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Relation Between Parathyroid Cell Mass and Plasma Calcium Concentration in Normal and Uremic Subjects:  A Theoretical Model With an Analysis of the Concept of Autonomy, and Speculations on the Mechanism of Parathyroid Hyperplasia

Alwyn M. Parfitt, MB, MRCP, MRACP
Arch Intern Med. 1969;124(3):269-273. doi:10.1001/archinte.1969.00300190009003.
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In experiments in cows Ramberg et al 1 found that plasma parathyroid hormone (PTH) level (dependent variable) was inversely related to plasma calcium level. Although there was considerable scatter, the calculated regression was significant, and could be represented by the following equation:

PTH (mμ/ml) = 8.2 — 0.7 Ca (mg/100 ml). (equation1a) This is shown as the continuous line in Fig 1. A more recent study by Potts et al2 showed a very similar linear inverse regression with much less scatter. If the coordinated response of the various target organs is such that plasma Ca (dependent variable) is linearly related to plasma PTH, then it is necessary to define only two points in order to express Ca as a function of PTH. It is a reasonable assumption that patients with idiopathic hypoparathyroidism have no circulating PTH, and the mean plasma Ca in 50 such patients was 5.3 mg/100 ml3

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