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Title: Modelling in the analysis of ion exchange between blood and bone
Author: Willans, Simon Mark
ISNI:       0000 0001 3568 5992
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1988
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The principal objective of the research was to model the outflow results of multiple tracer outflow dilution (M.T.O.D.) techniques from the canine tibia so as to obtain a more precise understanding of the physiological mechanisms underlying mineral exchange in bone. To date, M.T.O.D. techniques have been performed on the tibiae of greyhound dogs but the subsequent outflow results have produced information mainly at the capillary level for the diffusible tracers concerned such as capillary permeability-surface area PSC products from the widely used Crone-Renkin formulation. Back diffusion and heterogeneous capillary flow rates lacking from the formulation, however, have impaired the accuracy of PS(C). Outflow results from two series of previously performed M.T.O.D. experiments were modelled. In the first experimental series, outflow results from the ipsilateral femoral vein concerning l25l-albumin reference and 85Sr (Ca analogue), 86Rb (K analogue) diffusible tracers were used ; the tracers having being injected into the tibial nutrient arteries. In the second experimental series, 125l-albumin and 85Sr outflow results were used from parathyroidectomised dogs in which both tracers had been injected together before and after a dose of 0.0005 mg bovine parathyroid hormone (PTH). The problem of back diffusion was alleviated by optimising a homogeneous flow model to M.T.O.D. data. The model produced informative parameter estimates for 85Sr and 86Rb concerning fluid spaces and associated boundaries in Haversian systems largely comprising the diaphyseal cortex. Exchange was assumed to take place there by virtue of injecting the tracers into the tibial nutrient artery. Blood flow rates, known to be influential in governing the extent of tracer exchange in the diaphysis, were investigated using the microsphere technique. Flow rate heterogeneity was found to be substantial, as adjudged by distributions of relative deposition densities of microspheres in 40 pieces of cortex and 10 marrow samples in 6 tibiae. For the cortex, the distributions were positively skewed with a relative dispersion of around 40%. Additional work involving light microscopy suggested that the distribution of cortical flow rates were not attributable to particular changes in capillary density, which were relatively uniform at 2682 + 510 capillaries/cm2 (4 tibiae ; 240 observations). The findings concerning flow rate heterogeneity, together with the deduction that the cortex and marrow respectively received 65% and 35% of tibial nutrient artery flow, prompted the development of a parallel multicapillary model in which 4 capillary systems were alloted to the cortex and 1 such system to the marrow. Input to the model was a suitable form of the reference tracer outflow profile which describes the large vessel transport behaviour assumed identical for all tracers concerned. Parameter estimates (mean + s.d.) found by optimisation for 85Sr and 86Rb (n=6) were PSC = 0.045 + 0.021 and 0.047 + 0.022 ml/s respectively. Apparent volumes of distribution (n=5) for the interstitial fluid were 0.90 + 0.36 (85Sr) and 0.69 + 0.22 ml of diaphysis (86Rb). Additional studies involving gamma variates showed that model inputs were robust in terms of varying degrees of large vessel dispersion. Furthermore, simulation studies involving the effect of asymmetric transport on the resulting parameter estimates in the context of modelling the PTH data provided speculative evidence for the concept of a bone-lining cell membrane controlling uptake to bone surfaces.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Bone mineral exchange