Mathematical model of the human ankle joint

It has been suspected that the mechanical environment in which a particular joint functions has an effect on the initiation or progression of degenerative joint disease. The objective of this study is to define the mechanical environment of the ankle joint, specifically, the contact areas and pressure distributions, through the development and analysis of a simplified mathematical model. Since the state of pressure across articular surfaces during function is influenced by joint incongruity, cartilage thickness profile and the geometry of the opposing surfaces, these factors have been incorporated into the model formulation. Mathematical analysis of the model has resulted in pressure distributions in both the anterior-posterior and medial-lateral directions and contact area growth plots which correlate well with observed ankle contact patterns obtained from in vitro investigations. The significance of joint incongruity to these pressure distributions and to the relative immunity of the ankle joint to primary osteoarthritis is discussed.     

The inflammatory process of gout and its treatment

Gouty arthritis is a characteristically intense acute inflammatory reaction that erupts in response to articular deposits of monosodium urate (MSU) crystals. Important recent molecular biologic advances in this field have given us a clear picture of the mechanistic basis of gouty inflammation. The innate immune inflammatory response is critically involved in the pathology of gout. Specifically, MSU crystals promote inflammation directly by stimulating cells via Toll-like receptor signaling and by providing a surface for cleavage of C5 and formation of complement membrane attack complex (C5b-9), culminating in secretion of cytokines, chemokines, and other inflammatory mediators with a dramatic influx of neutrophils into the joint. Despite the detailed mechanistic picture for gouty inflammation, there are no placebo-controlled, randomized clinical studies for any of the therapies commonly used, although comparative studies have demonstrated that many nonsteroidal anti-inflammatory drugs are equivalent to indomethacin with respect to controlling acute gouty attacks. In general, the first line of anti-inflammatory therapy for acute gout is nonsteroidal anti-inflammatory drugs, and the selective cyclo-oxygenase-2 inhibitor celecoxib can be used where appropriate. The second line of treatment is glucocorticosteroids, given systemically (oral, intravenous, or intramuscular) or intra-articularly. Alternatively, synthetic adrenocorticotropic hormone is effective, partly via induction of adrenal glucocorticosteroids and partly via rapid peripheral suppression of leukocyte activation by melatonin receptor 3 signaling. The third line of treatment is oral colchicine, which is highly effective when given early in an acute gouty attack, but it is poorly tolerated because of predictable gastrointestinal side effects.     

A model that reproduces syndromes associated with human multiple myeloma in nonirradiated SCID mice

A human myeloma line was used to create a model of human multiple myeloma in vivo that would reproduce the pathophysiology of the disease, including the cachexia associated with cancer. Unirradiated severe combined immunodeficient (SCID) mice were used as surrogate hosts for in vivo experiments that allowed the effects of autocrine (human) verus paracrine (murine) cytokines on the development of myeloma to be studied. Serum levels of human paraprotein increased over time and with the number of cells transplanted. Transplanted mice developed major syndromes, cachexia and paralysis (due to invasion of bones by myeloma cells), associated with multiple myeloma. Analyses of serum samples obtained from transplanted mice revealed that when the mice were terminal, total serum protein decreased on average by 20%, whereas serum triglycerides decreased on average by 50%. These data indicate the mice were cachectic, which was confirmed by necropsy. The mice had low but measurable levels of both human and murine interleukin (IL)-6, soluble IL-6 receptor, and murine IL-10 in their sera. The presence of these cytokines and the IL-6 receptor in sera are also characteristics of human myeloma in patients. Since human cells do not respond to murine IL-6, it was possible to demonstrate clearly the importance of autocrine IL-6 in establishing myeloma in situ. By reproducing both the hallmarks of a cancer as well as the accompanying paraneoplastic syndromes, this model should be useful in designing more effective therapies for both the primary cancer as well as the accompanying secondary diseases.     

Temporal changes in human temporomandibular joint size and shape

Measurements approximating the size of the temporomandibular joint were taken on a series of genetically homogeneous populations from early Nubia, which span almost 10,000 years and embody a shift from a primarily hunting and gathering adaptation to a completely agricultural lifeway. A generalized trend of reduction of temporomandibular joint size was observed. In addition, a decrease in sexual dimorphism was apparent for all measures of joint size; a change primarily mitigated by reductions in male dimensions. The observed variation in size and form of the temporomandibular joint is most likely the result of the reduction in masticatory muscle robusticity and resultant changes in craniofacial form which have been documented for the transition from a hunting and gathering to an agricultural subsistence in Nubia.     

Animal model for testing human Ascaris allergens

Guinea pigs immunized through the nasal route by an antigenic preparation of humanAscaris lumbricoides produced predominantly homocytotropic antibodies. The sensitization of the homologous skin required a latency period. Hypersensitivity reaction was triggered within 30 min. of the antigen challenge. The antibodies were sensitive to heat and β-mercaptoethanol treatments and appeared to be similar to the IgE type of immunoglobulins of man and rabbit. The antigenic preparation elicited an immediate type of skin hypersensitivity reaction also in human subjects harbouring the Ascaris parasite. The guinea pig model appears suitable for testing the activity of Ascaris allergens.     

Metal ions and oxygen radical reactions in human inflammatory joint disease

Activated phagocytic cells produce superoxide (O2-) and hydrogen peroxide (H2O2); their production is important in bacterial killing by neutrophils and has been implicated in tissue damage by activated phagocytes. H2O2 and O2- are poorly reactive in aqueous solution and their damaging actions may be related to formation of more reactive species from them. One such species is hydroxyl radical (OH.), formed from H2O2 in the presence of iron- or copper-ion catalysts. A major determinant of the cytotoxicity of O2- and H2O2 is thus the availability and location of metal-ion catalysts of OH. formation. Hydroxyl radical is an initiator of lipid peroxidation. Iron promoters of OH. production present in vivo include ferritin, and loosely bound iron complexes detectable by the 'bleomycin assay'. The chelating agent Desferal (desferrioxamine B methanesulphonate) prevents iron-dependent formation of OH. and protects against phagocyte-dependent tissue injury in several animal models of human disease. The use of Desferal for human treatment should be approached with caution, because preliminary results upon human rheumatoid patients have revealed side effects. It is proposed that OH. radical is a major damaging agent in the inflamed rheumatoid joint and that its formation is facilitated by the release of iron from transferrin, which can be achieved at the low pH present in the micro-environment created by adherent activated phagocytic cells. It is further proposed that one function of lactoferrin is to protect against iron-dependent radical reactions rather than to act as a catalyst of OH. production.     

A geometric model of the human ankle joint.

A two-dimensional four-bar linkage model of the ankle joint is formulated to describe dorsi/plantarflexion in unloaded conditions as observed in passive tests on ankle complex specimens. The experiments demonstrated that the human ankle joint complex behaves as a single-degree-of-freedom system during passive motion, with a moving axis of rotation. The bulk of the movement occurred at the level of the ankle. Fibres within the calcaneofibular and tibiocalcaneal ligaments remained approximately isometric. The experiments showed that passive kinematics of the ankle complex is governed only by the articular surfaces and the ligaments. It was deduced that the ankle is a single-degree-of-freedom mechanism where mobility is allowed by the sliding of the articular surfaces upon each other and the isometric rotation of two ligaments about their origins and insertions, without tissue deformation. The linkage model is formed by the tibia/fibula and talus/calcaneus bone segments and by the calcaneofibular and tibiocalcaneal ligament segments. The model predicts the path of calcaneus motion, ligament orientations, instantaneous axis of rotation, and conjugate talus surface profile as observed in the experiments. Many features of ankle kinematics such as rolling and multiaxial rotation are elucidated. The geometrical model is a necessary preliminary step to the study of ankle joint stability in response to applied loads and can be used to predict the effects of changes to the original geometry of the intact joint. Careful reconstruction of the original geometry of the ligaments is necessary after injury or during total ankle replacement.     

Lactate administration reproduces specific brain and liver exercise‐related changes

The effects of exercise are not limited to muscle, and its ability to mitigate some chronic diseases is under study. A more complete understanding of how exercise impacts non‐muscle tissues might facilitate design of clinical trials and exercise mimetics. Here, we focused on lactate's ability to mediate changes in liver and brain bioenergetic‐associated parameters. In one group of experiments, C57BL/6 mice underwent 7 weeks of treadmill exercise sessions at intensities intended to exceed the lactate threshold. Over time, the mice dramatically increased their lactate threshold. To ensure that plasma lactate accumulated during the final week, the mice were run to exhaustion. In the liver, mRNA levels of gluconeogenesis‐promoting genes increased. While peroxisome proliferator‐activated receptor‐gamma co‐activator 1 alpha (PGC‐1α) expression increased, there was a decrease in PGC‐1β expression, and overall gene expression changes favored respiratory chain down‐regulation. In the brain, PGC‐1α and PGC‐1β were unchanged, but PGC‐1‐related co‐activator expression and mitochondrial DNA copy number increased. Brain tumor necrosis factor alpha expression fell, whereas vascular endothelial growth factor A expression rose. In another group of experiments, exogenously administered lactate was found to reproduce some but not all of these observed liver and brain changes. Our data suggest that lactate, an exercise byproduct, could mediate some of the effects exercise has on the liver and the brain, and that lactate itself can act as a partial exercise mimetic.

     

Two-dimensional model of calcium waves reproduces the patterns observed in Xenopus oocytes.

Biological excitability enables the rapid transmission of physiological signals over distance. Using confocal fluorescence microscopy, we previously reported circular, planar, and spiral waves of Ca2+ in Xenopus laevis oocytes that annihilated one another upon collision. We present experimental evidence that the excitable process underlying wave propagation depends on Ca2+ diffusion and does not require oscillations in inositol (1,4,5)trisphosphate (IP3) concentration. Extending an existing ordinary differential equation (ODE) model of Ca2+ oscillations to two spatial dimensions, we develop a partial differential equation (PDE) model of Ca2+ excitability. The model assumes that cytosolic Ca2+ couples neighboring Ca2+ release sites. This simple PDE model qualitatively reproduces our experimental observations.     

Compliant bipedal model with the center of pressure excursion associated with oscillatory behavior of the center of mass reproduces the human gait dynamics

Although the compliant bipedal model could reproduce qualitative ground reaction force (GRF) of human walking, the model with a fixed pivot showed overestimations in stance leg rotation and the ratio of horizontal to vertical GRF. The human walking data showed a continuous forward progression of the center of pressure (CoP) during the stance phase and the suspension of the CoP near the forefoot before the onset of step transition. To better describe human gait dynamics with a minimal expense of model complexity, we proposed a compliant bipedal model with the accelerated pivot which associated the CoP excursion with the oscillatory behavior of the center of mass (CoM) with the existing simulation parameter and leg stiffness. Owing to the pivot acceleration defined to emulate human CoP profile, the arrival of the CoP at the limit of the stance foot over the single stance duration initiated the step-to-step transition. The proposed model showed an improved match of walking data. As the forward motion of CoM during single stance was partly accounted by forward pivot translation, the previously overestimated rotation of the stance leg was reduced and the corresponding horizontal GRF became closer to human data. The walking solutions of the model ranged over higher speed ranges (~1.7 m/s) than those of the fixed pivoted compliant bipedal model (~1.5 m/s) and exhibited other gait parameters, such as touchdown angle, step length and step frequency, comparable to the experimental observations. The good matches between the model and experimental GRF data imply that the continuous pivot acceleration associated with CoM oscillatory behavior could serve as a useful framework of bipedal model.     

Age-related changes of elements in the human articular disk of the temporomandibular joint

To elucidate compositional changes of the articular disk (AD) of the temporomandibular joint (TMJ) by aging, elements of the ADs resected from 18 cadavers were determined by inductively coupled plasma atomic-emission spectrometry. It was found that calcium contents of ADs in TMJs increased progressively with aging, whereas the sulfur contents of the ADs decreased slightly with aging. Regarding the content of phosphorus, the contents increased progressively with aging. The study revealed that age-related changes of calcium contents in the ADs of TMJs were similar to those in women’s pubic symphyses, but not those in intervertebral disks and menisci.     

Contractile changes in opposing muscles of the human ankle joint with aging

The effects of aging on maximal voluntary strength and on the isometric twitch were determined in the ankle dorsiflexor and plantarflexor muscles of 111 healthy men and women aged 20-100 yr. Men were found to be stronger than women at all ages. In both sexes, the average values for maximum voluntary strength of the dorsiflexors and plantarflexors began to decline in the 6th decade. Although the absolute loss of strength was greater for the plantarflexor muscles, the relative losses were similar in the two muscle groups. During maximum voluntary effort, stimulation of motor nerves produced no additional torque in the majority of elderly men and women, indicating that these subjects remained able to utilize their descending motor pathways for optimal muscle activation. Comparisons of muscle compound action potentials, twitch torques, and muscle cross-sectional areas suggested that a decrease in excitable muscle mass was entirely responsible for the lower strength of the elderly. An additional effect of aging was the gradual prolongation of twitch contraction and half-relaxation times throughout the adult life-span.     

A dynamic model of the neural network, which reproduces the signal of the ganglion cells

A functional model of the neural network was proposed, which reproduces the signal of a ganglion cell during the formation of receptive fields with the antagonistic center and the periphery.     

A reduced mathematical model of the acute inflammatory response: I. Derivation of model and analysis of anti-inflammation

The acute inflammatory response, triggered by a variety of biological or physical stresses on an organism, is a delicate system of checks and balances that, although aimed at promoting healing and restoring homeostasis, can result in undesired and occasionally lethal physiological responses. In this work, we derive a reduced conceptual model for the acute inflammatory response to infection, built up from consideration of direct interactions of fundamental effectors. We harness this model to explore the importance of dynamic anti-inflammation in promoting resolution of infection and homeostasis. Further, we offer a clinical correlation between model predictions and potential therapeutic interventions based on modulation of immunity by anti-inflammatory agents.