# Biomedical Engineering Theory And Practice/Biomechanics

 Biomedical Engineering Theory And Practice Neuro engineering Biomechanics Biomechanics II

## Classical Mechanics

### Rigid Body Mechanics

Rigid body defined as a body on which the distance between any two given points remains constant in time regardless of external forces[1]. Or it is the body which does not deform under the influence of forces[1].Forces acting of rigid bodies can be also separated in two groups: The external forces, represent the action of other bodies on the rigid body under consideration; The internal forces are the forces which hold together the particles forming the rigid body. The body is only able to change its motion if it can push or pull against some external object. Only external forces can impart to the rigid body a motion. Rigid body makes analysis simple with less parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body.[2][3]Rigid-body mechanics studies the movement of interconnected bodies' system under the action of external forces.

### Kinematics

Kinematics describes the motion of points, bodies (objects) and systems of bodies (groups of objects) without consideration of the causes of motion. It is the branch of biomechanics concerned with the study of movement from a geometrical point of view.[4][5][6]

#### Type of Motions

Motions are classified into translation and rotation according to a fixed axis, general plane motion and motion about a fixed pin.

• Translation(Linear Motion):A motion is said to be a translation if any straight line inside the body keeps the same direction during the movement.All the particles forming the body move along parallel paths. If these paths are straight lines, the motion is said a rectilinear translation. If the paths are curved lines, the motion is a curvilinear motion.
• Rotation about a fixed axis(Angular Motion): Most of the individual limb motions are angular. The particles forming the rigid body move in parallel planes along circles centered on the same fixed axis. If this axis, called the axis of rotation intersects the rigid body, the particles located on the axis have zero velocity and zero acceleration.
• General plane motion:Any plane motion which is neither a translation or a rotation is defined as a general plane motion. Plan motion is that in which all the particles of the body move in parallel planes. Translation and rotation are plane motions.
• Motion about a fixed point:The three-dimensional motion of a rigid body attached at a fixed point, for example, the motion of a top on a rough floor, is known as motion about a fixed point.
• General motion:Any motion of a rigid body which does not fall in any of the cathegories above described.

#### Position

Position(also called Displacement) means an object’s location at any particular time.

#### Velocity

Velocity is defined as the rate at which location changes with time.

${\displaystyle \mathbf {Velocity} _{\mathrm {average} }={\Delta \mathbf {location} \over \Delta time}={\Delta S \over \Delta time}}$

#### Acceleration

Acceleration is the rate at which velocity changes with time.

${\displaystyle \mathbf {Acceleration} _{\mathrm {average} }={\Delta \mathbf {Velocity} \over \Delta time}={{Velocity}_{final}-{Velocity}_{initial} \over {Time}_{final}-{Time}_{initial}}}$

### Kinetics

Kinetics is the branch of biomechanics concerned with what causes a body to move the way it does.

#### Newton’s Laws of Motion

Newton's laws of motion are three fundamental laws for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion to the forces.

1. Newton's first law : If a body is at rest it remains at rest or if it is in motion it moves with uniform velocity until it is acted on by a resultant force.[7]The first law can be stated mathematically as ${\displaystyle \sum F=0}$${\displaystyle \mathrm {d} \mathbf {r} /\mathrm {d} t=0\,\!}$
2. Newton's second law:Acceleration is dependent on the forces acting upon an object and the mass of the object. Change in momentum is proportional to external force and reversely proportional to its mass. It can be stated mathematically as ${\displaystyle F=ma=\mathrm {d} \mathbf {v} /\mathrm {d} t}$.To consider rigid body three-dimensionally, Newton's second law should be extended to define the relationship between the movement of a rigid body and the system of forces and torques that act on it.
3. Newton's third law:For all force, there is an equal and opposite force. If one object A exerts a force FA on a second object B, then B simultaneously exerts a force FA on A: FA= −FA[8].

## Molecular Biomechanics

### Biomolecules and intermolecular forces

A comparison of the scales of various biological and technological objects.

## Tissue MechanicsI(Bone)

### Microscopic bone structure

Cross-section of a long bone showing both spongy and compact osseous tissue

Two types of bone can be founded microscopically up to the pattern of collagen forming the osteoid (collagenous support tissue of type I collagen embedded in glycosaminoglycan gel):

• Woven bone is characterized by randomly oriented collagen fibers. It is isotropic and mechanically weak[9]. It is actively resolved by 1 year.
• Lamellar bone has a highly organized parallel alignment of collagen into sheets (lamellae). It is anisotropic and mechanically strong [9].

### Bone Tissue:Cortical(Compact) Bone

Cortical bone,also called compact bone, dense bone in which the bony matrix is solidly filled with collage and Hydroxylapatite, leaving only tiny spaces (lacunae) that contain the osteocytes, or bone cells.[10]Its porosity is 5–30%.[11] Compact bone makes up 80 percent of the human skeleton.Cortical bone forms the cortex, or outer shell, of most bones[10] .

### Bone Tissue:Trabecullar(Cancellous or spongy) Bone

Compared to compact bone, cancellous bone has a higher surface area to mass ratio because it is less dense.It's porosity is %30-90[11]. It is composed of a network of rod- and plate-like elements that make the overall organ lighter and allow room for blood vessels and marrow where haematopoiesis, the production of blood cells, occurs. Cancellous bone is typically found at the ends of long bones, proximal to joints and within the interior of vertebrae.

### Bone Tissue Type and Implant

1. Type I bone is very hard and dense like oak wood as it contains mostly lamellae bone. This type of bone has less blood supply than all of the rest of the types of bone. The blood supply is required for the bone to harden or calcify the bone for the implant. Therefore, it needs approximately 5 months for this type to integrate with an implant[12].
2. Type II plexiform bone isn't as hard as type I. It is composed of layers of lamellae and woven bone. This type of bone usually takes 4 months to integrate with an implant[12]
3. Type III Haversian bone is composed of Harversian canal, concentric lamellae, lacunae with osteocytes and canaliculi.It is like balsa wood and less dense then type II. Because of lower density, it takes more time to work with an implant. 6 months time is suggested before loading an implant placed in this bone. Extended gradual loading of the implant could improve the bone density[12].
4. Type IV cancellous bone is the least dense of all of the bone types[11].This type takes the longest time to work with the implant after placement, which is usually 8 months. Additional implants is necessary to improve implant/bone loading distribution. Bone grafting or augmentation of bone are often needed. Bone expansion and or bone manipulation can improve initial implant fixation[12].

### Bone Cells

Bone cells

Bone cells are classified into four categories:osteoclasts destroy bones,osteoblasts build bones,osteocytes hold the bone together and, lining cells protect the bone.

#### osteoclast

Osteoclasts are usually found in bone surface called resorptive pits. Osteoclasts are large multinucleate cells that are responsible for the breakdown of bones[13]. The breakdown of bone is very important in bone health as it allows for bone remodeling. Osteoclasts are formed by the joining of many different cells created from the bone marrow that travel in the circulatory system[13]. Local acidic environment through H2 enhance the solubility of hyaluronic acid. High molecular weight hyaluronic acid regulates osteoclast formation by inhibiting receptor activator of NF-κB ligand through Rho kinase[14].

#### osteoblasts

Osteoblasts is primarily composed of Type I collagen. The osteoblast creates and repairs new bone by actually building around itself. After the osteoblast is finished working, it is actually trapped inside of the bone. When the osteoblast becomes trapped, it becomes known as an osteocyte[15]

#### osteocytes

Osteocytes are mature osteoblasts which have become trapped inside of lacunae surrounded by bone matrix. The osteocytes are numerous and believed to communicate with stress/strain signal[16].

#### lining cells

Bone lining cells come from osteoblasts which have become flattened. Bone lining cells are for the immediate release of calcium] in the bone if calcium in the blood is too low. Bone lining cells are also important in the protection of the bone from harmful chemicals. And bone lining cells are responsible for the maintenance of the bone fluids[17].

### Biomechanical Behaviour of Bone

#### Cortical Bone

It has relatively high compressive strength of about 170 MPa (1800 kgf/cm2)[18] but poor tensile strength of 104–121 MPa and very low shear stress strength (51.6 MPa)[19].

#### Trabecular Bone

Elastic behaviours depends on the anatomic sites, age, connectivity and so on. Modulus and strength are weak dependent on the strain rate[20]

## Tissue Mechanics II (Cartilage, Muscle, Ligament, Tendon)

Histological Architecture of the Joint Surface

All connective tissue including bone and adipose is characterized by distinctive cells surrounded by an extracellular matrix within a ground substance. The tissue is characterized based on the extracellular matrix. Blood is also belong to the connective tissue. Special connective tissue consists of reticular connective tissue, adipose tissue, cartilage, bone, and blood.[21]

### Cartilage

Cartilage is a flexible and rubbery but strong supportive connective tissue[22] Cartilage consists of cells called chondrocytes which are dispersed in a firm gel-like ground substance and produce and maintain the cartilaginous matrix composed mainly of collagen and proteoglycans. Cartilage is avascular (contains no blood vessels) and nutrients are diffused through the matrix. Cartilage is found in many areas in the bodies of humans and other animals, including the joints between bones, the rib cage, the ear, the nose, the bronchial tubes and the intervertebral discs.

There are three main types of cartilage: hyaline, elastic and fibrocartilage[23].

#### Hyaline cartilage

The type of protein fiber embedded within the matrix of cartilage determines the cartilage type[24]. It contains no nerves or blood vessels, and its structure is relatively simple. Hyaline cartilage matrix is mostly composed of type II collagen and chondroitin sulfate, both of which are also found in elastic cartilage. The optical density of these fibers is the same as the ground substance surrounding them and as a result, they are not visible within the extracellular matrix. Hyaline cartilage subsequently appears as a very uniform, glossy type tissue with evenly dispersed chondrocytes in lacunae. Typically, hyaline cartilage is covered by the perichondrium, except at the articular ends of bones. It is found directly under the skin, i.e. ears and nose. This membrane contains vessels that provide the cartilage with nutrition.

Articular cartilage indicates hyaline cartilage on the articular surfaces of bones.[25][26]

#### Elastic cartilage

Elastic cartilage or yellow cartilage is found in the pharyngotympanic (eusatachian) tubes, epiglottis, and ear lobes where needs dictate supportive tissues possess elasticity.It contains elastic fiber networks and collagen fibers.[27] The principal protein is elastin.

#### Fibrocartilage

Fibrocartilage (fibrous) contains type I collagen in addition to the normal type II arranged in layered arrays. compared to the very uniform appearance of hyaline cartilage, fibrocartilage possesses a more open or spongey architecture with gaps between lacunae and collagen fiber bundles. Fibrocartilage is found in the pubic symphysis, the annulus fibrosus of intervertebral discs, menisci, and the TMJ. It helps fill in the torn part of the cartilage; but, it is not enough for the replacement of the smooth, glassy articular cartilage that normally covers the surface of joints. The tendon transforms into fibrocartilage when subjected to compression[28]

### Articular cartilage

Articular cartilage is the loadbearing connective tissue of diarthrodial joints[26]. Surface is a large extracellular membrane (proteoglycans, collagens, water) with a sparse population of condrocytes[29].

Along with collagen fiber ultrastructure and ECM, chondrocytes contribute to the zones of articular cartilage—the superficial zone, the middle zone, the deep zone, and the calcified zone. Collagen is main structural macromolecule in ECM, and it occupy about 60% of the dry weight of cartilage. Type II collagen represents 90% to 95% of the collagen in ECM and forms fibrils and fibers intertwined with proteoglycan aggregates together along hyaluronic acid core. Collagen types I, IV, V, VI, IX, and XI also exist but contribute only a minor proportion. The minor collagens help to form and make the type II collagen fibril network stable. Water represents between 65% and 80% of the total weight.The relative water concentration decreases from about 80% at the superficial zone to 65% in the deep zone[30].Water and proteoglycans are critical to its ability to resist compressive loads.

Its principal function is to provide a smooth, lubricated surface for articulation and to facilitate the transmission of loads with a low frictional coefficient. The mechanical behavior of this tissue is dependent on the interaction of its fluid and solid components[26].

### Ligament and Tendon

A tendon is a tough fibrous bands of connective tissue that usually attaches muscle to bone. Tendons may also connect muscles to structures such as the eyeball. A tendon serves to move the bone or structure. A ligament is a short,fibrous bands of connective tissue which attaches bone to bone, and usually serves to hold structures together and stabilize them[31]. Ligament and tendon are different in the connection to the system. But, ligament and tendon are dense connective tissue and microscopically similar to including composition.

### Muscle Tissue

The body contains three types of muscle tissue: 1) skeletal muscle, 2) smooth muscle, and 3) cardiac muscle.

Muscle Tissue is a band or bundle of fibrous tissue in a human or animal body that has the ability to contract, producing movement in or maintaining the position of parts of the body. Muscle (myocytes) are elongated cells ranging from several millimeters to about 10 centimeters in length and from 10 to 100 micrometers in width.[32]. According to the function and location in the body,muscle tissue is divided into three:skeletal muscle, cardiac muscle and smooth muscle.Cardiac and skeletal muscles are "striated" as they include sarcomeres and are packed into highly regular arrangements of bundles; smooth muscle is not. While skeletal muscles are arranged in regular, parallel bundles, cardiac muscle connects at branching, irregular angles (called intercalated discs). Skeletal muscle is under the control of the somatic nervous system.In other words, it is voluntarily controlled.Cardiac muscle (heart muscle) is involuntary striated muscle in the walls of the heart, specifically the myocardium.

#### Comparison of Muscle Tissue[33]

 smooth muscle cardiac muscle skeletal muscle Anatomy Neuromuscular junction none none present Fibers fusiform, short (<0.4 mm) branching cylindrical, long (<15 cm) Mitochondria few numerous many to few (by type) Nuclei 1 1 few Sarcomeres none present, max. length 2.6 µm present, max. length 3.7 µm Syncytium]] none (independent cells) none (but functional as such) present Sarcoplasmic reticulum little elaborated moderately elaborated highly elaborated ATPase little moderate abundant Physiology Self-regulation spontaneous action (slow) yes (rapid) none (requires nerve stimulus) Response to stimulus unresponsive "all-or-nothing" "all-or-nothing" Action potential yes yes yes Workspace Force/length curve is variable the increase in the force/length curve at the peak of the force/length curve Response to stimulus

## Cellular Biomechanics

### Structure/function/properties of the cell

Structure of a typical animal cell

### Cell membranes

The molecular structure of the cell membrane.

### The cytoskeleton[34]

Cytoskeleton type[35] Diameter (nm)[36] Structure Subunit examples[35] Persistence Length (µm)
Microfilaments     6  double helix  actin 15
Intermediate filaments    10  two anti-parallel helix/dimers, forming tetramers
• vimentin (mesenchyme)
• glial fibrillary acidic protein (glial cells)
• neurofilament proteins (neuronal processes)
• keratins (epithelial cells)
• nuclear lamins
1-3
Microtubules    23  protofilaments, in turn consisting of tubulin subunits in complex with stathmin[37]  α-bubulin and β-tubulin 60,000

## Practise

6.1 A very brief review of basic mechanics: Vectors and kinematics, Force and Motion, Kinetic and Potential Energy and Work, Conservation of Energy, Energy Absorption, Center of Mass and Linear & Angular Momentum, Rotation, Torque, and Elasticity,Axial Stress and Strain Shear Stress, Bending, Torsion,Failure Under Load,

6.2 Cellular Biomechanics

6.3 Mechanics of Hard &Soft Tissue Tissues

6.4.1 mechanics of the Musculoskeletal & digestive systems

6.4.2 Joint Surface & Lubrication

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24. [1]
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32. Wikipedia, Cardiac Muscle
33. Wikipedia,Cytoskeleton
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36.