Biomechanics of Physical Rehabilitation and Kinematics of Exercise

Biomechanics of Physical Rehabilitation and Kinematics of Exercise

Joseph P. Weigel and Darryl Millis


Mechanics as developed by Sir Isaac Newton describes how force and mass interact in three-dimensional space and time on the surface of the earth. Biomechanics is the application of Newtonian mechanics to biologic systems. Newtonian mechanics is founded on three classic laws of motion. The first law describes the static state of a body under the influence of balanced force. The second law describes the motion or dynamic state of a body under the influence of unbalanced force. The third law describes the interaction between multiple bodies.

Law I (Law of Statics)

When the sum of all the forces acting on a body equals zero, the body is in a static state (i.e., the body is at rest or in unchanging, constant motion with no acceleration).



Under certain conditions, the static state is desirable. For example, to enhance the conditions for healing, fractured bones are managed by fixation systems designed to place fracture segments in a static state or at rest. It is therefore the goal of the surgeon to balance, both in direction and magnitude, all the forces that tend to cause motion of the fragments. In the case of a fractured tuber calcis the proximal fragment is under a large tension load caused by the pull of the attached gastrocnemius muscle. Without fixation this pull is unopposed, causing motion of the bone fragments, which disrupts the body’s attempt to bridge and stabilize the fracture. When a system of pins and a tension band wire are placed across the fracture, the wire, by virtue of its position and strength, counters the tension load of the gastrocnemius muscle with a corresponding compression load provided by the tension band wire. When the sum of the forces acting across the fracture equals zero, the fracture is in static equilibrium, a condition that fosters bone bridging. It is important to exercise caution when applying physical rehabilitation to animals with healing fractures such that these activities do not result in creating an imbalance of force, causing motion of the fracture. The static state of the fracture must be maintained even though the therapist is focused on motion of joints and the strength of muscles.

Static exercise can be an effective way of stretching and enhancing flexibility by the strategic and controlled application of force without producing motion. Static stretching may improve soft tissue extensibility, which increases the capacity for energy absorption and transfer when running, for example. Practical methods for preexercise preparation in animals have not been established. Dogs are often left sedentary for long periods and then are suddenly released for unrestrained activity, often at high performance levels. After long periods of relative inactivity, ligaments, muscle, tendons, and fascia are “tight,” less ductile and less able to tolerate acute strain. Stiff soft tissue has less capacity to absorb impact, lending itself to tearing or rupture. A common thread in the clinical history of cranial cruciate injury in the dog is the occurrence of sudden lameness during vigorous activity following long periods of inactivity.

Law II (Law of Dynamics)

When the sum of all the forces (resultant force) acting on a body is not equal to zero, the body is in a dynamic state (i.e., the body is not at rest and is in a state of changing motion or accelerating).



Force (F), is a vector and therefore has not only intensity (magnitude) but also direction. Acceleration (a), the change in velocity over time, also has intensity as well as direction. Newton’s second law directly relates the cause of motion to the motion itself. In terms of magnitude, the harder a body is pulled or pushed by an increasing force, the faster it moves as seen with increasing acceleration and velocity. In terms of direction, the body will move or accelerate in the same direction as the applied force that has caused the motion. Therefore motion analysis or dynamics involves the application of arithmetic functions but within three-dimensional space, which also necessitates the use of trigonometric functions. Newton’s second law of motion can be expanded to describe the associated concepts of motion such as impulse, momentum, energy, work, and power.

The physical therapist applies Newton’s second law of motion when the speed or acceleration (change in velocity over time) of a therapeutic exercise is increased. When speed or acceleration increase, the load (force) on the limb must also be increased to achieve the faster motion. For example, hitting a wall with an automobile at 5 miles an hour might dimple a bumper, but hitting the same wall with the same automobile at 100 miles an hour could result in irreparable damage. Going faster means greater force, which then increases the risk for exacerbating an injury or inducing new injury. For example, repeated rapid, forceful flexion of the stifle in the case of a contracted quadriceps muscle can result in avulsion of the tibial tuberosity. Slow range of motion (ROM) exercises, slow stretching, and slow walking keep the applied forces low, preserving and protecting healing tissues.

Law III (Law of Action and Reaction)

When several bodies interact, the force resulting from the interaction is equal in intensity to the force causing the interaction and will act along the same line but opposite in direction.

Newton’s third law describes the event when one body impacts another. Newton observed that when one mass, moving under the influence of a causative force, impacts a second mass, a reaction force occurs. This reaction force is equal to the magnitude of the impacting force (original causative force) but acts in the opposite direction. This is easily observed in the case of a bouncing ball. When a ball is dropped to the floor, it impacts the floor and then reverses direction, moving away from the floor. The initial throwing force is reversed after the impact into a reaction or “bouncing” force. If the bouncing ball is replaced by a bag of sand, the bag will not bounce; however, reaction forces are still created but are absorbed by the sand in the bag. When an animal moves across the floor there is both an elastic response (like the bouncing ball) where force is reflected and an inelastic response (like the bag of sand) where force is absorbed.

Newton’s third law is the basis for the use of a force plate in analyzing an animal’s gait. When in motion, the animal impacts the plate, which results in a reaction force that is recognized by the plate and analyzed by a computer program. The reaction force, recorded at the point of foot impact (foot strike), is directly related to the force of weight bearing. This reaction force, called the ground reaction force (GRF), is transmitted up the limb in part as an elastic reaction where it is reflected by the stiffer tissues, and in a large part as an inelastic response where it is absorbed by the softer tissues. This absorption of force is an important function of the limb and all its components, and as a result, is an important consideration in physical rehabilitation. The therapist can manipulate the reaction force by applying various forms of exercise. For example, the aquatic treadmill mitigates the reaction force by using the buoyancy of the animal in water to reduce its weight. Slinging the abdomen during ambulation also reduces the impact of weight, thereby decreasing the reaction force. Sometimes a reaction force is magnified so it can be a means of “active therapy” during which it can stretch contracted tissues. Exercising down an inclined plane magnifies the reaction force by increasing the magnitude of impact on the front limbs. Also, a reaction force can be magnified by applying a syringe cap to the foot of the sound limb to encourage a shift of weight bearing to the contralateral limb, accelerating its rehabilitation. Conditions of the terrain, such as the stiffness of the floor, obstructions in the gait pathway, or unstable flooring can alter the magnitude and direction of reaction forces. When devising therapeutic plans, the therapist should consider the nature of the reaction forces and how they can be modified for the patient’s benefit.

In the case of animal physical rehabilitation, the application of the Newtonian laws of motion can be an ominous challenge. The animal is a complex and sophisticated system of interconnected objects having complex patterns of motion. This chapter attempts to incorporate the fundamental concepts of biomechanics to the practice of animal rehabilitation.

The Body in Equilibrium: Statics

Force is intuitively understood as a measure of intensity but also it must be viewed with respect to direction. For example pulling on a car door causes it to open while pushing on it causes it to close. To know only how hard to pull or push is insufficient in understanding the design, operation, and composition of a car door. Similarly, in biomechanics it is not only beneficial to know how hard the leg impacts during an exercise but also from which direction the force is acting. For example, living bone responds to weight bearing by increasing its mass and this response is not only caused by the intensity of the weight but also by where on the bone the weight load is localized. The classic Wolff’s Law can be described as the case where bone increases in mass in response to force that tends to push it together, whereas it decreases in mass where the force tends to pull it apart. In the case of corrective osteotomies, the goal is to help improve limb alignment, distribution of weight bearing forces, and joint function by altering the anatomy and redirecting weight bearing, creating an improved mechanical environment.

When the animal is at rest (standing still), the forces acting on the body have not disappeared but have been counterbalanced by forces acting in opposite directions. Mechanical analysis of the body in this static state facilitates understanding of the types of forces at play. There are four basic forces: compression, tension, shear, and moment or torque. The kind of force depends on its direction. A force that tends to push on a body is referred to as compression; if it tends to pull on the body, it is called tension; if it tears or shreds the body, it is shear; and finally, if it tends to rotate or turn the body, it is a moment or torque.

To evaluate direction, a reference or coordinate structure is necessary. Commonly a three-axis rectangular system representing the three dimensions of space (height, width, and length) is used. By convention this axis system is composed of three perpendicular axes, labeled z for the vertical direction, y for the horizontal direction, and x for the transverse direction.

Rotation (Moment of a Force or Torque)

A force can also tend to cause a mass to rotate about a point called the center of rotation. The farther away from the center of rotation the force is applied, the greater is the tendency for rotation. This tendency is called “moment of a force,” and the distance from the center of rotation to the point of force application is called the moment arm. Mathematically, moment is represented by multiplying the force by the moment arm:



where M is the moment of the force, F is the force, and d is the moment arm.

Moment is critical to the understanding of how force acts in the musculoskeletal system. Although forces of body weight and muscle contraction push and pull at the body, they also cause rotation at each of the joints when these forces do not pass through the center of rotation of the joint. For example, there is a tendency toward flexion (rotation in one direction) of the joints in the front limb of a standing animal, which is caused by the body’s weight pushing down at a location that is off center of the respective joint. The animal is able to stand because the tendency toward flexion is counterbalanced by a tendency toward extension (counter rotation in the opposite direction) caused by contraction of several muscles, including the supraspinatus, triceps brachii, and extensor carpi radialis muscles. In the rear limb, flexion caused by the body’s weight at the hip, stifle, and tarsal joints is counterbalanced by contraction of the gluteal, quadriceps, and gastrocnemius muscles, which causes extension at each of these joints. The actions of these forces of weight and muscle contraction are defined as moments, which are very important, especially in the analysis of gait.

Moments of force are important in the effective function of muscle in sustaining weight bearing. For example, in the stifle the normal position of the patella creates an effective moment by the quadriceps about the center of rotation of the stifle such that extension of the stifle is maintained enough to bear weight. However, the function is altered when the patella is not in its normal position and is dislocated medially. In the dislocated position the moment arm of the tension force in the quadriceps is reduced or eliminated (Figure 24-1). The closer the tension force is to the center of rotation, the less extension is possible. Therefore a dog with luxating patellas is weak in the rear limbs and unable to bear weight normally or perform activities, such as jumping.

Lever Systems in the Body (Application of Moments of Force)

A lever is a simple machine using the principle of moments to overcome a resistance load. There are three classes of levers: Class I, in which the fulcrum (point of rotation) is between the effort force (applied force usually resulting from muscle contraction) and the resistance force (load force, which is generally the weight of the body or limb); Class II, in which the resistance is between the effort and fulcrum; and Class III, in which the effort is between the resistance and the fulcrum.

A variety of levers are used by the animal to extend and flex the various joints of the limbs. For example, extension of the elbow is accomplished with a Class I lever in which the fulcrum is located at the center of rotation of the joint, the resistance or load force is located at the point where the foot contacts the ground, and the effort or action force, which is produced in the triceps muscle, is located at its insertion point on the olecranon (Figure 24-2). With flexion of the elbow, a Class III lever is in operation in which the effort is located at the insertion of the biceps brachii, which is between the fulcrum (elbow joint) and the resistance force, which is located at the end of the antebrachium (Figure 24-3).

Class II levers are uncommon. An example is the rear foot, in which the weightbearing toes act as the fulcrum, the resistance or load force is the body weight just caudal to and at the foot, and the effort force is the gastrocnemius muscle (Figure 24-4).

In contrast, both extension and flexion of the stifle joint are accomplished with a Class III lever, in which the effort or action load is located at the insertion of the quadriceps muscle on the tibial tuberosity (for extension) or the insertion of the semitendinosus muscle on the proximal tibia (for flexion), which is located between the fulcrum (stifle joint) and the resistance force, which is located at the distal end of the limb.

The relative magnitudes of the effort versus the resistance is the value of understanding lever systems and their function in the musculoskeletal system. The effort force multiplied by its distance (moment arm, de) to the fulcrum is the effort moment. The resistance force multiplied by its perpendicular distance (moment arm, do) to the fulcrum is the load moment. In the balanced state in which the lever is not moving or moving without acceleration, the effort moment must equal the load moment. This Law of the Lever system establishes the relationship between the effort and resistance loads. When comparing the magnitude of required effort to overcome the magnitude of a specified resistance, compare the respective moment arms. If the effort moment arm is longer than the resistance moment arm, then the effort force necessary to overcome the resistance will be relatively less than the magnitude of the resistance.



In the case in which rotation is inhibited by contracture or fibrosis leading to decreased ROM, therapists use “passive” ROM exercise by pushing or pulling on the lower part of the limb to induce flexion or extension in a target joint. Passive ROM is often used to reduce the possibility of stiffness or to improve the mobility of stiff joints. In some of these exercises the lever action is altered. For example, stretching in flexion of a dog with hyperextension stiffness of the stifle presents the conditions for a Class II lever (Figure 24-5). The point of resistance is the insertion of the quadriceps muscle on the tibial tuberosity, which is located between the fulcrum (stifle joint), and the effort, which is the location of the therapist’s hold on the distal crus of the leg. In this case, the effort is relatively far from the stifle when compared with the resistance that is close to the joint. When the quadriceps is adhered to the underlying bone and joint capsule and has lost its elasticity, it has also lost its capacity to absorb energy and load. As the therapist pushes on the tibia to produce flexion in the stifle, the resistance load in the stiff quadriceps quickly rises, creating a magnitude of force that has the ability to result in tearing of the quadriceps or even avulsion of the tibial tuberosity. Because the moment arm length of the effort force is great, a large moment can be generated, potentially causing damage. It is important for the therapist to understand the relationship between the effort or action load and the reactive or resistance load when employing certain therapeutic exercises. In the previous example, moving the hands closer to the stifle joint reduces the moment arm length, and therefore makes it more difficult to generate a large moment, reducing the possibility of tissue damage.

Other exercises such as “wheel barrowing” on the front limbs or “dancing” on the rear limbs employ the use of lever systems. In the case of wheel barrowing or walking down an incline (to increase weight bearing on the front limbs), the spine becomes a Class II lever in which the resistance (center of gravity [COG] of the body) is located between the fulcrum at the shoulder joint and the effort in which the therapist is lifting the caudal end of the body. It is also important to note that as the spine is raised from the rear, the COG of the body moves to a location that is more dorsal to the shoulder, introducing a horizontal component of the weight, which acts as a shear force across the shoulder joint (Figure 24-6). As a result, increased stress in the joint capsule, collateral ligaments, and tendons will likely occur. This horizontal shear force may also cause an additional moment to occur at the level of the elbow joint, which is likely resisted by additional contraction of the triceps muscle. It has been observed that the angle of the shoulder joint becomes more extended with wheelbarrowing,1 which moves weight bearing from the center of the humeral head to a more cranial location where there is less articular cartilage and bone. Dancing is the reverse of this example; in dancing the spine is raised from the front and used as a Class II lever. As with the effects on the shoulders, the same likely occurs on the hips. For example, the addition of shear force across the hip joint has the potential of increasing mechanical stresses in the articular cartilage, which may be deleterious to a dysplastic joint. Increased moment across the stifle would likely be resisted by increased contraction of the quadriceps muscles, strengthening this muscle group. The effectiveness of physical rehabilitation exercises could be enhanced by detailed mechanical evaluation looking at not only the magnitudes of weight-bearing forces but also the altered direction of these forces.

Tissue Response to Force

To understand how force affects the body, the response of the various tissues to force is important to analyze. Each of the tissues involved respond differently because the composition of each is different. These responses are unique to the tissue and can be called the material properties of the tissue. These properties include measures of stiffness, elasticity, plasticity, strength, failure limits, and energy absorption. Basically, a tissue responds to force in two ways: first, an intrinsic resistance to the applied force is called stress; second, an accommodation to the applied force by a change in the shape of the tissue is called strain.


Stress is directly related to the magnitude of the applied force (i.e., the greater the applied force, the greater the stress within the tissue). Stress is also inversely related to the area over which the total force is acting (i.e. the larger the area, the lower the stress). This understanding of the nature of stress explains how a scalpel cuts the skin. A sharp blade has an extremely thin edge so that with light pressure the force is concentrated at the edge of the blade and the stress in the skin is very high, causing the skin to break away and separate. A dull blade with a wider edge requires more force to increase the stress to the skin and cause it to separate.

Stress is particularly important in the understanding of how articular cartilage responds to force applied across a joint surface. Under conditions in which the anatomy is normal and the joint is physiologically and mechanically normal, the surface of the joint spreads the applied forces over a wide area such that the stress at any specific point on the cartilage is low. However, if the joint is anatomically deranged, such as with a growth deformity, or is mechanically unstable, such as with hip dysplasia, joint forces are concentrated on smaller surface areas, causing high degrees of stress and subsequent breakdown of the articular cartilage (Figure 24-7).

Motion of a joint is not only important for the physiologic health of the articular cartilage, but also for the mechanical integrity of the cartilage. For example, long-term immobilization of a normal joint can induce osteoarthritis. The lack of motion results in a concentration of force over a small area of articular cartilage. This increases the stress, causing a breakdown in the cartilage structure, inducing an inflammatory response and osteoarthritis. Distributing weight-bearing forces over a wider area of the joint surface is one way to minimize articular cartilage stress, but also reducing the weight-bearing force itself while maintaining joint motion should reduce the stress. This may be accomplished with an aquatic treadmill in which the water tempers the weight-bearing force but allows normal ROM.


As a result of an applied force, a tissue can change shape. For example, a ligament stretched by a tension force will lengthen, and this increase in length is termed tensile strain. Likewise, compressive force compacts tissue, creating a compressive strain, and shear force translates portions of tissue, creating a shear strain. For some tissues, strain and strain rates may depend on the direction or orientation of the force causing the strain. Such a property is referred to as anisotropy. For example, depending on which direction the force is acting on a section of bone, the strain value is different. Bone is stronger under compression than it is under tension, meaning that the strain is less (i.e., the bone deforms less under a compressive load than it does under the same intensity load in tension). The opposite is true in the case of a ligament: the ligament deforms less under tension than it does under compression.

Stress versus Strain

For any tissue under the influence of force, its response can be graphed as stress versus strain, which demonstrates additional properties of the tissue response to force (Figure 24-8). The initial response in the graph is termed the toe region of the graph. This phenomenon is more typical with soft tissue such as a tendon or ligament as opposed to bone. A tendon in its completely relaxed state has a crimped or wavy pattern of the collagen fibers. When the tendon is mounted in the testing machine and then pulled, the initial recording represents a straightening of the crimp and does not represent any part of the strength of the tendon in tension. It is also helpful to pass through this “toe” region by “prestressing” the tendon (i.e., stretching the tendon to eliminate the crimp). The slope of the graph gives a measure of stiffness of the tissue. Steep slopes occur when the tissue is inflexible and brittle like that of bone, whereas a shallow slope represents tissue with flexibility, like that of muscle or tendon. The linear portion of the graph describes the elasticity of the tissue. In this range the tissue is deforming or undergoing strain, but when the load is removed, the tissue returns to its original length. The upper curved portion of the graph describes the plasticity of the tissue. In this range the tissue is deforming, but when the load is removed the tissue does not return to its original shape, meaning that a permanent change has taken place; therefore the tissue has undergone a “plastic deformation.” The peak of the curve is the highest level of stress the tissue tested can withstand and is referred to as the ultimate strength of the tissue. Failure under stress is demonstrated as a decreasing capability to maintain the stress and the value begins to drop as the load increases, or complete failure as the stress drops to zero, indicating that the tissue can no longer hold up under any applied load. In addition to these features, the area under the stress versus strain curve represents the amount of energy that is absorbed or stored in the material as it is loaded. Once failure occurs, the stored energy is released in the form of a fracture or tearing event.

For bone, the response is more predictable and consistent as compared with muscle, tendon, and ligament. Bone behaves in a linear way as a elastic solid, but for the soft tissues where the response is more variable and less predictable, the response is nonlinear. As opposed to bone, these tissues behave as a viscoelastic material. A viscoelastic solid’s properties, like stiffness, change over time. The response of a viscoelastic material additionally depends on factors like moisture content and temperature. For example, under the condition of cold temperatures, the tissue is stiffer so the stress is greater. When exercise is planned, often the tissues are physically warmed, which has the effect of reducing the stiffness and increasing its flexibility and elasticity. If the ligaments are cold and therefore stiff, a normal load could result in a higher than normal stress and in some cases the stress may be high enough to supersede the capacity of the ligament to remain intact, resulting in ligament damage.

Stress relaxation and creep are also additional phenomena that occur in viscoelastic materials. Stress relaxation is the condition when a tissue is deformed to a consistent state and the stress gradually diminishes over time. Although bone is more like an elastic solid, it exhibits some properties of viscoelasticity when compared with other solids, such as metal. The moisture in bone accounts for this response. In fracture repair, bolts and nuts are not used because of the viscoelasticity of bone. When a bolt and nut are used, the material in between is compressed. This material resists the compression by pushing back on the bolt and nut. This interaction of the applied force by the bolt and nut and the reactive force in the material stabilizes the bolt and nut. In a material that retains its stiffness the fixation remains stable; however, if the material is viscoelastic and its properties change, such as with bone, the stiffness decreases as water is squeezed from the bone. As the stiffness decreases, the push back decreases and the bolt and nut become loose and the fixation is lost. This phenomenon is referred to as stress relaxation in which the strain is constant but the stress decreases over time.

The converse event, in which the stress is constant and the strain changes over time, is referred to as creep. Creep is used frequently in passive ROM exercises in which a muscle tendon unit is stretched with a constant force and held for a period. During this time the strain in the muscle changes without increasing the force. The therapist can then relax the muscle, rest it, and then repeat the exercise, stretching the tissue to a new length while maintaining the pressure, allowing the tissue to stretch more without increasing the force. Understanding how creep functions, and that force does not have to be continuously increased to achieve lengthening, helps to make injuries, such as avulsion fractures, less likely to occur during therapy sessions.

The Body in Motion: Dynamics

When the forces acting on a body become unbalanced and the sum of these forces is not equal to zero (resultant force), the body will move in the same direction as the resultant force. The displacement, in terms of acceleration, is directly proportional to the resultant force by Newton’s second law:



where F is the resultant force, m is the mass, and a is the acceleration.

Evaluation of the left side, or the force side, of this equation is the science of kinetics, whereas evaluation of the right side, or the displacement side, is the science of kinematics.


Kinetic gait analysis can be used to evaluate normal weight bearing, identify alterations in weight bearing, aid in the diagnosis of disorders of locomotion, and evaluate treatment effects. The typical format for evaluating the forces involved in the motion of an animal is the use of the force platform. The force platform is a plate instrumented with a series of strain gauges or crystals and mounted into the floor. Because of their symmetry and convenient speed, the walk and trot are the conventional gaits that are used for evaluation of gait and assessment of lameness. The trot is usually the easier gait to obtain data. At a walk, dogs are more likely to be distracted and have a less consistent gait. When the animal steps on the plate, the sensitive strain gauges or crystals generate an electrical signal that is sent to a data processor and a computer. Multiple signals, collected over time, define the stance phase of the gait, from the time the foot strikes the plate until the instant the foot leaves the plate. The right side of the equation, the displacement side, is kept constant by setting the velocity and acceleration to a well-defined range, for example, trotting at a velocity of 1.7-2 m/s and acceleration of ± 0.4 m/s2. To generate a readable report, the animal is trotted across the plate such that the front and rear limb, on the same side, fully contact the plate once (Figure 24-9). Often an animal may not lead consistently or may be cautious of the plate by shifting weight, attempting to avoid contact. Therefore a single tracing is not considered reliable by itself. Several identical tracings (usually a minimum of three) are considered more reliable in presenting to the evaluator a more realistic representation of the actual gait routine for that animal.

The force plate is capable of measuring reaction forces in all three dimensions: the vertical (z axis), the horizontal (y axis), and the transverse direction (x axis). Pressure pads or mats have also been developed and have the advantage of being able to evaluate patients too small to participate in force platform analysis and to collect data from multiple limb strikes. This may allow the objective evaluation of small dogs and cats with conditions such as avascular necrosis of the femoral head and medial patella luxation.2,3 However, they typically only measure relative weight bearing by a limb rather than actual force, and they do not allow the resolution to z, y, and x forces.

Vertical Ground Reaction Forces

Pressure exerted in the vertical direction on the force plate generates an equal but opposite reaction force in the force plate. This vertical GRF represents the animal’s weight-bearing performance and is often measured as a percent of body weight. The term peak force represents the maximum value of the GRF during the stance phase of gait, whereas impulse represents the generation or dissipation of reaction force occurring over time. Normal peak vertical GRF for the front limb at a trot is 110-125% of body weight, and for the rear limb is 65-75% of body weight,4 and are typically symmetric with a single peak (Figure 24-10). Walking generates a biphasic Z force curve similar to that seen in humans, resulting in a classic m-shaped graph in which the initial peak represents the vertical force component associated with the initial paw strike in the early stance phase and the second peak represents the increase in vertical force at the time of toe off or propulsion (Figure 24-11).5 Typical peak vertical force (Zpeak) measurements for the fore- and rear limbs while walking are lower than those measured while trotting and are typically 60% and 30% of body weight, respectively. Zpeak is affected by the gait, velocity, and acceleration of the dog, the dog’s body weight, conformation, and musculoskeletal structure.68 In both the walk and the trot, Zpeak increases as the forward velocity of the animal increases.6,9

Impulse, the area under the force-versus-time curve, is the change in momentum over time. As velocity increases at a trot, the vertical impulse (VI) increases as a result of the increased force.6,9,10 When comparing only peak vertical GRFs between individuals, how rapidly the limb is loaded and how long the limb bears the load are overlooked. These factors affect the impulse value and are not reflected in the peak force. If the limb bears load longer, for a similar peak load, the impulse will be significantly greater (Figure 24-12). ZPeak of a rear limb is greater while trotting than while walking, but because the stance time is longer at a walk, the impulse is greater while walking than while trotting. Therefore changes in both peak reaction force and impulse should be evaluated when rating gait performance, and repeated evaluations may only be compared if the dog is ambulating at the same gait, and velocity, and there is no acceleration or deceleration while measuring GRFs.

The animal’s COG is particularly important in weight distribution at a stance or while in motion. Traveling uphill tends to shift the balance of forces toward the hindlimbs, and moving downhill shifts the forces to the forelimbs.8 These factors may affect the forces generated during muscle contraction and be used advantageously during strengthening programs. Further evaluation of kinetic information includes symmetry of the tracing, and comparisons of tracings to the contralateral limb and previous tracings. In cases of lameness, the peak vertical GRF and VI are significantly reduced. Coefficients of variation between trials range from 5% to 9% for Zpeak and VI, whereas variation is higher for braking and propulsive forces. Most of the variability is due to dog and trial variation, with little influence on variation by experienced handlers.11 The symmetry of the tracing can also be altered with lameness. If the shape of the tracing is shifted to the left or right, the animal is quickly loading the limb and peaking early in the stance phase and then slowly unloading the limb throughout the remainder of the stance phase, or slowly loading the limb and quickly unloading it. The clinical significance is not clearly understood regarding this shift, but one study has suggested that a combination of Zpeak and the falling slope (unloading the limb) is more valuable in assessing lameness caused by cruciate ligament disease than either measure by itself.12 Changes in the shape of the tracing could represent lameness because it is reasonable to surmise that a painful limb would not be allowed to increase its load all the way to midstance but would peak early, or the limb would be rapidly unloaded, when the limb pain reaches an intolerant level. However this shift has been seen in contralateral limbs that are compensating for lameness in other limbs. In the compensation mode, loading of the limb peaks early to reduce the load on the painful limb. The difference may be related to the Zpeak. In the case of the shift occurring with lameness, the Zpeak is less than normal, whereas in the case of compensation, the left shift in the compensating limb is normal or higher than normal.

The stance time may also be assessed. The stance time of the gait cycle is the time when the limb is in contact with the ground and depends largely on the velocity of the subject. As the velocity increases, the stance time decreases.9,10 In addition, a lame limb typically has a shorter stance time compared with the unaffected limb.7,8,10,12

Horizontal Ground Reaction Forces

Pressure exerted in the direction of the animal’s motion occurs when the animal places the foot on the plate. This creates a GRF that is equal to the applied pressure but in the opposite direction. This GRF pushes back against the forward motion of the animal resulting in a braking action. As with the vertical force, the intensity of this braking force increases to a peak value then begins to decrease (Figure 24-13). However, there are important differences. Unlike the Zpeak, the braking force rises and falls in the first half of the stance phase, such that the horizontal GRF is zero at the midpoint of the stance phase. In addition, the braking force is opposite to the direction of animal motion and is therefore negative and appears below the horizontal axis. After the animal passes the midpoint of the stance phase, the pressure exerted by the foot on the plate causes a GRF that is in the same direction as the animal’s motion. This GRF pushes the animal along its motion and is therefore a propulsive force. Similar to braking, the propulsive force increases to a peak value and then decreases. The propulsive force cycles completely within the second half of the stance phase. These forces of braking and propulsion occur along the y axis. Normally, the forelimbs have greater braking forces than propulsive forces, and the hindlimbs have greater propulsion as compared with braking.

Measurement of Static Weight Bearing

Force plate and motion analysis systems are costly and require a relatively large dedicated workspace. Therefore their use in private practice is limited. Subjective lameness scales have traditionally been used, but have significant limitations. Weight bearing at a stance may be one method to obtain quantitative data regarding the relative amount of force placed on each limb while standing. A computerized system to objectively evaluate weight bearing at a stance in dogs may be useful for this purpose (Figure 24-14). Preliminary studies indicate that there is good correlation between Zpeak at a trot determined by force plate analysis and static weight-bearing pressures in dogs with rear-limb lameness.13 In fact, the difference between the lame and contralateral sound limb may be greater at a stance because there are three other limbs to shift the weight to, and the limbs are in contact for a longer time than at a trot, allowing additional time to shift the weight.


Kinematics is the science of the right side of Newton’s fundamental equation of motion. The right side of the equation relates displacement to its cause, the unbalanced force. Typically the equation is stated using acceleration as the unit of displacement. Acceleration is the rate at which the velocity changes with respect to time. Velocity is the rate at which the displacement occurs with respect to time. When viewing an animal in motion, linear motion is easily understood as the animal is seen moving in a straight line from one point to another. However, when the internal mechanics of the animal’s muscles and bones are studied, the initiating action is more circular than linear. This is analogous to the motion of an automobile. When viewing the car in motion, the action is linear as the car moves from one point to another. However, when the internal mechanics of the car are studied, the action is circular involving drive shafts, axels, and wheels. In the car, the force is generated by the up-and-down motion of pistons and rods. The action of this force is transmitted to a rotating camshaft to circular gears and rotating drive shafts and ultimately to the wheels, which rotate to propel the car forward in linear motion. In the animal, the force is generated by the up-and-down contraction of actin and myosin elements in the muscle. The contraction of these muscle elements causes rotation of the bones about the joints, propelling the animal forward in linear motion. A car is rated in terms of torque (i.e., its ability to generate force for motion). Similarly, in the analysis of the forces that generate motion in the body, torque or angular moment is important. Because circular motion is important in the generation of body motion, angular displacements must be measured and from these measurements angular momentum can be derived.

Real-time photographic, optoelectric technology is effective in measuring angles during continuous motion. Optoelectric technology involves the use of infrared cameras positioned for views in three-dimensional space. The animal is prepared with reflective markers secured to the body at predetermined points (Figure 24-15). These points are anatomic features that represent joint anatomy. Infrared light emitted from individual cameras is reflected from these markers back to the camera (Figure 24-16). As the joints move, the cameras record the displacement of the markers. Data points are analyzed with respect to a three-dimensional grid set up and calibrated at the beginning of the test. Such a system can record joint angle excursion throughout a full stride. Typical data acquired include stride length, stance and swing times, joint angles in all planes of motion, and linear and angular joint velocity and acceleration.

A stride includes a single swing and stance phase. The stance time of gait is the period when the foot is in contact with the ground, and the swing phase occurs when the foot is off the ground between stance phases. The swing phase has three distinct movements. The limb initially swings caudally following propulsion. The limb is then pulled cranially, and finally travels briefly caudally toward the ground in preparation for the next stance phase.14,15 The distance from initial contact of one limb to the point of second contact of the same limb is termed stride length, and a gait cycle is a series of events that includes one stride for each of the four limbs.5,14,15

The joint angle data can be plotted over the period of a single stride (Figure 24-17). These patterns of motion are specific for each joint and gait. Some results have been obtained both for normal gait and for lameness associated with cranial cruciate deficiency16 and hip dysplasia.

Combining Kinetics and Kinematics

The evaluation of force (kinetics) and of displacement (kinematics) can be combined or connected via Newton’s second law of motion. This connection is possible when kinetic and kinematic data are synchronously obtained. Such effort requires special technology to coordinate data acquisition. Once this is achieved, the constant in Newton’s equation, mass, must be determined for the body segments involved in the analysis. This includes not only the mass value itself, but also the distribution of mass (mass moment of inertia). Therefore Newton’s second law may be expressed specifically for linear motion (the study of the entire animal moving in a linear fashion):



where F is the force (kinetics: evaluation of force), m is mass, and a is acceleration (kinematics: evaluation of linear displacement). Specifically for angular motion (the study of the interior forces of the muscles and the angular movements of the bones):



where image is the moment (kinetics: evaluation of moment of force), I is the mass moment of inertia, and image is the angular acceleration (kinematics: evaluation of angular displacement).

When kinetics and kinematics are connected mathematically, forces and moments of individual joints can be determined by calculating the values from force plate ground reaction and joint motion values. This approach is referred to as inverse dynamics.

Kinetic and Kinematic Gait Analysis Research

Normal Gait

Knowledge of typical weight-bearing patterns in normal dogs and those with orthopedic conditions provides information that may be valuable in the rehabilitation of patients. In a normal standing patient, each forelimb bears approximately 30% of the dog’s body weight, and each rear limb bears 20% of body weight. The relative proportion of weight bearing on the fore- and rear limbs is relatively consistent at the walk and trot, which are symmetric gaits. However, because of the relationship of velocity and acceleration to the forces placed on the limbs during the stance phase of gait, significant increases in absolute forces during weight bearing occur with increasing speed at various gaits. For example, a dog may have Zpeak measurements of 55% and 30% of body weight at a walk in each fore- and rear limb, respectively. The forces may increase to 100%, 118%, and 125% in the forelimbs and 70%, 80%, and 85% in the rear limbs while trotting at 1.5-1.8, 2.1-2.4, and 2.7-3 meters per second, respectively.

Several studies have evaluated normal GRFs and kinematic motion of dogs at the walk and trot.4,6,7,9-12,14,17-27 Studies in normal dogs indicate that each joint has a characteristic and consistent pattern of flexion and extension during the walk, but complex joint movements may occur during the swing phase.14,19,27 Two additional studies described kinematic motion of the joints of normal dogs at a trot.17,18 The coxofemoral and carpal joints were characterized by a single peak of maximal extension and the femorotibial, tarsal, scapulohumeral, and cubital joints had two peaks of extension, with one peak occurring prior to the stance phase, and a second peak occurring during the stance phase.17,18 There were insignificant differences between trials and few differences among dogs of similar body type. It was concluded that kinematic gait analysis may provide a reliable description of joint motion in dogs of similar size and conformation. A recent study has evaluated not only the joint angle excursions at a walk, but also defined angular velocity and acceleration rates of those movements. This study indicated that these parameters are consistent and repeatable and helps to further characterize the normal walking gait of hound-type dogs.27 Additional studies are warranted to determine the sensitivity and specificity of alterations in these parameters as indicators for specific causes of lameness.

Cranial Cruciate Ligament Disease

Following cranial cruciate ligament rupture (CCLR), Zpeak may be only 50% of normal at a walk, and dogs may be non–weight bearing at a trot.28 By 7 months after extracapsular surgical repair, weight bearing is usually equal in both rear limbs at a walk. Experimentally, Zpeak at the trot with an extracapsular repair technique was normal by 20 weeks after surgery.29 Weight bearing in the contralateral rear limb initially increases, likely as a result of redistribution of weight from the affected limb to normal limbs, then returns to normal as weight bearing improves on the affected limb.

Dogs with CCLR have variable degrees of lameness and demonstrate altered movement in the hip, stifle, and hock joints.16 The stifle joint angle in the cruciate-deficient state was more flexed throughout the stance and early swing phase of stride and failed to fully extend in late stance, when limb propulsion is typically developed. In addition, extension velocity was negligible. The hip and hock joint angles, in contrast, were extended more during the stance phase, perhaps as a result of compensatory changes.16 Paw velocity and stride length were also significantly reduced in dogs with CCLR walking on a treadmill as compared with the contralateral side, and to normal dogs.30

Changes in kinematics were evaluated over a 2-year period in dogs with CCL-deficient stifles.31 All changes occurred primarily between 6 and 12 months. Peak cranial tibial translation increased by 10 mm and the range of abduction and adduction motion nearly doubled (from 3.3 degrees to 6.1 degrees) after CCL transection and did not improve with time. These changes may overload secondary restraints such as the medial meniscus. This objective information further defines the pathologic gait of CCLR patients.

More sophisticated techniques have been used to quantify net joint moments, joint powers, and joint reaction forces (JRFs) across the hock, stifle, and hip joints in Labrador retrievers with and without CCL disease using inverse dynamics calculations.32 Kinematic, GRF, and morphometric data were combined in an inverse dynamic approach to compute hock, stifle, and hip net moments, powers, and JRF while trotting. Vertical and braking GRF and JRF were decreased in CCL-deficient limbs. In fact, the braking/propulsion ratio shifted from 50% : 50% in normal limbs to 33% : 66% of the stance phase in CCL-deficient limbs. It is possible that reduced braking may result in decreased cranial tibial thrust. In affected limbs, extensor moments at the hock and hip, flexor moment at the stifle, and power in all three joints were less than normal. Greater joint moment and power of the contralateral limbs compared with normal were also identified. Other compensatory changes included increased time spent with the sound foot on the ground and an increased amount of force applied to all joints of the sound limb, especially during propulsion, compared with normal and CCL-deficient limbs. Propulsion generated around that joint at push-off was three times greater than normal, reflecting increased stifle extensor muscle contraction. Lameness predominantly affected forces during the braking phase and extension during push-off, and a greater contribution of the contralateral limbs to propel the dog forward was identified. These changes may be somewhat protective against damage to the articular cartilage and joint and may be mediated, in part, by the nervous system and a response to pain. In one study using a CCL transection and hindlimb deafferentation model, extension of the hip, knee, and ankle joints of the unstable limb was increased, and braking of the unstable knee was delayed or attenuated.33 These changes are different than models that have not used deafferentation. The model used in this study results in rapid onset and progression of osteoarthritis with cartilage erosions present by 13 weeks, perhaps because there is no pain sensation or joint proprioception is altered. Stifle hyperextension resulting from limb deafferentation, and knee instability resulting from CCL transection may work synergistically to create increased tibiofemoral motion and changes in the loading of articular surfaces that result in rapid joint breakdown.

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Jul 8, 2016 | Posted by in SUGERY, ORTHOPEDICS & ANESTHESIA | Comments Off on Biomechanics of Physical Rehabilitation and Kinematics of Exercise
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