Parathyroid hormone temporal effects on bone formation and resorption |
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Authors: | Martin H Kroll |
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Institution: | (1) Department of Pathology, The Johns Hopkins Medical Institutions, 600 N. Wolfe St., Meyer B-125, Baltimore, MD 21287, USA |
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Abstract: | Parathyroid hormone (PTH) paradoxically causes net bone loss (resorption) when administered in a continuous fashion, and net
bone formation (deposition) when administered intermittently. Currently no pharmacological formulations are available to promote
bone formation, as needed for the treatment of osteoporosis. The paradoxical behavior of PTH confuses endocrinologists, thus,
a model bone resorption or deposition dependent on the timing of PTH administration would de-mystify this behavior and provide
the basis for logical drug formulation. We developed a mathematical model that accounts for net bone loss with continuous
PTH administration and net bone formation with intermittent PTH administration, based on the differential effects of PTH on
the osteoblastic and osteoclastic populations of cells.
Bone, being a major reservoir of body calcium, is under the hormonal control of PTH. The overall effect of PTH is to raise
plasma levels of calcium, partly through bone resorption. Osteoclasts resorb bone and liberate calcium, but they lack receptors
for PTH. The preosteoblastic precursors and preosteoblasts possess receptors for PTH, upon which the hormone induces differentiation
from the precursor to preosteoblast and from the preosteoblast to the osteoblast. The osteoblasts generate IL-6; IL-6 stimulates
preosteoclasts to differentiate into osteoclasts. We developed a mathematical model for the differentiation of osteoblastic
and osteoclastic populations in bone, using a delay time of 1 hour for differentiation of preosteoblastic precursors into
preosteoblasts and 2 hours for the differentiation of preosteoblasts into osteoblasts. The ratio of the number of osteoblasts
to osteoclasts indicates the net effect of PTH on bone resorption and deposition; the timing of events producing the maximum
ratio would induce net bone deposition.
When PTH is pulsed with a frequency of every hour, the preosteoblastic population rises and decreases in nearly a symmetric
pattern, with 3.9 peaks every 24 hours, and 4.0 peaks every 24 hours when PTH is administered every 6 hours. Thus, the preosteoblast
and osteoblast frequency depends more on the nearly constant value of the PTH, rather than on the frequency of the PTH pulsations.
Increasing the time delay gradually increases the mean value for the number of osteoblasts. The osteoblastic population oscillates
for all intermittent administrations of PTH and even when the PTH infusion is constant. The maximum ratio of osteoblasts to
osteoclasts occurs when PTH is administered in pulses of every 6 hours.
The delay features in the model bear most of the responsibility for the occurrence of these oscillations, because without
the delay and in the presence of constant PTH infusions, no oscillations occur. However, with a delay, under constant PTH
infusions, the model generates oscillations. The osteoblast oscillations express limit cycle behavior. Phase plane analysis
show simple and complex attractors. Subsequent to a disturbance in the number of osteoblasts, the osteoblasts quickly regain
their oscillatory behavior and cycle back to the original attractor, typical of limit cycle behavior. Further, because the
model was constructed with dissipative and nonlinear features, one would expect ensuing oscillations to show limit cycle behavior.
The results from our model, increased bone deposition with intermittent PTH administration and increased bone resorption with
constant PTH administration, conforms with experimental observations and with an accepted explanation for osteoporosis. |
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