A mathematical model of calcium and phosphorus metabolism in two forms of hyperparathyroidism

Phosphate in Cardiovascular Disease: From New Insights Into Molecular Mechanisms to Clinical Implications

Hyperphosphatemia is a common feature in patients with impaired kidney function and is associated with increased risk of cardiovascular disease. This phenomenon extends to the general population, whereby elevations of serum phosphate within the normal range increase risk; however, the mechanism by which this occurs is multifaceted, and many aspects are poorly understood. Less than 1% of total body phosphate is found in the circulation and extracellular space, and its regulation involves multiple organ cross talk and hormones to coordinate absorption from the small intestine and excretion by the kidneys. For phosphate to be regulated, it must be sensed. While mostly enigmatic, various phosphate sensors have been elucidated in recent years. Phosphate in the circulation can be buffered, either through regulated exchange between extracellular and cellular spaces or through chelation by circulating proteins (ie, fetuin-A) to form calciprotein particles, which in themselves serve a function for bulk mineral transport and signaling. Either through direct signaling or through mediators like hormones, calciprotein particles, or calcifying extracellular vesicles, phosphate can induce various cardiovascular disease pathologies: most notably, ectopic cardiovascular calcification but also left ventricular hypertrophy, as well as bone and kidney diseases, which then propagate phosphate dysregulation further. Therapies targeting phosphate have mostly focused on intestinal binding, of which appreciation and understanding of paracellular transport has greatly advanced the field. However, pharmacotherapies that target cardiovascular consequences of phosphate directly, such as vascular calcification, are still an area of great unmet medical need.

Effect of replacing dicalcium phosphate with mono-dicalcium phosphate to supplement phosphorus on laying performance, phosphorus-calcium metabolism and bone metabolism of aged laying hens

The objective of this study was to evaluate the effect of replacing dicalcium phosphate (DCP) with mono-dicalcium phosphate (MDCP) to formulate low-phosphorus (P) diets on laying performance, egg quality, phosphorus-calcium metabolism, and bone metabolism of 69-78-week-old aged laying hens. Hy-Line Brown laying hens (n = 1,350, 69 weeks old) were randomly assigned to six treatments, each with five replicates of 45 hens. A corn-soybean meal-based diet was formulated to contain 0.12% non-phytate phosphorus (NPP), 3.81% calcium (Ca), and 1,470 FTU/kg phytase. The control group (CON) was supplemented with DCP inorganic phosphorus (Pi) at the NPP level of 0.20% (dietary NPP levels of 0.32%). Test groups (T1-T5) were supplemented with MDCP Pi at NPP levels of 0.07%, 0.11%, 0.15%, 0.18, and 0.20% (dietary NPP levels of 0.19, 0.23, 0.27, 0.30, and 0.32%, respectively). Calcium carbonate levels were adjusted to ensure all experimental diets contained the same Ca levels (3.81%). The feeding trial lasted 10 weeks, with hens increasing in age from 69 to 78 weeks. When supplemented with 1,470 FTU/kg phytase, extra DCP Pi or MDCP Pi did not affect (p > 0.05) laying performance (day laying rate, average egg weight, feed intake, feed-to-egg mass ratio, broken egg rate), egg quality (eggshell strength, albumen height, haugh units), or serum P, Ca, copper (Cu), iron (Fe), zinc (Zn), and manganese (Mn) levels. However, when laying hens were fed MDCP Pi (NPP levels of 0.07 to 0.20%), yolk color improved (p = 0.0148). The tibia breaking strength was significantly higher (p < 0.05) in the 0.18 and 0.20% NPP MDCP Pi groups than in the 0.20% NPP DCP Pi group. The breaking strength, Ca content, and P content of tibia in 0.11% and 0.15% NPP MDCP Pi hens were not significantly (p > 0.05) different from those in 0.20% NPP DCP Pi hens. Hens fed 0.07% NPP MDCP Pi had higher (p < 0.01) serum levels of osteoprotegerin (OPG), type-I collagen c-telopeptide (CTX-I), and tartrate-resistant acid phosphatase 5b (TRACP-5b) than those in all other groups. Serum levels of TRACP-5b and CTX-I in the 0.11% and 0.15% NPP MDCP Pi group were significantly lower than those in 0.18 and 0.20% NPP MDCP Pi groups and the 0.20% NPP DCP Pi group (p < 0.0001). Hens fed 0.07% and 0.11% NPP MDCP Pi had higher (p < 0.05) serum levels of parathyroid hormone (PTH) than those in all other groups. No differences were detected in serum calcitonin (CT), 1,25-dihydroxy-vitamin D3 (1,25-(OH)2D3), bone alkaline phosphatase (BAP), osteocalcin(OCN), and osteopontin (OPN) among all groups (p > 0.05). The expression of P transporters type IIa Na/Pi cotransporter (NaPi-IIa) in 0.11% and 0.15% NPP MDCP Pi hens were higher than those in 0.20% NPP MDCP Pi group and 0.20% NPP DCP Pi group (p < 0.05). The results indicated that both renal P reabsorption and bone resorption were involved in adapting to a low-P diet. In summary, when MDCP was used instead of DCP to supplement P, NPP levels could be reduced to 0.11% (dietary NPP level of 0.23%) without negative effects on laying performance and skeletal health of aged hens. In addition, MDCP was more beneficial than DCP for tibia quality. The results of the current study would provide references for the application of MDCP in low-P diets of aged laying hens.

Mathematical Models of Parathyroid Gland Biology: Complexity and Clinical Use

Altered parathyroid gland biology is a major driver of chronic kidney disease-mineral bone disorder (CKD-MBD) in patients with chronic kidney disease. CKD-MBD is associated with a high risk of vascular calcification and cardiovascular events. A hallmark of CKD-MBD is secondary hyperparathyroidism with increased parathyroid hormone (PTH) synthesis and release and reduced expression of calcium-sensing receptors on the surface of parathyroid cells and eventually hyperplasia of parathyroid gland cells. The KDIGO guidelines strongly recommend the control of PTH in hemodialysis patients. Due to the complexity of parathyroid gland biology, mathematical models have been employed to study the interaction of PTH regulators and PTH plasma concentrations. Here, we present an overview of various model approaches and discuss the impact of different model structures and complexities on the clinical use of these models.

Development of a quantitative systems pharmacology model of chronic kidney disease: metabolic bone disorder

Chronic kidney disease mineral bone disorder (CKD-MBD) is a virtually universal complication of kidney diseases, starting early in the course of disease and resulting in devastating clinical consequences ranging from bone fragility to accelerated atherosclerosis and early cardiovascular death. Guidelines for therapeutic goals for CKD-MBD have been published, and achievement of these guidelines is associated with improved survival. However, the incomplete understanding of CKD-MBD and the individual variability in the manifestations of CKD-MBD have made it difficult to achieve these guidelines. We hypothesized that the progression of MBD through all stages of CKD, including end-stage kidney disease, could be represented by a quantitative systems pharmacology/systems biology (QSP) model. To address this hypothesis, we constructed a QSP model of CKD-MBD, building on an open-source model of calcium and phosphorus metabolism. Specifically, we estimated and validated the model using data from 5,496 patients with CKD enrolled in the Chronic Renal Insufficiency Cohort study. Our model accurately predicted changes in markers of mineral metabolism related to progressing CKD. We demonstrated that the incorporation of fibroblast growth factor 23 and the soft tissue compartment is essential for accurate modeling of the changes in calcium, phosphorus, intact parathyroid hormone, and calcitriol in CKD-MBD. We conclude that our systems biology model accurately represents CKD-MBD disease progression and can be used as a test bench for improving therapeutic interventions.

Use of a Systems Pharmacology Model Based Approach Toward Dose Optimization of Parathyroid Hormone Therapy in Hypoparathyroidism

We present an application of a quantitative systems pharmacology (QSP) model to support a regulatory decision, specifically in assessing the adequacy of the proposed dosing regimen. On January 23, 2015, the US Food and Drug Administration (FDA) approved Natpara (human parathyroid hormone (PTH)) to control hypocalcemia in patients with hypoparathyroidism. Clinical trial results indicated that although once-daily PTH reduced calcium and vitamin D dose requirement while maintaining the normocalcemia, the regimen was not adequate to control hypercalciuria. We hypothesized that the lack of control on urinary calcium excretion was due to the short half-life of PTH. The QSP model-based simulations indicated that a more frequent dosing regimen may provide better control on hypercalciuria while maintaining normocalcemia. A postmarketing trial was recommended to assess pharmacokinetics (PKs) and pharmacodynamics (PDs) of PTH dose and dosing regimen. Although other modeling approaches may be feasible, in this specific case, QSP model-based simulations fulfilled the information gap to support recommendations of this postmarketing trial.

Coupling between phosphate and calcium homeostasis: a mathematical model

We developed a mathematical model of calcium (Ca) and phosphate (PO₄) homeostasis in the rat to elucidate the hormonal mechanisms that underlie the regulation of Ca and PO₄ balance. The model represents the exchanges of Ca and PO₄ between the intestine, plasma, kidneys, bone, and the intracellular compartment, and the formation of Ca-PO₄-fetuin-A complexes. It accounts for the regulation of these fluxes by parathyroid hormone (PTH), vitamin D₃, fibroblast growth factor 23, and Ca²⁺-sensing receptors. Our results suggest that the Ca and PO₄ homeostatic systems are robust enough to handle small perturbations in the production rate of either PTH or vitamin D₃ The model predicts that large perturbations in PTH or vitamin D₃ synthesis have a greater impact on the plasma concentration of Ca²⁺ ([Ca²⁺]_p) than on that of PO₄ ([PO₄]_p); due to negative feedback loops, [PO₄]_p does not consistently increase when the production rate of PTH or vitamin D₃ is decreased. Our results also suggest that, following a large PO₄ infusion, the rapidly exchangeable pool in bone acts as a fast, transient storage PO₄ compartment (on the order of minutes), whereas the intracellular pool is able to store greater amounts of PO₄ over several hours. Moreover, a large PO₄ infusion rapidly lowers [Ca²⁺]_p owing to the formation of CaPO₄ complexes. A large Ca infusion, however, has a small impact on [PO₄]_p, since a significant fraction of Ca binds to albumin. This mathematical model is the first to include all major regulatory factors of Ca and PO₄ homeostasis.

Transient modulation of calcium and parathyroid hormone stimulates bone formation

Intermittent administration of parathyroid hormone can stimulate bone formation. Parathyroid hormone is a natural hormone that responds to serum calcium levels. In this study, we examined whether a transient increase and/or decrease in the serum calcium can stimulate bone formation. Using a mathematical model previously developed, we first predicted the effects of administration of parathyroid hormone, neutralizing parathyroid hormone antibody, calcium, and EGTA (calcium chelator) on the serum concentration of parathyroid hormone and calcium. The model predicted that intermittent injection of parathyroid hormone and ethylene glycol tetraacetic acid transiently elevated the serum parathyroid hormone, while that of parathyroid hormone antibody and calcium transiently reduced parathyroid hormone in the serum. In vitro analysis revealed that parathyroid hormone's transient changes (both up and down) elevated activating transcription factor 4-mediated osteocalcin expression. In the mouse model of osteoporosis, both intermittent administration of calcium and ethylene glycol tetraacetic acid showed tendency to increase bone mineral density of the upper limb (ulna and humerus) and spine, but the effects varied in a region-specific manner. Collectively, the study herein supports a common bone response to administration of calcium and its chelator through their effects on parathyroid hormone.

Novel calcium infusion regimen after parathyroidectomy for renal hyperparathyroidism

Aim

Calcium infusion is used after parathyroid surgery for renal hyperparathyroidism to treat postoperative hypocalcaemia. We compared a new infusion regimen to one commonly used in Malaysia based on 2003 K/DOQI guidelines.

Methods

Retrospective data on serum calcium and infusion rates was collected from 2011–2015. The relationship between peak calcium efflux (PER) and time was determined using a scatterplot and linear regression. A comparison between regimens was made based on treatment efficacy (hypocalcaemia duration, total infusion amount and time) and calcium excursions (outside target range, peak and trough calcium) using bar charts and an unpaired t‐test.

Results

Fifty‐one and 34 patients on the original and new regimens respectively were included. Mean PER was lower (2.16 vs 2.56 mmol/h; P = 0.03) and occurred earlier (17.6 vs 23.2 h; P = 0.13) for the new regimen. Both scatterplot and regression showed a large correlation between PER and time (R‐square 0.64, SE 1.53, P < 0.001). The new regimen had shorter period of hypocalcaemia (28.9 vs 66.4 h, P = 0.04), and required less calcium infusion (67.7 vs 127.2 mmol, P = 0.02) for a shorter duration (57.3 vs 102.9 h, P = 0.001). Calcium excursions, peak and trough calcium were not significantly different between regimens. Early postoperative high excursions occurred when the infusion was started in spite of elevated peri‐operative calcium levels.

Conclusion

The new infusion regimen was superior to the original in that it required a shorter treatment period and resulted in less hypocalcaemia. We found that early aggressive calcium replacement is unnecessary and raises the risk of rebound hypercalcemia.

The management of hypocalcaemia after parathyroidectomy in renal patients can be difficult and runs a high risk of dangerous hypocalcaemia. This article explores a new calcium infusion protocol in this setting with encouraging results.

The efficacy of cinacalcet combined with conventional therapy on bone and mineral metabolism in dialysis patients with secondary hyperparathyroidism: a meta-analysis

Cinacalcet, the first calcimimetic to be approved for the treatment of secondary hyperparathyroidism (SHPT) in the chronic kidney disease patients, offers a novel therapeutic approach to SHPT. The aim of this meta-analysis is to access the efficacy and safety of cinacalcet on bone and mineral metabolism disorders in the dialysis patients with SHPT. Randomized controlled trials on cinacalcet combined with vitamin D and/or phosphate binders in the dialysis patients with SHPT were identified in Pubmed, Sciencedirect, and the Cochrane library. Data were analyzed with RevMan software. We compared the proportion of patients achieving the biochemical targets recommended by the Kidney Disease Outcomes Quality Initiative (KDOQI) guidelines and the incidence of adverse events between the cinacalcet and control groups. Six trials involving 2,548 patients were included. A greater proportion of patients in the cinacalcet group compared with the conventional group achieved the KDOQI targets. The relative risks (RRs) were parathyroid hormone (PTH) (RR = 3.51, 95 % CI: 2.38-5.17), calcium (RR = 2.04, 95 % CI: 1.76-2.37), phosphorus (RR = 1.15, 95 % CI: 0.83-1.60), and calcium-phosphorus product (Ca × P) (RR = 1.41, 95 % CI: 1.18-1.69), the number of patients simultaneously achieving the KDOQI targets for PTH + Ca × P was also greater (RR = 3.89, 95 % CI: 2.36-6.41), with p < 0.001 for each. The most common adverse events were nausea, vomiting, diarrhea, and hypocalcemia, which had a higher incidence in the cinacalcet group, but were usually mild to moderate in severity and transient. Compared with conventional therapy, treatment with cinacalcet results in more patients achieving KDOQI targets and offers an effective and safety therapeutic option for controlling mineral and bone disorders in the dialysis patients with SHPT.

Evaluation of the 'putative' role of intraoperative intact parathyroid hormone assay during parathyroidectomy for secondary hyperparathyroidism. A retrospective study on 35 consecutive patients: intraoperative iPTH assay during parathyroidectomy

In the surgical treatment of secondary hyperparathyroidism (2HPT) of chronic kidney disease (CKD), a parathyroidectomy (PTx) of 4 glands can only be presumed as 'total', and indications for autoimplantation are complex. Intraoperative rapid parathyroid hormone assay could be useful to predict a radical resection. We evaluated iPTH levels 20 min and 24 h after a 4-gland PTx in 35 patients to determine the predictive value of intraoperative iPTH assay. We analysed retrospectively 35 patients affected by 2HPT of CKD, 13 undergoing total parathyroidectomy (TP) and 22 TP + autoimplantation (TPai), after removing 4 glands in 33 cases and 5 glands in 2. Intact PTH assays were acquired after 40 min before induction of anaesthesia, after removing both ipselateral glands, at 20 min after surgery and on postoperative day 1. 20 min after 4-gland PTx, a decrease of iPTH levels >80 % of the preoperative value was observed in 27 of 35 cases (77.1 %) and <80 % in 8 of 35 cases (22.8 %). In 6 of these 8 patients, iPTH levels were within the normal range 24 h after surgery. Although the intraoperative iPTH assays are of interest in the treatment of 2HPT, the predictive value of this method is not entirely satisfactory. In fact, a 4-gland PTx ensures euparathyroidism in most cases, even when intraoperative iPTH assays are not trustworthy; however, intraoperative iPTH assay, although not a perfect 'tool', is a proved aid for the surgeon in making his decision.