Achenie and Ogunnaike, is an in silico simulation of the
dynamic behavior of calcium-regulation system in human, as
shown in Fig. 2. The dynamic behavior of PTH, CTL, bone
cell proliferation, plasma Ca and phosphate (PO4) can be sim-
ulated in the form of nonlinear ordinary differential equation.
In this model, the effect of calcitonin is ignored since its role in
Ca regulation is not as important as those of PTH and of CTL.
Additionally, all hormones and ions are uniformly distrib-
uted in the ECF and their concentration are identical to that
in the plasma. In this Ca-regulation system, PTG serves as
controller and sensor, while kidneys, bone and intestines can
be viewed as actuators. The process has 13 measured varia-
bles (11 continuous process measurements and 2 binary
measurements). The details of measurement variables are
listed in Table 1. The sampling time is 0.25 h. A set of 6 prede-
fined experimental stimuluses are introduced into the Ca-
regulation system, the details are listed in Table 2.
This Ca-regulation model can simulate healthy statuses
and 6 pathologies (Table 3). These pathologies can be classi-
fied into 2 major categories: hypocalcemia and hypercalcemia
(as shown in Fig. 3). To be specific, Autosomal Dominant
Hypoparathyroidism (ADH), Hypoparathyroidism (HoPT)
and Vitamin D deficiency (VDD) can be classified as hypo-
calcemia. Familial Benign Hypercalcemia (FBH), Primary
Hyperparathyroidism (PHPT), and Humoral Hypercalcemia
of Malignancy (HHM) can all be defined as hypercalcemia.
Specifically, ADH, characterized by the low PTH, hypo-
calcemia as well as hypercalciuria, is caused by an over-
sensitive Calcium-Sensing Receptors. Conversely, FBH, is
represented by high PTH and hypocalciuria.
These two diseased states can be viewed as Calcium-
sensor defects. HoPT, characterized by relative low or even
no PTH secretion, reduced CTL and hypercalciura, and
PHPT, featured by excessive excretion of PTH and hypercal-
cemia, can be categorized as controller defects in the
Fig. 2. Control flow chart of calcium/phosphate regulation process.
TABLE 1
Monitored Variables in Ca-Regulation Process
No. Variable Name
Con1 Plasma Calcium
Con2 Plasma phosphate
Con3 Parathyroid hormone (PTH) level
Con4 Calcitriol (CTL) level
Con5 Urinary Calcium
Con6 Bone cell proliferation(CB ratio)
Con7 Calcium in kidneys
Con8 Urinary phosphate
Con9 Phosphate in kidneys
Con10 Phosphate in bone
Con11 PTH-related peptide(PTHrP)(optional)
Bi1 Ca in meal(optional, binary)
Bi2 Phosphate in meal(optional, binary)
TABLE 2
Experimental Stimulus (Disturbances) Introduced
in Ca-Regulation Process
No. Stimulus type Duration (h) Medicine infusion
1 Khosla [31] 2 Calcium gluconate
2 Ramirez hyper [11] 120 Sodium citrate
3 Ramirez hypo [11] 120 Sodium citrate
4 Goodman hyper [12] 120 Calcium gluconate
5 Parfitt Hypo [32] 2 Sodium edetate (EDTA)
6 Haden hyper [33] 90 Sodium citrate
TABLE 3
Pathologies Pattern in Ca-Regulation Process
Category Pathologies Parameter Setting
FBH 12% reduction in K
sens
Hyper- PHPT 25% increase in B
ca
and A
ca
HHM 500% increase the PTHrP rate
ADH 12% increase in K
sens
Hypo- HoPT 25% decrease in A
ca
and B
ca
VDD 80% reduction in Kidney CTL
790 IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS, VOL. 15, NO. 3, MAY/JUNE 2018