9 Mathematical modelling of hollow-fiber haemodialysis modules
-
Nunzio Cancilla
,
Luigi Gurreri
Abstract
This chapter provides an overview of the principles and modelling of membrane-based modules for haemodialysis, the most common renal replacement therapy. Following an introduction on the structure, function and diseases of the kidney, the technological evolution of membranes for blood purification is outlined and the main transport mechanisms involved are described, making a distinction between pure haemodialysis, haemodiafiltration and haemofiltration. The main performance figures of a hollow-fiber module are introduced and their dependence on the parameters that characterize the device is illustrated. A multi-scale modelling approach is then presented, in which preliminary single-fiber CFD simulations are used to derive the hydraulic permeability of a fiber bundle and the relevant mass transfer coefficients as functions of the local velocities. The predicted correlations are then fed to a module-scale model, in which blood and dialysate compartments are simulated as interpenetrated porous media while appropriate source terms account for the exchange of solutes and water between the two fluids. The model predictions are three-dimensional flow and concentration distributions, from which, in particular, performance figures such as clearance and ultrafiltration flow rate can be extracted as functions of the module geometrical and physical characteristics. Validation tests are also presented and the results of a parametrical sensitivity assessment are discussed.
Abstract
This chapter provides an overview of the principles and modelling of membrane-based modules for haemodialysis, the most common renal replacement therapy. Following an introduction on the structure, function and diseases of the kidney, the technological evolution of membranes for blood purification is outlined and the main transport mechanisms involved are described, making a distinction between pure haemodialysis, haemodiafiltration and haemofiltration. The main performance figures of a hollow-fiber module are introduced and their dependence on the parameters that characterize the device is illustrated. A multi-scale modelling approach is then presented, in which preliminary single-fiber CFD simulations are used to derive the hydraulic permeability of a fiber bundle and the relevant mass transfer coefficients as functions of the local velocities. The predicted correlations are then fed to a module-scale model, in which blood and dialysate compartments are simulated as interpenetrated porous media while appropriate source terms account for the exchange of solutes and water between the two fluids. The model predictions are three-dimensional flow and concentration distributions, from which, in particular, performance figures such as clearance and ultrafiltration flow rate can be extracted as functions of the module geometrical and physical characteristics. Validation tests are also presented and the results of a parametrical sensitivity assessment are discussed.
Chapters in this book
- Preface V
- List of contributing authors
-
Part I Chemical engineering and medicine
- 1 A systems engineering approach to medicine 3
-
Part II Modelling physiology
- 2 Computational modelling in liver system and liver disease 21
- 3 Inhaled aerosols as carriers of pulmonary medicines and the limitations of in vitro–in vivo correlation (IVIVC) methods 49
- 4 Modelling drug permeation across the skin: a chemical engineering perspective 73
- 5 Chemical engineering contribution to hemodialysis innovation: achieving the wearable artificial kidneys with nanomaterial-based dialysate regeneration 103
-
Part III Disease and treatment
- 6 Precision medicine in hypothyroidism: an engineering approach to individualized levothyroxine dosing 127
- 7 Glucose sensors in medicine: overview 167
- 8 Macroscopic transport models for drugs and vehicles in cancer tissues 185
- 9 Mathematical modelling of hollow-fiber haemodialysis modules 203
- 10 Chemical engineering methods in better understanding of blood hydrodynamics in atherosclerosis disease 243
- 11 On the development of pharmacokinetic models for the characterisation and diagnosis of von Willebrand disease 263
-
Part IV Pharmacokinetics and drug delivery
- 12 An introduction to quantitative systems pharmacology for chemical engineers 293
- 13 A novel strategy for brain cancer treatment through a multiple emulsion system for simultaneous therapeutics delivery 315
- 14 Model-based dose selection for gene therapy for haemophilia B 333
- 15 Lipid-based nanoparticles for nucleic acids delivery 359
- Index
Chapters in this book
- Preface V
- List of contributing authors
-
Part I Chemical engineering and medicine
- 1 A systems engineering approach to medicine 3
-
Part II Modelling physiology
- 2 Computational modelling in liver system and liver disease 21
- 3 Inhaled aerosols as carriers of pulmonary medicines and the limitations of in vitro–in vivo correlation (IVIVC) methods 49
- 4 Modelling drug permeation across the skin: a chemical engineering perspective 73
- 5 Chemical engineering contribution to hemodialysis innovation: achieving the wearable artificial kidneys with nanomaterial-based dialysate regeneration 103
-
Part III Disease and treatment
- 6 Precision medicine in hypothyroidism: an engineering approach to individualized levothyroxine dosing 127
- 7 Glucose sensors in medicine: overview 167
- 8 Macroscopic transport models for drugs and vehicles in cancer tissues 185
- 9 Mathematical modelling of hollow-fiber haemodialysis modules 203
- 10 Chemical engineering methods in better understanding of blood hydrodynamics in atherosclerosis disease 243
- 11 On the development of pharmacokinetic models for the characterisation and diagnosis of von Willebrand disease 263
-
Part IV Pharmacokinetics and drug delivery
- 12 An introduction to quantitative systems pharmacology for chemical engineers 293
- 13 A novel strategy for brain cancer treatment through a multiple emulsion system for simultaneous therapeutics delivery 315
- 14 Model-based dose selection for gene therapy for haemophilia B 333
- 15 Lipid-based nanoparticles for nucleic acids delivery 359
- Index
