Fig. 3
Functional forms for \(f_{3}(t)\), \(f_{4}(t)\), \(f_{5}(t)\), \(f_{6}(t)\) and \(f_{7}(t)\). The assumed age-related changes of (a) vitamin D production (\(f_{3}(t)\)) and renal function (\(f_{4}(t)\)) where \(f_{3}=f_{4}=10^{0.1-0.006\text {age}}\), (b) macrophage and epithelial cell membrane permeability (\(f_{5}(t)=1\times 10^{-10}\text {age}^{5}-3.7\times 10^{-8}\text {age}^{4}+4.9\times 10^{-6}\text {age}^{3}-2.3\times 10^{-4}\text {age}^{2}+4.7\times 10^{-3}\text {age}\) \(+9.6\times 10^{-1}\)) and (c) metabolism of intracellular 25(OH)D to 1,25(OH)2D (\(f_{6}(t)\)) and VDR:1,25(OH)2D binding (\(f_{7}(t)\)) where \(f_{6}=f_{7}=10^{0.3-0.002\text {age}}\). As in Fig. 2, age=(t+7300)/365 years and \(0\le t\le 21900\) days.
