We observe the effect of force F on a body of cross-section S. If we decompose the force into normal and tangential components, we can define normal σn and tangential σt stress (pressure) as: σn = Fn / S and σt = Ft / S.

[Audio] The degree of deformation of the body is determined by relative deformation (stretching) δ . Robert Hooke (UK, 1635−1703) law, established that relative deformation is proportional to stress: δ ≅ σ Hooke's law for longitudinal deformations Stretching (absolute stretch: ΔL=L-L0) δ = ΔL/L0 ΔL/L0 = (1/Eχ) Fn/S or δ = (1/Eχ) σn where Eχ is Young's modulus of elasticity (degree of elasticity of the body). If Fn has the opposite direction, the original length of the body will decrease (compression). Example: the length of the leg bones is L = 1.2 m and radius r = 1 cm. What are δ and ΔL if a man of mass m = 70 kg stands on one leg. Young's modulus of elasticity for bone is 18 109 N/m2. ΔL/L = m g/(Eχ r2 π), ΔL = 0.146 mm..

[Audio] Example: anterior hamstring, has a modulo elasticity 1.9 109 N/m2. Therefore, this tendon extends by 2.5 % compared to its length when walking/running. A special type of quasi-longitudinal deformation is bending, which is a combination of compression and stretching. The force acts tangentially, and the point of attack is on the axis of the body..

[Audio] Shearing Tangential force whose point of attack is on the rim cross section causes elastic shear deformation. δ = AA`/L = tg α Torsion (twisting). The tangential force acts as a tangent to the cross-sectional area of the body. It is most dangerous for bones (open and irregular fractures), which are difficult to heal. It is dangerous when twisting the vertebral column, which causes the disc to pop out of the space between the vertebrae..

[Audio] The limits of Hooke's law P limit of proportionality, E elastic limit, C breaking limit. With an increase in the intensity of the external force, passing the point E, the body does not return to its original state after the end of the force (plastic deformation). Crossing point C, tearing of the body occurs. Hooke's law is valid only in the field of OP. Knowing the value of the critical stress (σn)c, for tearing a certain tissue, we can calculate the value of the critical force Fc, and we get: Fc = σc S = S Ej ΔL/Lo Bone fracture.

[Audio] Functional adaptation of bones During life, bones are continuously optimized for their supporting role through the process of functional adaptive remodeling. Osteogenesis (the process of creation and formation of bones) enables the bone to functionally adapt to the forces acting on it, in terms of changing the structure and in terms of changing the form. If the degree of use of a part of the body or organ increases, it increases (hypertrophy), and if not, then it decreases (atrophy). "The law of bone transformation" was defined by Julius Wolff (D) in 1892 and reads: any force that permanently or very frequently acts on a certain bone of the musculoskeletal system leads to the hardening of that bone, i.e., increase in bone cell density and bone thickness. The shape of the bone changes during life depending on the functions it performs..

[Audio] Measurement of bone mass (density) in the body-osteodensitometry Osteoporosis is a disease in which bones, due to loss of minerals, become brittle. That is why it is necessary to measure the bone mass (m = ρ V, ρ -density, V-volume). The most commonly used method is based on the absorption of a beam of X or γ radiation that is passed through the bone (absorptiometry of X rays with two different energies). In an X-ray tube with a stationary target, X radiation of energy 70 and 140 (keV) is alternately emitted. The result of the measurement is the intensity absorption curve for the bone section. The obtained results (absorption curves) are compared with the average values of younger adults and the average values of the population of the same age as the patient. Bone mass (BM) is proportional to the logarithm of the intensity ratio before (Io) and after passing through the bone (I): BM (gr/cm2) = k log(Io/I).