Abstract
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.
