Mathematical simulation of the body fluid regulating system in dog

A mathematical model of body fluid volume and osmolality regulation was developed which incorporated the major nonlinearities of fluid assimilation, exchange, distribution and excretion. The non-linear differential equations define compartmental material balances for water, urea, sodium, protein and antidiuretic hormone (ADH). The parameters of these equations were calculated using analytical solutions and available steady-state experimental data. The model was used to simulate the renal response to five input forcings: (1) intraesophageal water infusion; (2) water ingestion; (3) intravenous ADH injection; (4) intravenous water infusion; and (5) intermittent water loading. The model yielded continuous simulation curves which agreed reasonably well with the available transient and steady-state experimental data. The model predicted that stimulating volume receptors via changes in left atrial pressure accounts for only 15–20% of changes in ADH secretion rate, whereas stimulation of the osmotic receptors via changes in plasma osmolality accounts for the remaining 80–85% of changes. Thus, it appears that regulation of ADH secretion is largely dependent upon plasma osmolality during forcings which do not appreciably alter the cardiovascular blood volume.