Van C. Mow

A standardized method for the assessment of shoulder function

The American Shoulder and Elbow Surgeons have adopted a standardized form for assessment of the shoulder. The form has a patient self-evaluation section and a physician assessment section. The patient self-evaluation section of the form contains visual analog scales for pain and instability and an activities of daily living questionnaire. The activities of daily living questionnaire is marked on a four-point ordinal scale that can be converted to a cumulative activities of daily living index. The patient can complete the self-evaluation portion of the questionnaire in the absence of a physician. The physician assessment section includes an area to collect demographic information and assesses range of motion, specific physical signs, strength, and stability. A shoulder score can be derived from the visual analogue scale score for pain (50%) and the cumulative activities of daily living score (50%). It is hoped that adoption of this instrument to measure shoulder function will facilitate communication between investigators, stimulate multicenter studies, and encourage validity testing of this and other available instruments to measure shoulder function and outcome.

Fluid transport and mechanical properties of articular cartilage: A review

This review is aimed at unifying our understanding of cartilage viscoelastic properties in compression, in particular the role of compression-dependent permeability in controlling interstitial fluid flow and its contribution to the observed viscoelastic effects. During the previous decade, it was shown that compression causes the permeability of cartilage to drop in a functional manner described by k = ko exp (epsilon M) where ko and M were defined as intrinsic permeability parameters and epsilon is the dilatation of the solid matrix (epsilon = tr delta u). Since permeability is inversely related to the diffusive drag coefficient of relative fluid motion with respect to the porous solid matrix, the measured load-deformation response of the tissue must therefore also depend on the non-linearly permeable nature of the tissue. We have summarized in this review our understanding of this non-linear phenomenon. This understanding of these flow-dependent viscoelastic effects are put into the historical perspective of a comprehensive literature review of earlier attempts to model the compressive viscoelastic properties of articular cartilage.

Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures

The anatomic forms of diarthrodial joints are important structural features which provide and limit the motions required for the joint. Typically, the length scale of topographic variation of anatomic forms ranges from 0.5 to 15 cm. Articular cartilage is the thin layer of hydrated soft tissue (0.5-5.0 mm thick) covering the articulating bony ends in diarthrodial joints. This tissue has a set of unique mechanical and physicochemical properties which are responsible for its load-carrying capabilities and near-frictionless qualities. The mechanical properties of articular cartilage are determined at the tissue-scale level and these properties depend on the composition of the tissue, mainly collagen and proteoglycan, and their molecular and ultrastructural organization (ultra-scale: 10(-8)-10(-6) m). Because proteoglycans possess a high density of fixed negative charges, articular cartilage exhibits a significant Donnan osmotic pressure effect. This physicochemically derived osmotic pressure is an important component of the total swelling pressure; the other component of the total swelling pressure stems from the charge-to-charge repulsive force exerted by the closely spaced (1-1.5 nm) negative charge groups along the proteoglycan molecules. Thus these interactions take place at a nano-scale level: 10(-10)-10(-9) m. Finally, cartilage biochemistry and organization are maintained by the chondrocytes which exist at a micro-scale level (10(-7)-10(-6) m). Significant mechanoelectrochemical transduction occurs within the extracellular matrix at the micro-scale level which affects and modulates cellular anabolic and catabolic activities. At present, the exact details of these transduction mechanisms are unknown. In this review, we present a summary of the hierarchical features for articular cartilage and diarthrodial joints and tables of known material properties for cartilage. Also we summarize how the multi-scale interactions in articular cartilage provide for its unique material properties and tribological characteristics.

Variations in the intrinsic mechanical properties of human articular cartilage with age, degeneration, and water content.

UNLABELLED In a series of 103 specimens from the lateral facet of the human patella, the intrinsic mechanical properties of articular cartilage were measured using a confined compression creep test. By considering the cartilage as a porous, permeable solid filed with fluid, this experimental procedure allowed the determination of the intrinsic equilibrium modulus of the cartilage matrix and its permeability to fluid flow. The intrinsic equilibrium modulus and the permeability both were highly correlated with the water content of the tissue; as water content increased, the matrix of the tissue became softer and more permeable. There was only a marginal decrease in the equilibrium modulus of the tissue with increasing age and surface degeneration. The permeability of the cartilage matrix was not significantly correlated with age or degeneration. CLINICAL RELEVANCE We concluded that the visual or histological appearance of a cartilage specimen may be a poor indicator of its ability to function as the bearing material in the intact joint. A more reliable indicator of the functional properties of a specimen can be obtained either by direct mechanical testing or by biochemical analysis of its composition.

Material properties and structure-function relationships in the menisci.

The menisci serve several important biomechanical functions in the knee. They distribute stresses over a broad area of articular cartilage, absorb shocks during dynamic loading, and probably assist in joint lubrication. These functions enhance the ability of articular cartilage to provide a smooth, near-frictionless articulation and to distribute loads evenly to the underlying bone of the femur and tibia. In addition, the menisci provide stability to the injured knee when the cruciate ligaments or other primary stabilizers are deficient. The ability to perform these mechanical functions is based on the intrinsic material properties of the menisci as well as their gross anatomic structure and attachments. The material properties of the menisci are determined by their biochemical composition and, perhaps more important, by the organization and interactions of the major tissue constituents: water, proteoglycan, and collagen. Interactions among the important constituents of the fibrocartilage matrix cause meniscal tissue to behave as a fiber-reinforced, porous, permeable composite material similar to articular cartilage, in which frictional drag caused by fluid flow governs its response to dynamic loading. The menisci are one-half as stiff in compression and dissipate more energy under dynamic loading than articular cartilage. Energy dissipation, or shock absorption, by the menisci is the result of high frictional drag caused by low permeability of the matrix, which is about one-sixth as permeable as articular cartilage. The dynamic shear modulus of meniscal tissue is only one-fourth to one-sixth as great as that of articular cartilage. The coarse, circumferential Type I collagen fiber bundles of the meniscus give the tissue great tensile stiffness (range, 100-300 megapascals) and strength. The highly oriented collagen ultrastructure of the menisci makes the tissue anisotropic in tension, compression, and shear and appears to dominate its behavior under all loading conditions.

Biphasic indentation of articular cartilage-II. A numerical algorithm and an experimental study

Part I (Mak et al., 1987, J. Biomechanics 20, 703-714) presented the theoretical solutions for the biphasic indentation of articular cartilage under creep and stress-relaxation conditions. In this study, using the creep solution, we developed an efficient numerical algorithm to compute all three material coefficients of cartilage in situ on the joint surface from the indentation creep experiment. With this method we determined the average values of the aggregate modulus. Poissons ratio and permeability for young bovine femoral condylar cartilage in situ to be HA = 0.90 MPa, vs = 0.39 and k = 0.44 x 10(-15) m4/Ns respectively, and those for patellar groove cartilage to be HA = 0.47 MPa, vs = 0.24, k = 1.42 x 10(-15) m4/Ns. One surprising finding from this study is that the in situ Poissons ratio of cartilage (0.13-0.45) may be much less than those determined from measurements performed on excised osteochondral plugs (0.40-0.49) reported in the literature. We also found the permeability of patellar groove cartilage to be several times higher than femoral condyle cartilage. These findings may have important implications on understanding the functional behavior of cartilage in situ and on methods used to determine the elastic moduli of cartilage using the indentation experiments.

Biphasic indentation of articular cartilage—I. Theoretical analysis

A mathematical solution has been obtained for the indentation creep and stress-relaxation behavior of articular cartilage where the tissue is modeled as a layer of linear KLM biphasic material of thickness h bonded to an impervious, rigid bony substrate. The circular (radius = a), plane-ended indenter is assumed to be rigid, porous, free-draining, and frictionless. Double Laplace and Hankel transform techniques were used to solve the partial differential equations. The transformed equations and boundary conditions yielded an integral equation of the Fredholm type which was analyzed asymptotically and solved numerically. Our asymptotic analyses showed that the linear KLM biphasic material behaves like an incompressible (v = 0.5) single-phase elastic solid at t = 0+; the instantaneous response of the material is governed by the shear modulus (mu s) of the solid matrix. The linear KLM biphasic material behaves like a compressible elastic solid with material properties defined by those of the solid matrix, i.e. (lambda s, mu s) or (mu s, v s) as t----infinity. The transient viscoelastic creep and stress-relaxation behavior, 0 less than t less than infinity, of this material is controlled by the frictional drag (which is inversely proportional to the permeability k) associated with the flow of the interstitial fluid through the porous-permeable solid matrix. For given values of the Poissons ratio of the solid matrix v s and the aspect ratio a/h, where a is the radius of the indenter and h is the thickness of the layer, the creep behavior with respect to the dimensionless time H Akt/a2 is completely controlled by the load parameter P/2 mu sa2 and the stress relaxation behavior is completely controlled by the rate of compression parameter R0 = kH A/V0h where H A = lambda s + 2 mu s and the equilibrium strain u0/h. This mathematical solution may now be used to describe an indentation experiment on articular cartilage to determine the intrinsic material properties of the tissue, i.e. permeability k, and the elastic coefficients of the solid phase (lambda s, mu s) or (mu s, v s).

An asymptotic solution for the contact of two biphasic cartilage layers

The purpose of this study was to present a solution for the contact of two biphasic cartilage layers which can be used for dynamic loading, is not restricted to predictions over small time periods, and predicts biologically meaningful changes in contact areas over time. The proposed solution was based on the work of Ateshian et al. (1994, J. Biomechanics 27, 1347-1360) who retained the first term of an asymptotic expansion and used an approximate integration which is valid for short time periods. The solution proposed here uses an exact integration, is valid over long time periods, and can be used for increasing loading. The new solution corrects a limitation of the work by Ateshian et al., which manifests itself immediately (i.e. at time t = 0+ s): the rate of change in the contact radius (and therefore, the contact area) is increasing in Ateshian et al.s solution for a constant force, whereas it is decreasing in the new solution. An increasing rate of change in the contact radius suggests that the contact radius (area) is unbounded, and a steady-state solution cannot be reached, which is physically not correct for the contact of two joint surfaces. In the new solution, the contact radius reaches a steady-state value given sufficient time.

Excursion of the Rotator Cuff Under the Acromion Patterns of Subacromial Contact

Nine fresh-frozen, human cadaveric shoulders were el evated in the scapular plane in two different humeral rotations by applying forces along action lines of rotator cuff and deltoid muscles. Stereophotogrammetry deter mined possible regions of subacromial contact using a proximity criterion; radiographs measured acromio humeral interval and position of greater tuberosity. Con tact starts at the anterolateral edge of the acromion at 0° of elevation; it shifts medially with arm elevation. On the humeral surface, contact shifts from proximal to dis tal on the supraspinatus tendon with arm elevation. When external rotation is decreased, distal and poste rior shift in contact is noted. Acromial undersurface and rotator cuff tendons are in closest proximity between 60° and 120° of elevation; contact was consistently more pronounced for Type III acromions. Mean acro miohumeral interval was 11.1 mm at 0° of elevation and decreased to 5.7 mm at 90°, when greater tuberosity was closest to the acromion. Radiographs show bone- to-bone relationship; stereophotogrammetry assesses contact on soft tissues of the subacromial space. Con tact centers on the supraspinatus insertion, suggesting altered excursion of the greater tuberosity may initially damage this rotator cuff region. Conditions limiting ex ternal rotation or elevation may also increase rotator cuff compression. Marked increase in contact with Type III acromions supports the role of anterior acromioplasty when clinically indicated, usually in older patients with primary impingement.

The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration.

A one-dimensional ultrafiltration problem of fluid flow through a soft permeable tissue or gel under high pressure and compressive strain is solved. A finite deformation biphasic theory is used to model the behavior of the soft porous permeable solid matrix. This theory includes a Helmholtz free energy function which depends on the three principal invariants (I, II, III) of the right Cauchy-Green tensor and which satisfies the Baker-Ericksen inequalities on the principal stresses and strains. The dependence of the porosity phi f and the solidity phi s on deformation is deduced and a generalization of the exponential strain-dependent functional form for the permeability, k = k0 exp (M epsilon), of Lai and Mow (Biorheology 103, 111-123, 1980) is proposed. In this one-dimensional problem, we show that the dependence of the permeability on phi f, phi s, and III is equivalent to its dependence on hydration as proposed by Fatt and Goldstick (J. Colloid Sci. 20, 962-988, 1965). The exact solution of the ultrafiltration problem is derived and asymptotic and numerical methods are used to evaluate it. For high pressures and finite strains, the solution provides some surprising effects. The theory predicts that a material starting with a homogeneous porosity will have a strongly non-homogeneous porosity throughout the column during ultrafiltration. The resulting change in pore size through the filtration column may be very important in understanding its filtration characteristics. It is also found that there is a long delay time, up to 10 to 15 min, before the filtration velocity reaches an equilibrium. In filtration experiments where the rate of mass transport across the tissue or column of gel is important, sufficient time must be allowed for the steady state to be reached.