Phosphate transport in organs

For more info about our services contact : help@bestpfe.com

Table of contents

1 Introduction 
1.1 General introduction on calcium homeostasis
1.1.1 Overview of calcium homeostasis
1.1.2 Transport mechanisms in organs involved in calcium homeostasis
Bone
The intestine
The kidney
1.1.3 Regulation of calcium homeostasis
Parathyroid hormone
The calcium sensing receptor (CaSR)
Vitamin D
Calcitonin
1.2 Overview of phosphate homeostasis
1.2.1 Phosphate distribution in the organism
1.2.2 Phosphate transport in organs
Intestinal absorption of phosphate
Renal phosphate handling
1.2.3 Hormonal control of phosphate homeostasis
FGF23, a regulator of phosphate homeostasis
Phosphate, a regulator of PTH and vitamin D
1.2.4 Precipitation of calcium-phosphate
Acid base equilibria between phosphate components
Binding of calcium and phosphate
Mechanisms of calcium-phosphate precipitation
Regulation of bone mineralization by fetuin-A
Precipitation of calcium and phosphate in the urine
1.3 Historical perspectives on Mathematical Models of Calcium Homeostasis
1.3.1 The first calcium kinetic studies
1.3.2 A global model of calcium Homeostasis
1.3.3 Dividing the bone compartment into two exchangeable pools
1.3.4 Toward more elaborate models
The model of Hurwitz
The latest models of calcium homeostasis
1.3.5 PTH modeling review
A sigmoidal relationship between PTH and calcium
The first model of PTH synthesis and secretion
A more elaborate model of PTH synthesis and secretion
An asymmetric exocytosis function for PTH secretion
A subpopulation of PT cells to model PTH dynamics
1.3.6 About Vitamin D and FGF23
Modeling the vitamin D3 synthesis pathway
Modeling the effects of FGF23
1.4 Aim of this thesis
1.4.1 Building of model of calcium homeostasis
2 Experimental measurements of some bone parameters 
2.1 Aim of these experiments
2.2 Method
2.2.1 Determination of the total calcium and phosphate bone content in mice
Kinetic study of calcium exchanges between plasma and the bone compartment
2.3 Results
2.3.1 Calcium and phosphate content in the bone
2.3.2 Kinetic part
2.4 Discussion
2.4.1 About the total pool of calcium and phosphate in bone
2.4.2 About the kinetic experiments
2.4.3 Conclusion
3 Model of calcium homeotasis, PTH synthesis and secretion, and vitamin D3 effects 
3.1 Mathematical model of PTH synthesis and secretion
3.1.1 Modeling PTH synthesis
3.1.2 PTH exocytosis from the cell
3.1.3 PTH dynamics in plasma
3.1.4 Parameters
3.1.5 Mathematical analysis of the PTH model
Non-dimensionalization
Existence and unicity
Explicit solutions
Expected values at steady state
Building of the plane phase
Simulation results
3.1.6 Possible improvements to the PTH model
3.2 Mathematical model of calcium homeostasis with PTH
3.2.1 Calcium balance in the intestine, bone, kidney and plasma.
3.2.2 Mathematical analysis of the PTH-calcium model
Non-dimensionalization of the model
Identification of steady state
Numerical stability of the steady state
3.2.3 Parameters of the PTH-calcium model
Determination of unknown parameters
Parameters of the calcium/PTH model
3.3 Mathematical model of calcium homeostasis with PTH and vitamin D3
3.3.1 Hormonal part of the model
Balance equation for vitamin D3
Effect of vitamin D3 on PTH production
3.3.2 Effect of vitamin D3 on calcium metabolism
Regulation of intestinal calcium absorption
Regulation of bone remodeling
Regulation of kidney reabsorption
3.3.3 Equations of the model
Equations of the hormonal system
Equations of calcium homeostasis regulated by PTH and D3
Parameters of the calcium homeostasis model
3.4 Summary of the mathematical properties of the model
3.5 Discussion and improvements to the model
4 A Mathematical Model of Calcium Homeostasis in the Rat 
4.1 Introduction
4.2 Mathematical Model
4.2.1 PTH synthesis and secretion
4.2.2 Vitamin D3
4.2.3 Calcium exchanges between organs
The intestinal compartment
The bone compartment
The kidney compartment
The plasma compartment
4.2.4 Determination of unknown parameters
4.2.5 Numerical methods
4.3 Results
4.3.1 Experimental Measurements
4.3.2 Model Validation
Acutely induced hypocalcemia
Acutely induced hypercalcemia
4.3.3 Model Predictions
4.4 Discussion
5 A Model of Calcium and Phosphate Homeostasis in the Rat 
5.1 Mathematical model
5.1.1 Hormone conservation equations
FGF23 dynamics
Conservation of Vitamin D3
5.1.2 Conservation equation for PTH
5.1.3 Modeling calcium-phosphate binding in plasma and bone
Formation of CaHPO4 and CaH2PO+4 salts in plasma
Regulation of bone mineralization by fetuin-A
Calcium and phosphate in the rapid bone pool
5.1.4 Equations for phosphate
Intestinal absorption of phosphate
Intracellular phosphate
Hormonal control of phosphate reabsorption in the kidney
Phosphate in the bone compartment
Phosphate binding to Na+
Phosphate in plasma
5.1.5 Determination of unknown parameters
5.1.6 Improvement to the calcium homeostasis model
Calcium binding to proteins
Conservation equation for plasma calcium
5.2 Summary of the main equations
5.3 Results
5.3.1 Model validation
Calcium and Phosphate in Primary Hyperparathyroidim
FGF23 deficiency
Intravenous injection of Phosphate
Phosphate gavage
5.3.2 Model Predictions
Primary hyperparathyroidism
Primary hypoparathyroidism
Vitamin D3 deficiency
5.4 Discussion
5.4.1 Scope of the model
5.4.2 Model limitations
5.4.3 Calcium and phosphate metabolism
5.4.4 Calcium and phosphate metabolism dysfunctions
6 Discussion and General Conclusion 
6.1 What does our model bring to the understanding of calcium homeostasis?
6.2 What is still missing?
6.3 Further extensions?