Spinal Facts - Happy New Year 2007!

Important Biomechanical Parameters

Why are millimeters important?

The bony vertebral bodies are the primary load-bearing structures of the spine. Bone is an anisotropic material, exhibiting different mechanical properties when loaded in different directions. It is strongest and stiffest in compression. Bone remodels in response to the mechanical demands placed on it i.e. cycling, which are affected by the external loads as well as the muscle loading. Within the dense cortical shell of the vertebral body is the cancellous bone of the trabecular system. The trabecular system can be considered as a structural frame supporting the outer cortical shell of the vertebra. The natural synovial joint is a type of mechanical bearing. The lubricant (synovial fluid) and the bearing surfaces (articular cartilage) form a bearing system, which has excellent performance under the loading conditions encountered in normal human activities. That changes with cycling. The vertebral facet joint is a type of synovial joint and is the only synovial joint of the spine.

Synovial Fluid
Synovial fluid is highly non-Newtonian as it rapidly decreases its viscosity at high shear rates i.e. spine angle over the top tube. Some form of elastohydrodynamic or micro-elastohydrodynamic mechanism occurs as the joint moves, which helps to maintain a fluid film between the articular cartilage of the two bones. The high viscosity helps to maintain a fluid film by resisting squeezing out with the joint at rest.

Articular Cartilage
Articular cartilage is the structural material of the bearing. Along with lubricating synovial fluid it allows articulating joints to move and support loads without wearing. This biological system is more efficient at lubrication than any man-made material.

Articular cartilage comprises 80% water, with the remaining 20% made up of a collagen fiber network and proteoglycan matrix. This can be modeled as a biphasic material in which the initial application of a load results in a change in geometry of the material and pressure gradients being set up in the fluid phase of the material. These pressures cause fluid flow out of the cartilage resulting in a second phase of deformation. This resistance to flow is controlled by the permeability of the cartilage and the hydrophilicity of the proteoglycan matrix.
Articular cartilage is viscoelastic and has an ultimate compressive stress of 5MPa.

Ligaments
Ligaments work as passive tensile restraints, controlling the separation of their attachment sites. Mechanical properties of ligaments are expressed graphically as load-elongation curves. Two distinct regions can be identified: At low loads, the 'Toe Region' has minimal stiffness associated with the 'crimp' pattern exhibited by collagen fibrils. As the load is increased, fibrils begin to straighten and these 'crimps' begin to decrease. Once the crimping has been removed, the load-elongation curve becomes a straight line signifying a constant stiffness and this region is referred to as the 'Linear Region”. The stiffness of this region are the values most often reported in the literature. The ‘ultimate load’ is the load at which the ligament is defined to have failed. This is typically the peak load. The area under this load-elongation curve is the energy absorbed by the ligament.
Material properties of ligaments are described in terms of stress-strain curves. These can be obtained from the load-elongation curves of the whole ligament normalized with the geometry of the ligament by the ligament length and cross-sectional area. These curves have a similar shape to the load-elongation curves. The stress-strain curve is geometry independent and modulus, ultimate stress, and ultimate strain values are obtained.
At low loading rates ligaments are viscoelastic structures: they display time- and history-dependent behavior. This is displayed in two ways: stress relaxation and creep . With time, the stress required to hold a ligament at a constant length will decrease to a steady value (stress relaxation), and with time, the length of a ligament will increase to a steady length as a constant stress is applied to the ligament (creep). This may lead to creep rupture. Essentially, the viscoelastic nature of ligaments is due to fluid flow. At high rates there is not sufficient time for the fluid to flow. At rates, such as those associated with traumatic events, ligaments behave elastically.
Ligament properties change with age. Linear stiffness, ultimate load and energy absorbed to failure all decrease with increasing age.

Intervertebral Discs
Intervertebral discs are the primary motion structure between the vertebral bodies (note that there is no disc between the occipital (C0) and C1 and between C1 and C2). The disc is not a synovial joint. It consists of three distinct parts: The centrally located nucleus pulposus, which is a loose and fibrous network accounting for 30-50% of the disc surface area. The annulus fibrosus, in which the outer fibrous portions are arranged in concentric bands like a tree trunk; these adjacent bands are oriented at 120º to each other. The third part is the end-plate which is composed of hyaline cartilage and connects the disc to the vertebral bodies.
Intervertebral discs are viscoelastic structures, which exhibit creep when a load is applied and held constant i.e cycling for hours. The observation that we are several “millimeters shorter at the end of the day” is attributed to the creep behavior of the discs. If there is too much load on the spine at the start of the ride, creep will add more load at the end of the ride. It is important to maintain a light stretch to reduce the creep behavior of the discs, but not too much with longer rides!

Mechanical and Material Properties
The properties of a structure, such as the vertebral column, are referred to as mechanical properties. Mechanical properties include the load-displacement behavior, stiffness, ultimate load and energy absorbed to failure. Another term for mechanical properties is 'structural properties'. Material properties are the structural properties that have been normalized for geometry, and are thus a more general description of the properties of the material itself. Material properties include stress, strain, Young's Modulus (related to stiffness) and strain energy.

Vertebral Coordinate Systems (VCS)
Coordinate systems are used to quantify the direction of load and motion. The specific definition of a coordinate system is arbitrary, but in order for scientists to compare their results a common coordinate system is desired. Unfortunately, a standard coordinate system for the spine has yet to be established. We present the coordinate system adopted from White and Panjabi (1990).
In the VCS, the origin lies in the center of the vertebral body. The X-axis is to the right, the Y-axis is in the cranial direction, and the Z-axis is in the anterior direction.

Loads and Displacements
The loads on the spine can be described as either linear (Force) or as rotational (Moment) or more important a combination of both.
Force - The three primary components of a force are compression, tension and shear. With respect to the vertebral coordinate system there are three independent forces along each of the coordinate axes.
Moments - Moments (M) or torque are couples of equal and opposite force (F) that act at a distance (D), defined simply as F x D = M. With respect to the VCS there are independent moments. A positive moment about X, for example, produces flexion.
Displacement of the spine is complex, three-dimensional, and varies with the level and posture of the spine i.e. over top tube and ones leg rpm. As with loads, displacements can be described as linear, rotational, or a combination of both. Your spine posture should change given the loads you place on it.
Linear - Linear motion is a translation of the vertebral body and there are three independent directions of translation each along an axis of the VCS.
Rotational - Rotational motions can occur about each axis of the VCS and in combinations.

Viscoelasticity
Viscoelasticity is time-dependent elastic behavior. Viscoelastic behavior is typically associated with energy loss through dissipation of heat and/or the flow of fluid. The energy loss of the load-displacement is the area enclosed by the load-displacement curve and is termed hysteresis.
Viscoelasticity is typically quantified with two types of experiment. The load-displacement relation defines recall, material and structural behavior. With viscoelastic behavior time is the third variable. Therefore, experiments to explicitly study viscoelasticity hold one of these three variables constant. In a ‘ creep test ’, a fixed load is applied and the resulting displacement over time is recorded. i.e. laying on our back with hips against a fixed wall. In a ‘ stress relaxation test ’, the displacement is fixed and the resulting decrease in stress or load over time is recorded. This allows us to find a truer spine length.

Physiological Cross-Sectional Area
Muscle strength and loading is difficult to quantify, as direct measurement of muscle forces is currently impractical. A number of different approaches for quantification of muscle forces have been applied in the literature. Electromyography can indicate the intensity of muscle activation, but it is not yet possible to determine accurately the force exerted by each muscle in a complex. One approach is to relate a muscle's ability to generate force to its size and architecture. Cross-sectional area has been used to measure force ratios. The physiological cross-sectional area (PCSA), (cross-sectional area of the muscle perpendicular to all of its fibers), is however believed to provide a better estimation of muscle strength, being proportional to the number and cross-sectional area of the tension-producing fibers. The PCSA can indicate the contribution of each muscle in a group of muscles, particularly when they reach a limiting stress, such as in strenuous activity.

Joint Mechanics
The Spine as a Whole
The spine is comprised of vertebral bodies joined by the intervertebral disc and various ligaments. The spine consists of three general regions: cervical, thoracic and lumbar. Each region possesses unique anatomical characteristics and mechanics. Some characteristics transform continuously from region to region while other characteristics are distinct for each region. The smallest spinal unit of each region is the functional spinal unit FSC. Note that the anatomy and mechanical properties of the spine vary with the spine region.
Typically, female anatomy and material properties vary less than those of males. Typically, female upper body anatomy is less in weight and size. The upper body acts as a counter weight for the legs to work. They do better to load their spine and achieve a lower position over the top tube.
Age can also dramatically decrease the mechanical properties. Functional spinal units are addressed when we have the intervertebral disc and various ligaments, nervous tissues, connective soft tissue all move to their limit of constraints. This is when the spine reaches its limits of the applied load (Units deg or mm) and stiffness (Units N/mm or Nm/deg) with extension This double–action locks the joint, as the ligaments do not elongate further. Exceeding this limit affects the handling, the ability to adjust to the terrain, breathing, etc…

Functional Spinal Unit (FSU)
A functional spinal unit consists of an inferior and superior vertebral body and all of the connective soft tissue between them. Contractile and nervous tissues are excluded. An FSU is the smallest functional unit of the spine below C2

Motion Descriptions
When the motion of a functional spinal unit (FSU) lies within an anatomical plane of the vertebral coordinate system (VCS), the planar motion is relatively straightforward to describe. Planar motion is often a combination of rotation and translation. One approach to describing planar motion is to define a rotation angle and a center of rotation (COR). These two variables completely describe any planar motion. Throughout a range of motion, the COR may be fixed or may move with the degree of motion.
When the motion of an FSU is not planar, describing the 3D motion completely is non-trivial. We prefer to use the helical axis of motion (HAM) variables, also known as the screw axis. The HAM variables consist of a rotation (theta) about and a translation (t) along a unique axis in space. Typically, the HAM translation for normal spine motion is minimal. When the spinal motion is planar, then the HAM axis is perpendicular to that plane of motion and the point of intersection of the HAM axis with the plane of motion is the COR.

Coupled Motions
Coupled motions are defined as motions that are not in the principal direction of the applied load; they are inherently coupled to the principal motion. For example, loading that produces left lateral bending can also produce axial rotation and flexion. The axial rotation and flexion are coupled to the lateral bending and in the healthy spine these motions cannot be separated.
Functional Spinal Unit (FSU) Mechanics
The mechanical behavior of the FSU is described by the relationship between the applied loads and the resulting motions. This relation is often non-linear.

Range of Motion (ROM)
ROM is the motion that occurs between the limits of the applied load (Units deg or mm). The loads from big gears and creep in a 40K are not the same vs. the long haul (many hours).

Stiffness (K)
The K is the slope of the load-motion curve (Units N/mm or Nm/deg). It is important to define at which point on the curve the stiffness is calculated. Typically it is defined in the secondary region of the curve where stiffness is constant over that range.

Neutral Zone (NZ)
The NZ is the zone between opposite directions of loading within which the stiffness is minimal. Physically this corresponds to a zone of “joint sloppiness” or laxity. The NZ is calculated in a variety of ways, but most commonly it is defined as the motion occurring below a given low load “Sweetspot” of the saddle & tilt or as the motion between the two X-axis intercepts of the extended secondary.

Occipital-Atlanto-Axial Region
The occipital-atlanto-axial region of the spine is certainly the most unique region of the spine and is often referred to as the C0-C1-C2 joint. The significant mechanical interaction directly between C0 and C2 necessitates that this region be considered as a single functional unit. In this joint there are no vertebral discs and the articular surfaces and the ligaments are the primary components maintaining the structural stability of the joint.
The superior articular surfaces of C1 are cupped to accept and articulate with the occipital condyles, while the inferior surfaces of C1 are flat and sloped medially to laterally and articulate with the superior articular surface. This shape helps to confine the axis of rotation of C1 relative to C2.
The two primary ligamentous structures of C0-C1-C2 are the transverse ligament and the alar ligaments. The transverse ligament is the posterior restraint of the dens of C2 and has a cross-section of 18mm 2 and a length of 20mm. It is one of the strongest spinal ligaments with an ultimate load of approximately 450N. Understanding this, it is important to rotate the eyes upward and keep them level verses the rotation of the head.
The alar ligaments arise from the lateral portions of the dens and insert at the base of the C0 condyles. The alar ligaments are the primary restraint to axial rotation of C0-C1-C2. The alar ligaments have a cross-sectional area of 22mm 2 and a length of 20mm. Their ultimate load is 280N.
The alar ligaments restrain axial rotation to the left and right through a unique double-action mechanism. The normal range of axial rotation of C0-C1 on C2 is 45 degrees in both directions. The laxity of the alar ligaments permits this large range of axial rotation. As the limit of rotation is reached, both alar ligaments simultaneously tighten. Once tightened each attempts to force rotation of C0-C1 about its own origin. This double–action locks the joint, as the ligaments do not elongate further. Therefore, if one alar ligament is damaged rotation to both sides is increased, and the secondary restraints such as the facet capsules and tectorial membrane resist further rotation.
The C0-C1-C2 joint is the most mobile joint in the spine. In flexion-extension there is a small neutral zone (NZ) of 4 o and a range of motion (ROM) of 45 o . In total (left plus right) axial rotation, the NZ (65 o ) comprises most of the 90 o of the ROM. Over 85% of axial rotation occurs at the C1-C2 joint. Total lateral bending possesses a NZ of 6 o and a ROM of 20 o that is equally split between C0-C1 and C1-C2.
The degree of coupled motion in C0-C1-C2 varies with the direction of motion, the posture and the level. In flexion-extension there is essentially no coupled motion. In lateral bending the coupled motion is greater at C1-C2 than at C0-C1. The coupled motion consists of both flexion-extension and axial rotation, although the direction and magnitude of each of these coupled motions varies with the initial posture. Axial rotation at C1-C2 is the most prominent coupled motion due to the large NZ in axial rotation and the shape of the articular facets. These same factors results in a minimal amount of coupled motion at C1-C2 when the primary motion is axial rotation. Conversely, flexion-extension and lateral bending both occur as coupled motions at C0-C1 with axial rotation. From another perspective, the natural tendency of the spine is to move in physiological directions. When loads are applied in directions that would produce non-physiological motion the spine responds by redirecting the loads to reproduce physiological motions.

Mid-and Lower Cervical Region
The vertebral joints of C2-C3 through C7-T1 constitute the mid- and lower cervical region of the spine. The functional spinal units (FSUs) in this region are more typical of those in the lower spine. The vertebral bodies can typically support compressive loads of 1500N or more.
The articular facets of this region have minimal curvature and are oriented in antero-superior to postero-inferior inclination.
The anterior longitudinal ligament (ALL) is a broad ligament that attaches along the anterior wall of the vertebral bodies. Its primary role is to limit the distraction of the anterior vertebral body during extension. The ALL has a stiffness of 12N/mm. The strength of the ALL in tension is 110N. The failure deformation at this load is 9mm.
The posterior longitudinal ligament (PLL) is analogous to the ALL but attaches along the posterior wall of the vertebral body. The PLL has a stiffness of 12N/mm. The strength of the PLL in tension is 75N. The failure deformation at this load is 6mm. This is the weakest area of failure (ALL vs. PLL).
The capsular ligaments encompass the facet joints. Their failure load is approximately 200N at a deformation of 8mm.
Ligamentum flavum fails at a tension load of 140N at a deformation of 8mm.
The interspinous ligaments are weaker than the other primary ligaments and fails in tension at about 35N at a deformation of 7mm.
Thoracic Region
The mechanics of the functional spinal units (FSUs) of the thoracic region (image) have received the least attention of any region of the spine, in part because the thoracic region is well stabilized by the rib cage and its articulation with the thoracic vertebrae. Therefore mechanical testing without the ribcage has little clinical relevance, while testing with the rib cage possesses enormous practical challenges. The strength of the vertebral bodies in compression range, with the vertebral level, from values similar to the cervical region to values similar to the lumbar region.
The facets are fairly flat as in the cervical region, but there is a transition in the orientation from the cervical facets to a nearly vertical orientation in the thoracolumbar region.
The range of motion (ROM) in flexion and extension are approximately 5 o in flexion/extension, 18 o in total axial rotation, and 12 o in total lateral bending for each FSU from T1-T2 to T9-T10. From T10 to L1, the reported ROM increases by about 5 o in flexion/extension, decreases by about 10 o in total axial rotation, and increases by about 4 o in total lateral bending.
The bending stiffness of the thoracic FSUs are 2.5Nm/deg in both flexion/extension and axial rotation, and are slightly stiffer in lateral bending.

Lumbar Region
The lumbar region contains the largest vertebral bodies and connective structures of the spine. The vertebral bodies fail in compression at approximately 5500N. The facets of the lumbar region are a continuation of the transition from the cervical to thoracic region. The lumbar facets reach a more vertical orientation than the thoracic facets, and also possess a curved shape in which the facet surfaces lie in both the frontal plane and the sagittal plane.
The six major ligaments possess a range of mechanical properties, which typically exceed those of the other regions. Even with better mechanical properties, physiological loads and limit patterns can (damage or irriate the spinal cord or nerve roots).
The anterior longitudinal ligament (ALL) has a cross-sectional area of 52mm 2 and its length is estimated as 13mm, although it must be appreciated that the ALL fibers can run the length of several bodies and defining specific attachment points along the anterior wall of the vertebral body is not easily done. The ALL typically fails at a load of 450N and at a deformation of 15mm.
The posterior longitudinal ligament (PLL) is smaller but somewhat analogous to the ALL as it attaches along the posterior wall of the vertebral body. The PLL has a cross-sectional area of 16mm 2 and an estimated length of 11mm. Its strength is reported to be 320N with a failure deformation of 5mm, making it much stiffer than the ALL.
The ligamentum flavum appears to be unique in that it can exhibit significantly more strain than the other spinal ligaments and is believed possess a large resting tension to. These factors prevent the ligamentum flavum from buckling into the spinal canal during extension as the attachment points approximate one another. The ligamentum flavum has a cross-section of 65mm 2 and a length estimated to be 19mm. Its strength is approximately 285N and fails at a deformation of 12mm.
The capsular ligaments of the lumbar spine fail at approximately 220N with a deformation of 11mm.
The interspinous ligaments fail at approximately 125N with a deformation of 13mm.
The supraspinous ligament has a cross-sectional area of 23mm 2 and a length of 11mm. It fails at a tensile load of 150N with a deformation of 30mm.
The principal motions of the lumbar spine are described by the neutral zone (NZ) and range of motion (ROM) values.
These motions occur about rotation axes that are located anteriorly and posteriorly for flexion and extension, respectively. In left and right lateral, the locations of the rotation axes have been reported to lie on the side opposite the direction of lateral bending. While in axial rotation, the rotation axes lie on the posterior portion of the vertebral body.
Lumbosacral Joint
The neutral zone (NZ) and range of motion (ROM) values of the lumbosacral joint are reached by allowing gravity and time, while laying on your back.

Spinal Stability
Spinal stability is the most clinically important biomechanical parameter, but also the most elusive.
In the text by White and Panjabi, spinal stability is defined as “…The ability of the spine under physiological loads to limit patterns of displacement so as not to damage or irritate the spinal cord or nerve roots and, in addition, to prevent incapacitating deformity or pain due to structural changes ...“.
More definitive guidelines for surgeons have been provided by them and by others. These guidelines are typically specific measurements for which a range of normal values is given. When the spine measurements lies beyond a given threshold value it is considered an indication of instability.
From an engineering perspective, a system is said to be stable if it returns to its initial state after a perturbation. With an axial compressive load of more than 20lbs the ligamentous lumbar spine is unstable, it cannot remain upright and buckles. Thus the musculature of the spine is essential in maintaining spinal stability, so do your core training!

Leonardo DaVinci was the first bioengineer to appreciate this instability and hypothesized that the musculature of the spine performed in the same way as the guy wires of a ship’s mast.