What Are Degrees of Flexion? Biomechanics & Motion

Creator: Dr. Mohammed Hutaif
Published: 2023-01-25

Basic concepts
Definitions
Biomechanics—science of forces, internal or external, on the living body
Statics—action of forces on rigid bodies in a system in equilibrium
Dynamics—bodies that are accelerating and the related forces
Kinematics—study of motion (displacement, velocity, and acceleration) without reference to forces
Kinetics—relates the effects of forces to motion
Principal quantities
Basic quantities—described by International System of Units (SI); metric system
Length (m), mass (kg), time (sec)
Derived quantities: derived from basic quantities
Velocity
Time rate of change of displacement (meters/second)
Rate of translational displacement:
linear velocity
Rate of rotational displacement:
angular velocity
Acceleration
Force
Time rate of change of velocity (m/sec2)
Can also be linear or angular
□ Newton’s laws
Action causing acceleration of a mass (body) in a certain direction
Unit of measure: newton (N) = kg • m/sec2
First law: inertia
If the net external force ( F ) acting on a body is zero, the body remains at rest or moves with a constant velocity.
This law allows static analysis: Σ F = 0 (sum of external forces = zero)
Second law: acceleration
Acceleration (a) of an object of mass (m) is directly proportional to the force (F) applied to the object:
This law is used in dynamic analysis.
Third law: reactions
For every action (force), there is an equal and opposite reaction (force).
This law leads to free-body analysis.
This law also assists in the study of interacting bodies.
Scalar and vector quantities
Scalar quantities
Have magnitude but no direction
Examples: volume, time, mass, and speed (not velocity)
Vector quantities
Have magnitude and direction
Examples: force and velocity
Vectors have four characteristics
Magnitude (length of the vector)
Direction (head of the vector)
Point of application (tail of the vector)
Line of action (orientation of the vector)
Vectors can be added, subtracted, and split into components (resolved)
Resultant of two vectors: principle of
“parallelogram of forces”
Free-body analysis
Forces, moments, and free-body diagrams to analyze the action of forces on bodies
Force
A mechanical push or pull (load) that causes
external (acceleration) and internal (strain) effects
Unit of measure: the newton (N)
Force vectors ( F ): can be split into independent components for analysis
Usually in the x and y directions ( F x ,
F y ).
With angle (θ) between F x and F y .
A normal force is perpendicular to the surface on which it acts.
A tangential force is parallel to the surface.
A compressive force shrinks a body in the direction of the force.
A tensile force elongates a body.
Moment ( M )
Rotational effect of a force
Moment = force ( F ) multiplied by the perpendicular distance (the moment arm or lever arm = d ) from point of rotation:
Torque is a moment from a force perpendicular to the long axis of a body, causing rotation.
A bending moment is from a force parallel to the long axis.
The mass moment of inertia is the resistance to rotation.
Product of mass times the square of the moment arm:
Affects angular acceleration
Free-body diagram
A free-body diagram is a sketch of a body (or segments) isolated from other bodies that shows all forces acting on it.
The weight of each object acts through its center of gravity.
Center of gravity in the human body is just anterior to S2.
Finite element analysis
Complex geometric forms and material properties are modeled.
A structure is modeled as a finite number of simple geometric forms.
Typically triangular or trapezoidal elements
A computer matches forces and moments between neighboring elements.
Finite element analysis is often used to estimate internal stresses and strains.
Example: stress/strain at bone-implant interface
Other important basic concepts
Work
The product of a force and the displacement it causes
Work ( W ) = force ( F; vector components parallel to displacement) × distance (displacement produced by F )
Unit of measure: joule (J) = N • m
Energy
Ability to perform work (unit of
measure is also joule)
Laws of conservation of energy:
Energy is neither created nor destroyed.
It is transferred from one state to another.
Potential energy
Stored energy
Potential of a body to do work as a result of its position or configuration (e.g., strain energy)
Kinetic energy—energy caused by
motion (½mv2)
Friction (f)
Resistance to motion when one body slides over another
Produced at points of contact
Oriented opposite to the applied force
When applied force exceeds f , motion begins.
Proportional to coefficient of friction and applied normal (perpendicular) load
Piezoelectricity
Independent of contact area and surface shape
Biomaterials

□ Strength of materials
Electrical charge when a force deforms a crystalline structure (e.g., bone)
Concave (compression) side: charge is electronegative
Convex (tension) side: charge is electropositive
Study of relations between externally applied loads and resulting internal effects
Loads
Forces acting on a body
Compression, tension, shear, and torsion
Deformations
Temporary (elastic) or permanent (plastic) change in shape
Load changes produce deformational changes.
Elasticity—ability to return to resting length after undergoing lengthening or shortening
Extensibility—ability to be lengthened
Stress
Intensity of internal force
Stress = force/area
Internal resistance of a body to a load
Unit of measure: pascal (Pa) = N/m2
Strain
Normal stresses
Compressive or tensile
Perpendicular to the surfaces on which they act
Shear stresses
Parallel to the surfaces on which they act
Cause a part of a body to be displaced in relation to another part
Stress differs from pressure:
Pressure is the distribution of an
external force to a solid body.
However, they share the same definition (force/area) and unit of measure (Pa).
Relative measure of deformation (six components) resulting from loading
Strain = change in length/original length
Can also be normal or shear
Strain is a proportion; it has no units.
Strain rate
Strain divided by time load is applied
(units = sec −1).
Hooke’s law: stress is proportional to strain up to a limit.
The proportional limit
Within the elastic zone
Young’s modulus of elasticity (E)
Measure of material stiffness
Also a measure of the material’s ability to resist deformation in tension
E = stress/strain
E is the slope in the elastic range of the stress-strain curve.

FIG. 1.60 Stress-strain curve. E, Young’s modulus of elasticity.
The critical factor in load-sharing capacity
Linearly perfect elastic material
A straight stress-strain curve to the point of failure
Modulus = stress at failure (ultimate stress) divided by strain at failure (ultimate strain)
E is unique for every type of material
A material with a higher E can withstand greater forces than can material with a lower E.
Shear modulus
Ratio of shear stress to shear strain
A measure of stiffness
Unit of measure: pascal (Pa)
Stress-strain curve ( Fig. 1.60)
Derived by loading a body and plotting stress versus strain
The curve’s shape varies by material.
Proportional limit—transition point at which stress and strain are no longer proportional
The material returns to its original length when stress is removed: elastic behavior.
Elastic limit (yield point)
This is the transition point from elastic to plastic behavior.
Beyond this point, the material’s structure is irreversibly changed.
The elastic limit equals 0.2% strain in most metals.
Plastic deformation—irreversible change after load is removed
Occurs in the plastic range of the curve
After the elastic limit, before the breaking point
Ultimate strength—maximum strength obtained by the material
Breaking point—point at which the material fractures
Ductile—if deformation between elastic limit and breaking point is large
Brittle—if deformation between elastic limit and breaking point is small
Strain energy (toughness)
Capacity of material (e.g., bone) to absorb energy
Area under the stress-strain curve
Total strain energy = recoverable strain energy (resilience) + dissipated strain energy
A measure of the toughness of material
Material definitions
Brittle materials (e.g., PMMA)
Ability to absorb energy before failure
Stress-strain curve is linear up to failure.
These materials undergo only recoverable (elastic) deformation before failure.
They have little or no capacity for plastic deformation.
Ductile materials (e.g., metal)
These materials undergo large plastic deformation before failure.
Ductility is a measure of post-yield deformation.
Viscoelastic materials (e.g., bone and ligaments)
Stress-strain behavior is time-rate dependent.
Depends on load magnitude and rate at which the load is applied
A function of internal friction
Exhibit both fluid (viscosity) and solid (elasticity) properties
Modulus increases as strain rate increases.
Exhibit hysteresis
Loading and unloading curves differ.
Energy is dissipated during loading.
Most biologic tissues exhibit viscoelasticity.
Isotropic materials
Mechanical properties are the same for all directions of applied load (e.g., as with a golf ball).
Anisotropic materials
Mechanical properties vary with the direction of the applied load.
Example: bone is stronger with axial load than with radial load.
Homogeneous materials
Have a uniform structure or composition throughout
Rigidity
Bending rigidity of a rectangular structure:
Proportional to the base multiplied by the height cubed:

□ Metals
Bending rigidity of a cylinder
Related to the fourth power of the radius
Examples: intramedullary nails, half-pins
Fatigue failure
Occurs with cyclic loading at stress below ultimate tensile strength
Depends on magnitude of stress ( S ) and number of cycles ( n )
Endurance limit
Maximum stress under which the material will not fail regardless of number of loading cycles
If the stress is below this limit, the material may be loaded cyclically an
infinite number of times (>106 cycles) without breaking.
Above this limit, fatigue life is expressed by the S-n curve:
Creep (cold flow)
Progressive deformation response to constant force over an extended period
Sudden stress followed by constant loading causes continued deformation.
Can produce permanent deformity
May affect mechanical function (e.g., in TJA)
Corrosion ( Table 1.43)
Chemical dissolving of metals
Table 1.43 Types of Corrosion Corrosion Description --- Galvanic | Dissimilar metals a ; electrochemical destruction Crevice | Occurs in fatigue cracks with low O2 tension Stress | Occurs in areas with high stress gradients Fretting | From small movements abrading outside layer Other | For example, inclusion, intergranular
a Metals such as 316 L stainless steel and cobalt-chromium-molybdenum (Co-Cr-Mo) alloy produce galvanic corrosion.
May occur in the body’s high-saline environment
Stainless steel (type 316L)
The metal most susceptible to both crevice corrosion and galvanic corrosion
Risk of galvanic corrosion highest between 316L stainless steel and cobalt-chromium (Co-Cr) alloy
Modular components of THA
Direct contact between similar or dissimilar metals at the modular junctions
Results in corrosion products
Examples: metal oxides, metal chlorides
Corrosion can be decreased in the following ways:
Using similar metals
Proper implant design
Passivation by an adherent oxide layer
Effectively separates metal from solution
Example: stainless steel coated with chromium oxide
Types of metals
Orthopaedic implants
Three types of alloys: steel (iron-based), cobalt-based, titanium-based
316L stainless steel
Iron-carbon, chromium, nickel, molybdenum, manganese
Nickel: increases corrosion resistance and stabilizes molecular structure
Chromium: forms a passive surface oxide, improving corrosion resistance
Molybdenum: prevents pitting and crevice corrosion
Manganese: improves crystalline stability
“L”—low in carbon: greater corrosion
resistance
Cobalt alloys
Cobalt-chromium-molybdenum (Co-Cr-Mo)
65% cobalt, 35%
chromium, 5% molybdenum
Special forging process
Nickel may be added to improve ease of forging.
Greater ultimate strength than titanium
Ion release
Co-Cr: macrophage proliferation and synovial degeneration
Ions excreted through the kidneys
Titanium alloy (Ti-6Al-4V)
Poor resistance to wear (notch sensitivity)
Particulate may incite a histiocytic response.
The relationship between titanium and neoplasms is uncertain.

--- FIG. 1.61 Comparison of Young’s modulus (relative values, not to scale) for various orthopaedic materials. Al2O3, Alumina; Co-Cr-Mo, cobalt-chromium-molybdenum; PMMA, polymethylmethacrylate.
Nonmetal materials
Polishing, passivation, and ion implantation improve its fatigue properties.
Titanium is extremely biocompatible
Rapidly forms an adherent oxide coating (self-passivation); decreases corrosion
Most closely emulates axial and torsional stiffnesses of bone
High yield strength
Tantalum—passive material designed to elicit a response (bone ingrowth)
Surface oxide layer as barrier to corrosion
Used as augmentation of cancellous defects
Stiffness (E) differences ( Fig. 1.61)
Polyethylene (discussed in Chapter 5, Adult R reconstruction)
PMMA (bone cement)
Used for fixation and load distribution for implants
Acts as a grout, not an adhesive
Mechanically interlocks with bone
Reaches ultimate strength within 24 hours
Can be used as an internal splint for the patient with poor bone stock
PMMA can be used as a temporary internal splint until the bone heals.
If bone fails to heal, PMMA will ultimately fail.
Poor tensile and shear strength
Is strongest in compression and has a low E
Not as strong as bone in compression
Reducing voids (porosity) increases cement strength and decreases cracking.
Vacuum mixing, centrifugation, good technique
Cement failure often caused by microfracture and fragmentation.
Insertion can lead to a precipitous drop in BP.
Wear particles can incite a macrophage response
Leads to prosthesis loosening
Ceramics
Silicones
Polymers for replacement in non–weight-bearing joints
Poor strength and wear capabilities
Frequent synovitis with extended use
Metallic and nonmetallic elements bonded ionically in a highly oxidized state
Good insulators (poor conductors)
Biostable (inert) crystalline materials such as Al2O3 (alumina) and ZrO2 (zirconium dioxide)
Bioactive (degradable) noncrystalline substances such as bioglass
Typically brittle (no elastic deformation)
High modulus (E)
High compressive strength
Low tensile strength
Low yield strain
Poor crack resistance characteristics
Low resistance to fracture
Best wear characteristics, with polyethylene and a low oxidation rate
High surface wettability and high surface tension
Highly conducive to tissue bonding
Less friction and diminished wear (“smooth surface”)
Small grain size allows an ultrasmooth finish.
Less friction
Calcium phosphates (e.g., hydroxyapatite) may be useful as coatings (plasma sprayed) to increase attachment strength and promote bone healing.
Mechanical properties of tissue
Bone
Composite of collagen and hydroxyapatite
Collagen: low E , good tensile strength, poor compressive strength
Calcium apatite: stiff, brittle, good compressive strength
Anisotropic
Strongest in compression
Weakest in shear
Intermediate in tension
Resists rapidly applied loads better than slowly applied loads
Cancellous bone is 25% as dense, 10% as stiff, and 500% as ductile as cortical bone.
Cortical bone excellent at resisting torque.
Cancellous bone good at resisting compression and shear.
Bone is dynamic.
Able to self-repair
Changes with aging: stiffer and less ductile
Changes with immobilization: weaker
Bone aging
To offset loss in material properties, bone remodels to increase inner and outer cortical diameters.
Area moment of inertia increases.
Bending stresses decrease.
Stress concentration effects
Occur at defect points within bone or at implant-bone interface (stress risers)
Reduce overall loading strength
Stress shielding by load-sharing implants
Induces osteoporosis in adjacent bone
Decreases normal physiologic bone stresses
Common under plates and at the femoral calcar in high-riding THA
A hole measuring 20%–30% of bone diameter reduces strength up to 50%.
Regardless of whether it is filled with a screw
Area returns to normal 9–12 months after screw removal.
Cortical defects can reduce strength 70% or more.
Oval defects less than rectangular defects
Fracture
Smaller stress riser (concentration)
Type is based on mechanism of injury.
Tension: typically transverse and perpendicular to load and bone axis
Compression: crush fracture
Shear
Commonly around joints
Load parallel to the bone surface
Ligaments and tendons
Fracture parallel to the load
Bending
Eccentric loading or direct blows
Begins on the tension side of the bone
Continues transversely/oblique
May bifurcate to produce a butterfly fragment
High-velocity bending: produces comminuted butterfly fracture
Four-point bending: produces segmental fracture
Torsion
Shear and tensile stresses around the longitudinal axis
Most likely to result in a spiral fracture
Torsional stresses proportional to the distance from the neutral axis to the periphery of a cylinder
Greatest stresses in a long bone under torsion are on the outer (periosteal) surface
Comminution
A function of the amount of energy transmitted to bone
Can sustain 5%–10% tensile strain before failure.
In contrast, bone can sustain only 1%–4% tensile strain.
Failure commonly results from tension rupture of fibers and shear failure among fibers.
Most ligaments can undergo plastic strain to the point that function is lost but structure remains in continuity.
Articular cartilage
Ultimate tensile strength is only 5% that of bone.
E is only 0.1% that of bone.
However, because of its viscoelastic properties, is well suited for compressive loading.
Metal implants
Screws
Plates
Is biphasic
Solid phase depends on structural matrix.
Fluid phase depends on deformation and shift of water within solid matrix.
Relatively soft and impermeable solid matrix requires high hydrodynamic pressure to maintain fluid flow.
Significant support provided by the fluid component
Stress-shielding effect on the matrix
Pitch: distance between threads
Lead: distance advanced in one revolution
Root diameter: minimal/inner diameter is proportional to tensile strength
Outer diameter: determines holding power (pullout strength)
To maximize pullout strength
Large outer diameter
Small root diameter
Fine pitch
Strength varies with material and moment of inertia.
Bending stiffness is proportional to the third
power of the thickness (t 3 ).
Doubling thickness increases
bending stiffness eightfold.
Plates are load-bearing devices.
Most effective on a fracture’s tension side
Types include:
Static compression
Best in upper extremity
Can be stressed for compression
Dynamic compression
Example: tension band plate
Neutralization
Resists torsion
Buttress
Blade
Locking
Protects bone graft
Stress concentration at open screw holes can lead to implant failure.
Increased resistance to torsional deformation
Absorb axial forces transmitted from screws
Do not require compression to bone; preserve periosteal blood supply
Biomechanical advantages for osteoporotic fractures without cortical contact
Hybrid locking
Both nonlocked and locked screws are used.
Nonlocked screws assist in reduction.
Locked screws create a fixed-angle device or can be used in patients with osteoporosis.
Intramedullary nails
Load-sharing devices
Bicortical locked screws provide increased strength in torsion compared with unicortical locked screws.
Require high polar moment of inertia to maximize torsional rigidity and strength
Mechanical characteristics
Torsional rigidity
Amount of torque needed to produce a unit angle of torsional deformation
Depends on both material properties (shear modulus) and structural properties (polar moment of inertia)
Bending rigidity
Amount of force required to produce a unit amount of deflection
Depends on both material properties (elastic modulus) and structural properties (area moment of inertia, length)
Related to the fourth power of the nail’s radius
Increasing nail diameter by 10% increases bending rigidity by 50%.
Better at resisting bending forces than rotational
Reaming
forces
Allows greater torsional resistance
Larger contact area
A larger nail; increased rigidity and strength
Unslotted nails
Smaller diameter
Stronger fixation
At the expense of flexibility
Increased torsional stiffness: greatest advantage of closed-section nails over slotted nails
Intramedullary nail insertion for femoral shaft fracture
External fixators
Hoop stresses are lowest for a slotted titanium alloy nail with a thin wall
Posterior starting points decrease hoop stresses and iatrogenic comminution of fractures
Implant failure is more common with smaller-diameter unreamed nails
Conventional external fixators
Fracture reduction is the most important factor for stability of fixation with external fixation.
Other factors to enhance stability (rigidity) include
Larger-diameter pins (second most important factor)
Additional pins
Decreased bone-rod distance
Pins in different planes
Pins separated by more than 45 degrees
Increased mass of the rods or stacked rods
A second rod in the same plane increases resistance to bending.
Rods in different planes
Increased spacing between pins
Placement of central pins closer to the fracture site
Placement of peripheral pins farther from the fracture site (near-near, far-far).
Circular (Ilizarov) external fixators
Thin wires (usually 1.8 mm in diameter)
Fixed under tension (usually between 90 and 130 kg)
Circular rings
Half-pins may also be used.
Offer better purchase in diaphyseal (not metaphyseal) bone
Optimum orientation of implants on the ring
At a 90-degree angle to each other
Maximizes stability
A 90-degree angle not always possible
Anatomic constraints such as neurovascular structures
Bending stiffness of frame
Independent of the loading direction
Because the frame is circular
Each ring should have at least two implants.
Wires or half-pins may be used.
The construct is most stable when an olive wire and a half-pin are at a 90-degree angle to each other on a ring.
Two wires are used on a ring.
One wire should be superior to the ring and one inferior.
Tensioned wires on the same side can cause the ring to deform.
Factors that enhance stability of circular external fixators
Larger-diameter wires (and half-pins)
Decreased ring diameter
Use of olive wires
Additional wires or half-pins (or
both)
Wires (or half-pins or both) crossing at a 90-degree angle
Increased wire tension (up to 130 kg)
Placement of the two central rings close to the fracture site
Decreased spacing between adjacent rings
Increased number of rings
Joint arthroplasty implants: discussed in Chapter 5, Adult Reconstruction chapter
Biomechanics
General definitions
Degrees of freedom
Rotations and translations each occur in the x, y,
and z planes.
Thus six parameters, or degrees of freedom, describe motion.
Translations may be relatively insignificant for many joints.
Are often ignored in biomechanical analyses
Joint reaction force (R)
R is the force within a joint in response to forces acting on the joint.
Both intrinsic and extrinsic
Muscle contraction about a joint: the major contributing factor
R is correlated with predisposition to degenerative changes.
Joint contact pressure (stress) can be minimized by
Decreasing R
Increasing contact area
Coupled forces—rotation about one axis causes obligatory rotation about another axis (occurs in some joints).
Such movements (and associated forces) are
coupled.
Example: lateral bending of the spine accompanied by axial rotation
Joint congruence
Related to the fit of two articular surfaces
A necessary condition for joint
motion
Can be evaluated radiographically
High congruence increases joint contact area
Low congruence decreases joint contact area
Movement out of a position of congruence increases stress in cartilage.
Allows less contact area for distribution of joint reaction force
Predisposes the joint to degeneration
Instant center of rotation
Point about which a joint rotates
In some joints (knee), the instant center changes during the arc of motion, following a curved path.
Effect of joint translation and morphologic features
It normally lies on a line perpendicular to the tangent of the joint surface at all points of contact.
Rolling and sliding ( Fig. 1.62)
During motion, almost all joints roll and slide to remain in congruence.
Pure rolling:
Instant center of rotation is at the rolling surfaces.
Contacting points have zero relative velocity.
No “slipping” of one surface on the other

--- FIG. 1.62 (A) Rolling contact occurs when the circumferential distance of the rolling object equals the distance traced along the plane. This can occur only when there is no sliding—that is, when the relative velocity at the point of contact (P) is zero. (B) For rolling contact, the point P of the wheel has zero velocity because it is in contact with the ground. Therefore P is the instant center of rotation (ICR) of the wheel. This diagram shows the actual velocity of points along the wheel as it rolls along the ground. (C) Rolling and sliding contact occurs when the relative velocity at the contact point is not zero.
(D) Pure sliding occurs when the wheel rotates about a stationary axis (O) . In this case, the wheel would have no forward motion.
From Buckwalter JAet al: Orthopaedic basic science: biology and biomechanics of the musculoskeletal system, ed 2, Rosemont, IL, 2000, American Academy of Orthopaedic Surgeons, p 145.
Pure sliding
Occurs with pure translation or rotation about a stationary axis
No angular change in position
No instant center of rotation
“Slipping” of one surface on the other
Friction and lubrication
Friction : resistance between two objects as one slides over the other
Not a function of contact area
Coefficient of friction: 0 = no friction
Lubrication: decreases resistance between surfaces
Hip biomechanics
Articular surfaces, lubricated with synovial fluid, have a coefficient of friction 10 times better than that of the best synthetic systems.
Coefficient of friction for human joints: 0.002–0.04
Coefficient of friction for metal-on-UHMWPE (ultra-high-molecular-weight polyethylene) joint arthroplasty: 0.05–0.15
Not as good as that of human joints
Elastohydrodynamic lubrication
Primary lubrication mechanism for articular cartilage during dynamic function
Kinematics
ROM ( Table 1.44)
Instant center
Simultaneous triplanar motion for this ball-and-socket joint makes analysis impossible.
Kinetics
Joint reaction force (R) in the hip can reach three to six times body weight (W).
Primarily as a result of contraction of the muscles crossing the hip
Decreases with cane in contralateral hand
Other considerations
Stability
Sourcil
Deep-seated ball-and-socket joint is intrinsically stable.
Condensation of subchondral bone under superomedial acetabulum
R is maximal at this point
Gothic arch
Remodeled bone supporting the acetabular roof
Sourcil at its base
Neck-shaft angle
Varus angulation
Decreases R
Increases shear across the neck
Leads to shortening of the lower extremity
Alters muscle tension resting length of the abductors
May cause a persistent limp
Valgus angulation
Increases R
Decreases shear
Neutral or valgus angulation better for THA
PMMA resists shear poorly
Arthrodesis ( Fig. 1.63)
Position: 25–30 degrees of flexion, 0 degrees of abduction and rotation
External rotation is better than internal rotation.
If the implant is fused in abduction, the patient will lurch over the affected lower extremity with an excessive trunk shift.
This will later result in low back pain.
Knee biomechanics
Kinematics
Effects
Increases oxygen consumption
Decreases gait efficiency to approximately 50% of normal
Increases transpelvic rotation of the contralateral hip
ROM
10 degrees of extension (recurvatum) to 130 degrees of flexion
Functional ROM is nearly full extension to about 90 degrees of flexion.
117 degrees: required for squatting and lifting
110 degrees: required for rising from a chair after TKA
Rotation varies with flexion
At full extension, rotation is minimal.
At 90 degrees of flexion, ROM is 45 degrees of external rotation and 30 degrees of internal rotation.
Amount of abduction or adduction is essentially 0 degrees.
A few degrees of passive motion are possible at 30 degrees of flexion.
Table 1.44 Hip Biomechanics: Range of Motion Average Functional Motion Range Range (Degrees) (Degrees) --- Flexion | 115
| 90 (120 to
squat) Extension | 30
| Abduction | 50
| 20 Adduction | 30
| Internal rotation | 45
| 0 External rotation | 45
| 20
Knee motion is complex about a
changing instant center of rotation.
Polycentric rotation
Excursions of 0.5 cm for the medial meniscus and 1.1 cm for the lateral meniscus are possible during a 120-degree arc of motion.
Kinetics
Joint motion
Instant center traces a J-shaped curve about the femoral condyle.
Moves posteriorly with flexion
Flexion and extension involve both rolling and sliding.
Femur rotates internally (tibia rotates externally) during the last 15 degrees of extension
“Screw home” mechanism
Related to differences in radii of curvature for the medial and lateral femoral condyles and the musculature
Posterior rollback increases maximum knee flexion.
Tibiofemoral contact point moves posteriorly.
Normal rollback is compromised by PCL sacrifice of posterior cruciate ligament (PCL), as in some TKAs.
Axis of rotation of the intact knee is in the medial femoral condyle.
Patellofemoral joint has sliding articulation
Patella slides 7 cm caudally with full flexion.
Instant center is near the posterior cortex above the condyles.
Knee stabilizers
Ligaments and muscles play the major stabilizing role ( Table 1.45).
ACL
Typically subjected to peak loads of 170 N during walking
Up to 500 N with running
Ultimate strength in young patients: about 1750 N
Failures by serial tearing at 10%–15% elongation
PCL: sectioning increases contact pressures in the medial compartment and the patellofemoral joint.
Joint forces
Tibiofemoral joint
Knee joint surface loads
Three times body weight during level walking
Up to four times body weight with stair walking
Menisci
Help with load transmission
Bear one-third to one-half body weight
Removal increases contact stresses

--- FIG. 1.63 Recommended positions for arthrodesis of common joints. CMC, Carpometacarpal; DIP, distal interphalangeal; MCP,
metacarpophalangeal;
MTP,
metatarsophalangeal; PIP, proximal interphalangeal.
Up to four times the load transfer to bone
Quadriceps produces maximum anterior force on the tibia at 0–60 degrees of knee flexion
Patellofemoral joint
Patella aids in knee extension.
Increases the lever arm
Stress distribution
Has the thickest cartilage in the entire body
Bears the greatest load
Bears half the body
weight with normal walking
Table 1.45 Knee Stabilizers Direction Structures --- Medial | Superficial M (primary), joint capsu medial meniscus, ACL/PCL Lateral | Joint capsule, band, LCL (middle), lateral meniscus, ACL/PCL (
degrees) Anterior | ACL (primary joint capsu Posterior | PCL (primary) joint capsu PCL tighte with intern rotation Rotatory | Combinations MCL chec external rotation; A checks internal rotation
IT, Iliotibial.
Bears seven times the body weight with squatting and jogging
Loads proportional to ratio of quadriceps force to knee flexion
In descending stairs, compressive force
reaches two to three times body weight.
Patellectomy
Length of the moment arm is decreased by width of patella: 30% reduction.
Power of extension is decreased by 30%.
During TKA, the following factors enhance patella tracking
External rotation of the femoral component
Lateral placement of the femoral and tibial components
Medial placement of the patellar component
Avoidance of malrotation of the tibial component
These actions avoid internal rotation.
Axes of the lower extremity ( Fig. 1.64)
Mechanical axis of the lower extremity
Center of femoral head to center of ankle
Normally passes just medial to the medial tibial spine
Vertical axis
From the center of gravity to the ground
Anatomic axes
Along the shafts of the femur and tibia
Where these axes intersect at the knee, valgus angle is normal.
Mechanical axis of the femur
From center of the femoral head to center of the knee
Mechanical axis of the tibia
From center of the tibial plateau to center of the ankle
Relationships
Mechanical axis of the lower extremity is in 3 degrees of valgus angulation from the vertical axis.
Anatomic axis of the femur is in 6 degrees of valgus angulation from the mechanical axis.
Nine degrees versus the vertical axis
Anatomic axis of the tibia is in 2–3 degrees of varus angulation from the mechanical axis.
Arthrodesis (see Fig. 1.63)
Position: 0 to 7 degrees of valgus angulation, 10 to 15 degrees of flexion
Ankle and foot biomechanics
Ankle
Kinematics

FIG. 1.64 Axes of the lower extremity. Modified from Helfet DL: Fractures of the distal femur. In Browner BD et al, editors: Skeletal trauma, Philadelphia, 1992, Saunders, p 1645.
Instant center of rotation within the talus
Lateral and posterior points at the tips of the malleoli
Change slightly with movement
Talus described as a cone
Body and trochlea wider anteriorly and laterally
Therefore talus and fibula externally rotate
slightly with dorsiflexion
Dorsiflexion and abduction are coupled.
ROM
Kinetics
Dorsiflexion: 25 degrees
Plantar flexion: 35 degrees
Rotation: 5 degrees
Tibiotalar articulation
Major weight-bearing surface of the ankle
Supports compressive forces up to five times body weight (W)
Shear (backward to forward) forces are decreased by muscle activation/contraction
Large weight-bearing surface area decreases joint stress
Fibular/talar joint transmits about one sixth of the force
Table 1.46 Arches of the Foot Arch Skeletal Keystone Ligament Sup Components --- Medial longitudinal | Calcaneus, talus, navicular, three cuneiform bones, first to third metatarsals
| Talus
head
| Spring
(calcaneon Lateral longitudinal | Calcaneus,
cuboid, fourth and fifth metatarsals
| |
Plantar apone Transverse | Three
cuneiform bones, cuboid, metatarsal bases
| |
Table 1.47 Range of Motion of Spinal Segments Level | Flexion/Extension (Degrees) | Lateral Bending (Degrees) | Rotation (Degrees) | Ins Cen | ---|---|---|---|---| Occiput–C1 | 13
| 8
| 0
| Sk C1–C2 | 10
| 0
| 45
| Wa C2–C7 | 10–15
| 8–10
| 10
| Ver Thoracic spine | 5
| 6
| 8
| Ver Lumbar spine | 15–20
| 2–5
| 3–6
| Dis
Highest net muscle moment occurs during terminal-stance phase of gait.
Other considerations
Stability based on articulation shape (mortise maintained by talar shape) and ligament support
Stability is greatest in dorsiflexion.
During weight bearing, tibial and talar articular surfaces contribute most to stability.
Windlass action
Full dorsiflexion is limited by the plantar aponeurosis.
Further tension on the aponeurosis (toe dorsiflexion) raises the arch.
A syndesmosis screw limits external rotation.
Arthrodesis (see Fig. 1.63): neutral dorsiflexion, 5–10 degrees of external rotation, 5 degrees of hindfoot valgus angulation
Surgeon should anticipate 70% loss of sagittal plane motion of the foot.
Subtalar joint (talus-calcaneus-navicular)
Axis of rotation
In the sagittal plane: 42 degrees
In the transverse plane: 16 degrees
Functions like an oblique hinge
Pronation coupled with dorsiflexion, abduction, and eversion
Supination coupled with plantar flexion, adduction, and inversion
ROM
Pronation: 5 degrees
Supination: 20 degrees
Functional ROM: approximately 6 degrees
Transverse tarsal joint (talus-navicular, calcaneal-cuboid)
Motion based on foot position
Two axes of rotation: talonavicular and calcaneocuboid
Eversion (early stance)
The joint axes are parallel.
ROM is allowed.
Inversion (late stance)
External rotation of the lower extremity causes the joint axes to intersect.
Motion is limited.
Foot
Transmits 1.2 times body weight with walking
Three times body weight with running
Has three arches ( Table 1.46)
Second metatarsal (Lisfranc) joint is “keylike.”
Stabilizes second metatarsal
Allows it to carry the most load with gait
First metatarsal bears the most load during standing
Expected life of Plastazote shoe insert in active adults is less than 1 month.
Fatigues rapidly in compression and shear
Should be replaced frequently or supported with other materials such as Spenco or PPT foam
Spine biomechanics
Kinematics
ROM by anatomic segment ( Table 1.47)
Analysis based on the functional unit
Motion segment: two vertebrae and the intervening soft tissues
Six degrees of freedom exist about all three axes.
Coupled motion
Simultaneous rotation, lateral bending, and flexion or extension
Especially axial rotation with lateral bending
Instant center of rotation within the disc
Normal sagittal alignment of the lumbar spine: 55–60 degrees of lordosis
The lordosis exists because of the disc spaces (not the vertebrae).
Most lordosis occurs between L4 and S1.
Loss of disc space height can cause loss of normal lumbar lordosis.
Iatrogenic flat back syndrome of the lumbar spine
Result of a distraction force
Supporting structures
Anterior supporting structures
Anterior longitudinal ligament
Posterior longitudinal ligament
Vertebral disc
Posterior supporting structures
Intertransverse ligaments
Capsular ligaments and facets
Ligamentum flavum (yellow
ligament)
Halo vest—most effective device for controlling cervical motion
Because of pin purchase in the skull
Apophyseal joints
Resist torsion during axial loading
Attached capsular ligaments resist flexion.
Guide the motion segment
Direction of motion determined by orientation of the facets of the apophyseal joint
Varies with each level
Cervical spine facets
Orientation: 45 degrees to the transverse plane
Parallel to the frontal plane
Thoracic spine facets
Orientation: 60 degrees to the transverse plane
Also 20 degrees to the frontal plane
Lumbar spine facets
Orientation: 90 degrees to the transverse plane
Also 45 degrees to the frontal plane
They progressively tilt up (transverse) and inward (frontal).
Cervical facetectomy of more than 50% causes loss of stability in flexion and torsion.
Torsional load resistance in the lumbar spine
Facets contribute 40%
Disc contributes 40%
Ligamentous structures contribute 20%
Kinetics
Disc
Behaves viscoelastically
Demonstrates creep
Deforms with time
Demonstrates hysteresis
Absorbs energy with repeated axial loads
Later decreases in function
Compressive stresses highest in the nucleus pulposus
Tensile stresses highest in the annulus fibrosus
Stiffness increases with compressive load.
Higher loads increase deformation and creep rate.
Repeated torsional loading (shear forces)
Vertebrae
Such repeated loading may separate the nucleus pulposus from the annulus and end plate.
Nuclear material may then be forced through an annular tear.
Loads increase with bending and torsional stresses.
After subtotal discectomy, extension is the most stable loading mode.
Disc pressures are lowest with lying supine, higher with standing, and highest with sitting.
Carrying loads
Disc pressures are lowest when the load is close to the body.
Strength is related to bone mineral content and vertebrae size.
Increased in lumbar spine
Fatigue loading may lead to pars fractures.
Compression fractures occur at the end plate.
Table 1.48 Shoulder Biomechanics: Muscle Forces Motion Muscle Forces Comments ---
Glenohumeral Abduction | Deltoid, supraspinatus
| Cuff
depresses head Adduction | Latissimus dorsi, pectoralis major, teres major
| Forward flexion | Pectoralis major, deltoid (anterior), biceps
| Extension | Latissimus dorsi
| Internal rotation | Subscapularis, teres major
| External rotation | Infraspinatus, teres minor, deltoid (posterior)
| Scapular Rotation | Upper trapezius, levator scapulae (anterior), serratus anterior, lower trapezius
| Works
through a force couple Adduction | Trapezius, rhomboid, latissimus dorsi
| Abduction | Serratus anterior, pectoralis minor
| 1. Vertebral body stiffness is decreased in osteoporosis.
Caused by loss of horizontal trabeculae
Spinal arthrodesis is helpful
Increasing implant stiffness
Increases probability of successful fusion
Increases likelihood of decreased bone mineral content of the bridged vertebrae
Shoulder biomechanics ( Table 1.48)
Kinematics
Scapular plane
Positioned 30 degrees anterior to the coronal plane
The preferred reference plane for ROM
Abduction requires external rotation of the humerus.
To prevent greater tuberosity impingement
With internal rotation contractures, abduction limited to 120 degrees
Abduction
Glenohumeral motion: 120 degrees
Scapulothoracic motion: 60 degrees
In ratio of 2:1
Varies over the first 30 degrees of motion
Kinetics
Stability
Scapulothoracic motion
Acromioclavicular joint movement during the early part
Sternoclavicular movement during the later portion
With clavicular rotation along the long axis
Surface joint motion in the glenohumeral joint is a combination of rotation, rolling, and translation.
Zero position
Abduction of 165 degrees in the scapular plane
Minimal deforming forces about the shoulder
Ideal position for reducing shoulder dislocations
Also for reducing “fractures with traction”
Limited about the glenohumeral joint
Humeral head surface area larger than glenoid area:
48 × 45 mm versus 35 × 25 mm
Bony stability is limited
Relies on humeral head inclination (125 degrees) and retroversion (25 degrees)
Also relies on slight glenoid retrotilt
Inferior glenohumeral ligament (anterior band)
The most important static stabilizer
Superior and middle glenohumeral ligaments: secondary stabilizers to anterior humeral translation
Inferior subluxation prevented by negative intraarticular pressure
Rotator cuff muscles
Dynamic contribution to stability
Arthrodesis (see Fig. 1.63): 15–20 degrees of abduction, 20–25 degrees of forward flexion, 40–50 degrees of internal rotation
Excessive external rotation should be avoided
Other joints
Acromioclavicular joint
Scapular rotation through the conoid and trapezoid ligaments
Scapular motion through the joint itself
Sternoclavicular joint
Clavicular protraction/retraction in a transverse plane through the coracoclavicular ligament
Clavicular elevation and depression in the frontal plane
Also through the coracoclavicular ligament
Clavicular rotation around the longitudinal axis
Elbow biomechanics
Functions
A component joint of the lever arm when the hand is positioned
Fulcrum for the forearm lever
Weight-bearing joint in patients using crutches
Activities of daily living
Kinematics
Flexion and extension
Kinetics
Stability
0–150 degrees
Functional ROM: 30 to 130 degrees
Axis of rotation: the center of the trochlea
Pronation and supination
Pronation: 80 degrees
Supination: 85 degrees
Functional pronation and supination: 50 degrees each
Axis: capitellum through radial head to ulnar head (forms a cone)
Carrying angle
Valgus angle at the elbow
For boys and men: 7 degrees; for girls and women: 13 degrees
Decreases with flexion
Flexion is accomplished primarily by the brachialis and biceps.
Extension is accomplished by the triceps.
Pronation is accomplished by pronators (teres and quadratus).
Supination is accomplished by the biceps and supinator.
Static loads approach, and dynamic loads exceed, body weight.
Provided partially by articular congruity
Table 1.49 Columns of the Wrist Column Function Comments --- Central | Flexion-extension
| Distal carpal row and lunate (link) Medial | Rotation
| Triquetrum Lateral | Mobile
| Scaphoid
Three necessary and sufficient constraints for stability
Coronoid
Lateral (ulnar) collateral ligament (LCL)
Anterior band of the MCL
Forearm
Most important: anterior oblique fibers
Stabilizes against both valgus angulation and distractional force at 90 degrees
Most important secondary stabilizer against valgus stress: radial head
About 30% of valgus stability
Important at 0 to 30 degrees of flexion and pronation
In extension, capsule is the primary restraint to distractional forces.
Lateral stability is provided by LCL, anconeus, and joint capsule.
Unilateral arthrodesis (see Fig. 1.63): 90 degrees of flexion
Bilateral arthrodesis (see Fig. 1.63)
One elbow at 110 degrees of flexion for the hand to reach the mouth
Other at 65 degrees of flexion for perineal hygiene
Arthrodesis is difficult to perform and (fortunately) rarely required.
Ulna transmits 17% of the axial load
Line of the center of rotation runs from radial head to distal ulna
Wrist and hand biomechanics
Wrist
Part of an intercalated link system
Kinematics
Normal ROM
Flexion: 65 degrees
Functional: 10 degrees
Extension: 55 degrees
Functional: 35 degrees
Radial deviation: 15 degrees
Functional: 10 degrees
Ulnar deviation: 35 degrees
Functional: 15 degrees
Flexion and extension
Two-thirds radiocarpal
One-third intercarpal
Radial deviation
Primarily intercarpal movement
Ulnar deviation
Relies on radiocarpal and intercarpal motion
Instant center is usually the head of the capitate, but it varies.
Columns of the wrist are listed in Table 1.49.
Link system
A system of three links in a “chain”
Radius, lunate, and capitate
Less motion is required at each link.
However, it adds to instability of the chain.
Stability is enhanced by strong volar ligaments.
Relationships
Also by the scaphoid, which bridges both carpal rows
Carpal collapse
Ratio of carpal height to third MC height: normally 0.54
Ulnar translation
Ratio of ulna-to-capitate length to third MC height
Normal is 0.30
Distal radius normally bears about 80% of distal radioulnar joint load.
Distal ulna bears 20%
Ulnar load bearing increases with ulnar
lengthening and decreases with ulnar shortening.
Wrist arthrodesis is relatively common.
Hand
Dorsiflexion of 10–20 degrees is good for unilateral fusion (see Fig. 1.63).
Bilateral fusion
Avoided if possible
If necessary, other wrist should be fused at 0–10 degrees of palmar flexion.
Kinematics
ROM
Arches
Metacarpophalangeal (MCP) joint
Universal joint, 2 degrees of freedom
Flexion: 100 degrees
Abduction-adduction: 60 degrees
Proximal interphalangeal (PIP) joints
Flexion: 110 degrees
DIP joints
Flexion: 80 degrees
Stability
Two transverse arches
Proximal through carpus
Distal through metacarpal heads
Five longitudinal arches
Through each of the rays
MCP joint
Volar plate and the collateral ligaments
Collateral ligaments: taut in flexion, lax in extension
PIP and DIP joints
Rely more on joint congruity
Ratio of ligament surface to articular surface is large.
Other concepts
Table 1.50 Recommended Positions of Flexion for Arthrodesis of the Joints of the Hand Joint | Degrees of Flexion | Other Factors | ---|---|---| MCP | 20–30
| PIP | 40–50
| Less radial than ulnar DIP | 15–20
| Thumb CMC | | Thumb MCP | 25
| MC in opposition Thumb IP
| 20
| 1. Hand pulleys prevent bowstringing and decrease tendon excursion.
Bowstringing increases moment arms.
Sagittal bands allow MCP extension.
With hyperextension of the MCP, the intrinsic muscles must function to produce PIP extension, because the extension tendon is lax.
Normal grasp
For boys and men: 50 kg
For girls and women: 25 kg
Only 4 kg needed for daily function
Normal pinch
For boys and men: 8 kg
For girls and women: 4 kg
Kinetics
Only 1 kg needed for daily activities
Joint loading with pinch mostly in MCP
Because MCP joints have large surface area, however, contact pressures (joint load/contact area) are lower.
DIP joints have the most contact pressure.
Subsequently develop the most degenerative changes with time (Heberden nodes)
Grasping contact pressures are decreased, focused on MCP.
Patients with MCP arthritis often had occupations in which grasping was required.
Compressive loads occur at the thumb with pinching.
At interphalangeal joint: 3 kg
At MCP joint: 5 kg
At carpometacarpal (CMC) joint: 12 kg
An unstable joint
Frequently leads to degeneration
Recommended positisions for arthrodesis of the hand are summarized in Table 1.50.