Soft Tissue Mechanics

Soft tissues

A primary group of tissue which binds, supports

and protects our human body and structures

such as organs is soft connective tissue.

Examples for soft tissues are muscles, tendons,

ligaments, blood vessels, skins or articular

cartilages among many others.

Tendons are muscle-to-bone linkages to stabilize the bonyskeleton (or to produce motion), while ligaments are bone-to-bone linkages to restrict relative motion.

Blood vessels are prominent organs composed of soft tissueswhich have to distend in response to pulse waves.

The skin is the largest single organ (16% of the human adultweight).

Soft connective tissues are complex fiber-reinforced compositestructures.

Their mechanical behavior is strongly influenced by thestructural arrangement of constituents such as collagen andelastin, and respective function in the organism.

Collagen: Collagen is a protein which is a major constituent ofthe extracellular matrix of connective tissue. It is the main loadcarrying element in soft tissues.

Elastin: Elastin, like collagen, is a protein which is a majorconstituent of the extracellular matrix of connective tissue.

It is present as thin strands in soft tissues such as skin, lung,ligaments.

Types of Muscles

Skeletal muscle

Skeletal Muscles are those which attach to bones and have the main function of contracting to facilitate movement of our skeletons.

Smooth muscle

- Smooth muscle is also sometimes known as involuntary muscle due to our inability to control its movements.

- Smooth muscle is found in the walls of hollow organs such as the Stomach, Oesophagus, Bronchi and in the walls of blood vessels.

Cardiac muscle (heart muscle)

This type of muscle is found solely in the walls of the heart. It has similarities with skeletal muscles in that it is striated.

Muscles are described as running from a proximal origin to a distal insertion.

A muscle generally receives its blood supply from one main artery, which enters the muscle in a single/branches.

A single nerve, which carries both motor efferents and sensory afferents.

Efferent nerves, otherwise known as motor neurons, carry nerveimpulses away from the CNS to effectors such as muscles or glands.

The opposite activity of direction or flow is afferent.

MuscleGross Morphology

Skeletal muscle

- Skeletal muscle is a fascinating biological tissue able to transform

chemical energy to mechanical energy.

- Skeletal muscle has three basic performance parameters that

describe its function:

Movement production

Force production

Endurance

- The production of movement and force is the mechanicaloutcome of skeletal muscle contraction.

Skeletal muscle..

The skeletal muscles like the joints, are designed to contribute to the bodys needs for mobility and stability.

Muscles serve a mobility function by producing or controlling the movements of a bony lever around a joints axis.

A human skeleton without muscles will collapse when placed in the erect standing position.

Skeletal muscles are length- and velocity-dependent force generators.

The muscles transmit force to bones via tendons.

Biological soft tissues are nonlinear, anisotropic, fibrous composites.

One can separate these tissues based on their mode of loading: cartilage is generally loaded in compression;

tendons and ligaments are loaded in tension; and muscles

generate active tension.

The structure and material properties differ to accommodate the tissue function.

Structure of Skeletal Muscle

- The functional unit that produces motion at a joint consists

of two discrete units, the muscle belly and the tendon.

- The muscle belly consists of the muscle cells, or fibers, thatproduce the contraction.

Structure of an Individual Muscle Fiber

- A skeletal muscle fiber is a long cylindrical, multinucleated

cell that is filled with smaller units of filaments (Fig).

- These filamentous structures are roughly aligned parallel tothe muscle fiber itself.

The largest of the filaments is the myofibril, composed ofsubunits called sarcomeres that are arranged end to end thelength of the myofibril.

Each sarcomere also contains filaments, known asmyofilaments. There are two types of myofilaments within eachsarcomere.

The thicker myofilaments are composed of myosin proteinmolecules, and the thinner myofilaments are composed ofmolecules of the protein actin.

Structure of muscle..

The myofilaments in each sarcomere are 1 to 2 m long; themyosin myofilaments are longer than the actin myofilaments.

Thus sarcomeres in humans are a few micrometers in length:varying from approximately 1.25 to 4.5 m with musclecontraction and stretch.

Sliding of the actin myofilament on the myosin chain is thebasic mechanism of muscle contraction.

The Sliding Filament Theory of Muscle Contraction

The sarcomere, containing the contractile proteins actin and

myosin, is the basic functional unit of muscle.

Contraction of a whole muscle is actually the sum of singularcontraction events occurring within the individual sarcomeres.

The organization of the sarcomere.

The thinner actin chains are more abundant than the myosin

myofilaments in a sarcomere.

The actin myofilaments are anchored at both ends of thesarcomere at the Z-line and project into the interior of thesarcomere where they surround a thicker myosin myofilament(Fig. 4.2).

The amount of these contractile proteins within the cells is

strongly related to a muscles contractile force.

Contraction results from the formation of cross-bridges

between the myosin and actin myofilaments, causing the actin

chains to slide on the myosin chain (Fig 4.3).

The tension of the contraction depends upon the number of

cross-bridges formed b/w the actin and myosin myofilaments.

The number of cross-bridges formed also depends on the

frequency of the stimulus to form cross-bridges.

Contraction is initiated by an electrical stimulus from the

associated motor neuron causing depolarization of the muscle

fiber.

When the fiber is depolarized, calcium is released into

the cell and binds with the regulating protein troponin.

The combination of calcium with troponin acts as a trigger,causing actin to bind with myosin, beginning the contraction.

Cessation (stop) of the nerves stimulus causes a reduction incalcium levels within the muscle fiber, inhibiting the crossbridgesb/w actin and myosin.

The muscle relaxes stimulation of the muscle fiber occurs at asufficiently high frequency, new cross-bridges are formed beforeprior interactions are completely severed, causing a fusion ofsucceeding contractions.

Ultimately a sustained, or tetanic, contraction is produced.

Modulation of the frequency and magnitude of the initialstimulus has an effect on the force of contraction of a wholemuscle.

The Connective Tissue System within the Muscle Belly

The muscle belly consists of the muscle cells, or fibers, andthe connective tissue that binds the cells together (Fig. 4.4).

The outermost layer of connective tissue that surrounds theentire muscle belly is known as the epimysium.

The muscle belly is divided into smaller bundles or fasciclesby additional connective tissue known as perimysium.

Finally individual fibers within these larger sheaths aresurrounded by more connective tissue, the endomysium.

Thus the entire muscle belly is invested in a large network ofconnective tissue.

The amount of connective tissue within a muscle and the size

of the connecting tendons vary widely from muscle to muscle.

The amount of connective tissue found within an individual

muscle influences the mechanical properties of that muscle.

Effect of Fiber Length on Joint Excursion

Fiber length has a significant influence on the magnitude of thejoint motion that results from a muscle contraction.

The fundamental behavior of muscle is shortening, and it isthis shortening that produces joint motion.

Each sarcomere can shorten to approximately the length of itsmyosin molecules.

Because the sarcomeres are arranged in series in a myofibril, amuscle fiber can produce is the sum of the shortening in all ofthe sarcomeres.

Thus the total shortening of a muscle fiber depends upon thenumber of sarcomeres arranged in series within eachmyofibril.

The more sarcomeres in a fiber, the longer the fiber is andthe more it is able to shorten (Fig. 4.5).

The amount a muscle fiber can shorten is proportional to itslength. A fiber can shorten roughly 50 to 60% of its length.

Sliding filament model of muscle

Basic Behaviors of the Skeletal Muscle

Extensibility the ability to be stretched or to increase in

length

Elasticity the ability to return to the original length after a

stretch

Irritability the ability to respond to a a stimulus

Ability to develop tension: the ability to decrease in length

Contractions

A concentric contraction is a type of muscle contraction in which the muscles shorten while generating force.

During a concentric contraction, a muscle is stimulated to contract according to the sliding filament mechanism.

An eccentric contraction occurs when a muscle is contracting, and an external force is trying to lengthen the muscle ( strain).

- An eccentric contraction is also a type of strengthening exercise for a muscle, when performed in a controlled manner.

An isometric contraction of a muscle generates force without changing length. An example can be found when the muscles of the hand and forearm grip an object.

Effect of Muscle

The moment arm depends on the location of the musclesattachment on the bone and on the angle between the line of pullof the muscle and the limb to which the muscle attaches.

This angle is known as the angle of application (Fig).

The sine of the angle of application, , can be measured directly.

Fig.: The relationship between a muscles moment arm and excursion.

Structural Organizaiton of Skeletal Muscle

Depends on muscle fiber, motor unit,

fiber types, and fiber architecture

- parallel fiber arrangement parallel to the

longitudinal axis of the muscle,

e.g. sartorius, biceps brachii, etc.

- pennate fiber arrangement at an angle to the longitudinal axis of the muscle, e.g. rectus femoris, deltoid, etc.

The greater the angle of pennation, the smaller the amount of effective force transmitted to the tendon

The angle of the pennation increases as tension progressively increases in the muscle fibers

Muscle Size and Its Effect on Force Production

The angle at which the fibers insert into the tendon also influences the total force.

This angle is known as the angle of pennation.

The tensile force generated by the whole muscle is the vector sum of the force components that are applied parallel to the muscles tendon (Fig. 4.11).

Therefore, as the angle of pennationincreases, the tensile component of the contraction force decreases.

Figure 4.11: The overall tensile force (FM) of a muscle is

the vector sum of the force of contraction of the pennate

fibers (FF).

Muscle strength

The muscles tensile force of contraction and its resulting moment are related by the following:

M = r X F

where M is the moment generated

F = the muscles tensile force applied at a distance,

r is the muscles moment arm

The primary factors influencing the muscles strength are

Muscle size, Muscle moment arm, Stretch of the muscle

Contraction velocity, Level of muscle fiber recruitment

Fiber types composing the muscle

Mechanical Properties of the Skeletal Muscle

Force-Length/Length-Tension Relationship

The tension that a muscle generates

varies with its length

Found when a muscle under isometric

contraction and for maximum activation

of the muscle

In a single muscle fiber,

peak force is noted at normal resting length

a bell-shaped length-tension curve

In a muscle, force generation capacity increases when the muscle is slightly stretched because of the effect of both active and passive components.

Force-Velocity Relationship

Muscle force decreases as the velocity of contraction increases (Hill, 1938)

- only true for concentric contraction

Muscle force decreases with increased velocity of contraction during concentric contraction whereas it increases with increased velocity of contraction during eccentric contraction.

Eccentric strength of a muscle can exceed isometric strength by a factor of 1.5 to 2.0, but this is true only under electric stimulation of the motor neuron.

Maximum strength can be generated either by recruitment of more motor unit or by increase in muscle length

Forcevelocity relationship

The speed at which a muscle changes length also affects the force it can generate.

Force declines in a hyperbolic fashion relative to the isometric force as the shortening velocity increases, eventually reaching zero at some maximum velocity.

The reverse holds true for when the muscle is stretched force increases above isometric maximum, until finally reaching an absolute maximum.

This has strong implications for the rate at which muscles can perform mechanical work (power).

Effects of the magnitude of the contraction velocity on force production in muscle

Contractile velocity of a muscle is

determined by the change in length per

unit time.

Thus an isometric contraction has zero

contraction velocity.

In contrast, a concentric contraction (shortening contraction), is shortening of the muscle, has a positive contraction velocity.

The contractile force is maximum when contraction velocity is zero (isometric contraction) and decreases as contraction velocity increases (Fig. 4.19).

Since power is equal to force times velocity, the muscle generates no power

at either isometric force (due to zero

velocity) or maximal velocity

(due to zero force).

Instead, the optimal shortening velocity for power generation is approximately one-third of maximum shortening velocity.

These two fundamental properties of muscle have numerous biomechanical consequences, including limiting running speed, strength, and jumping distance and height.

Muscle Architecture

Where M = muscle mass, = muscle density (1.056 g/cm3

in fresh tissue), = surface pennation angle, and L f = myofiber length.

This formulation provides a good estimate of experimentally measured

isometric muscle force output

It is typically described in terms of muscle length, mass, myofiber length, and physiological cross-sectional area (PCSA).

PCSA: The standard measure used to approximate the number offibers of a whole muscle, projected along the muscles line of action, it is calculated as:

Muscle Force-Velocity Relationship Under conditions of constant load the relationship between force and velocity is nearly hyperbolic.

The shortening force - velocity relation can be described by:

Where a and b are constants derived experimentally, P is muscle force,

Po is maximum tetanic tension, and v is muscle velocity.

Mechanical Model

The combined effects of muscle contraction and stretch of

the elastic components are represented mechanically by a

contractile element in series and in parallel with the elastic

components (Fig).

Fig: A mechanical model of the

contractile and elastic components of a

muscle.

A muscles contractile (actin andmyosin) and elastic (connective tissue)

components are modeled mechanically

as a combination of a contractile

element (CE) with springs that

represent the elastic elements that are

both in series (SE) and in parallel (PE)

with the contractile component.

Mechanical Model of a Muscle

contractile component muscle fiber series elastic component (SEC) tendon

parallel elastic component (PEC) muscle membrane

Neuromuscular disease

It is either directly, via intrinsic muscle pathology, or indirectly, via nerve pathology, impair the functioning of the muscles.

Neuromuscular diseases are those that affect the muscles and/or their nervous control.

In general, problems with nervous control can cause either spasticity or some degree of paralysis, depending on the location and the nature of the problem.

A large proportion of neurological disorders leads to problems with movement.

Some examples of these disorders include

- Amyotrophic Lateral Sclerosis (ALS or Lou Gehrig's Disease),

- Cerebrovascular accident (stroke),

- Parkinson's disease,

- Multiple sclerosis,

- Muscular dystrophy,

- Myasthenia gravis, etc

Cartilage

Cartilage is a flexible connective tissue found

in the joints between bones, the ear, the

nose , in joints, and the intervertebral discs.

It is not as hard and rigid as bone but is stiffer

and less flexible than muscle.

Cartilage is composed of specialized cells called

Chondroblasts , composed of Type II collagen fibers,

and elastin fibers.

It does not contain blood vessels. thus it heals very slowly.

These mechanical properties include the response of cartilage in frictional, compressive, shear and tensile loading.

Such experiments reveal that when the muscle is very short, stimulation produces a small contractile force.

As the stretch increases and stimulations continue, the tension in the muscle increases.

The overall tension of the muscle is greatest when the muscle is stretched maximally.

Structure of Soft Tissue

Cartilage

Articular cartilage is found at the

ends of bones, where it serves as

a shock absorber and lubricant between bones of 1-2mm

thickness.

The composition of articular cartilage consists of approximately 20% collagen, 5% proteoglycan, & remaining 75% water.

Tendons

A tendon is a tough band of fibrous connective tissue that usually connects muscle to bone and is capable of withstanding tension.

Tendons are similar to ligaments and fasciae as they are all made of collagen except that ligaments join one bone to another bone, and fasciae connect muscles to other muscles.

Tendons and muscles work together.

Normal healthy tendons are composed mostly of parallel arrays of collagen fibers closely packed together.

The mechanical properties of the tendon are dependent on the collagen fiber diameter and orientation.

- Finally, multiple fascicles are bundled into a complete tendon or ligament encased in a reticular membrane.

- Individual collagen fibrils also display some inherent elasticity, and these two features are believed to determine the bulk properties of passive tensile tissues.

FIGURE 2.1 Tendons are organized in progressively larger

filaments, beginning with molecular tropocollagen, and building

to a complete tendon encased in a reticular sheath.

Ligaments

It is most commonly refers to a band of

tough, fibrous dense regular connective tissue

comprising attenuated collagenous fibers.

Ligaments connect bones to other bones to form a joint.

Ligaments are viscoelastic. They gradually lengthen when

under tension, and return to their original shape when the

tension is removed.

They act as mechanical reinforcement.

Instability of a joint can over time lead to wear of the cartilage and eventually to osteoarthritis.

Tendon and Ligament

Because the biomechanical behavior of a tissue is deter-mined by its composition and structure, the mechanical properties of ligaments, tendons, and cartilage are also considerably different.

The structural properties are inuenced not onlyby the properties and geometry of the tissue but also by the mechanical properties of the bonetissue and muscletissue junctions.

The passive tensile tissues, tendon and ligament, are composed largely of water and collagen.

The collagen fibrils, with the 2040-nm fibrils being bundled into 0.212-m fibers.

The fibers are bundled into fascicles, supported by fibroblasts or tenocytes, and surrounded by a fascicular membrane.

Tendon & Ligament

Ultimate tensile stress of tendon considerably high (50-

100 MPa)

Viscoelastic behaviors

creep, stress-relaxation

strain rate sensitivity, different from bone

fast strain rate ligament injuries, slow rate

(avulsion fracture)

Partial failure

Geometry

Tendon & Ligament

Age

before maturity: more viscous & compliant

maturity: stiffness & modulus of elasticity

After middle age: viscosity, weak insertions