Modelling Optimization and Control of Biomedical Systems

Table of Contents

Cover

Title Page

List of Contributors

Preface

Part I

1 Framework and Tools: A Framework for Modelling, Optimization and Control of Biomedical Systems

1.1 Mathematical Modelling of Drug Delivery Systems

1.2 Model analysis, Parameter Estimation and Approximation

1.3 Optimization and Control

References

2 Draft Computational Tools and Methods

2.1 Introduction

2.2 Sensitivity Analysis and Model Reduction

2.3 Multiparametric Programming and Model Predictive Control

2.4 Estimation Techniques

2.5 Explicit Hybrid Control

References

3 Volatile Anaesthesia

3.1 Introduction

3.2 Physiologically Based Patient Model

3.3 Model Analysis

3.4 Control Design for Volatile Anaesthesia

Conclusions

Appendix

References

4 Intravenous Anaesthesia

4.1 A Multiparametric Model‐based Approach to Intravenous Anaesthesia

4.2 Simultaneous Estimation and Advanced Control

4.3 Hybrid Model Predictive Control Strategies

4.4 Conclusions

References

Part II

5 Part A: Type 1 Diabetes Mellitus: Modelling, Model Analysis and Optimization

5.a Type 1 Diabetes Mellitus: Modelling, Model Analysis and Optimization

Part B: Type 1 Diabetes Mellitus: Glucose Regulation

5.b Type 1 Diabetes Mellitus: Glucose Regulation

Appendix 5.1

Appendix 5.2

Appendix 5.3

References

Part III

6 An Integrated Platform for the Study of Leukaemia

6.1 Towards a Personalised Treatment for Leukaemia: From in vivo to in vitro and in silico

6.2 In vitro Block of the Integrated Platform for the Study of Leukaemia

6.3 In silico Block of the Integrated Platform for the Study of Leukaemia

6.4 Bridging the Gap Between in vitro and in silico

References

7 In vitro Studies: Acute Myeloid Leukaemia

7.1 Description of Biomedical System

7.2 Experimental Part

7.3 Cellular Biomarkers for Monitoring Leukaemia in vitro

7.4 From in vitro to in silico

References

8 In silico Acute Myeloid Leukaemia

8.1 Introduction

8.2 Chemotherapy Treatment as a Process Systems Application

8.3 Analysis of a Patient Case Study

8.4 Conclusions

Appendix 8A Mathematical Model

Appendix 8B Patient Data

References

Index

End User License Agreement

List of Tables

Chapter 01

Table 1.1 The most common types of empirical pharmacodynamic models.

Chapter 02

Table 2.1 Classification of the main order reduction techniques

Table 2.2 Summary of the literature on model order reduction for mp‐MPC applications.

Table 2.3 mp‐QP algorithm.

Table 2.4 Literature review on continuous parametric programming techniques for static problems.

Table 2.5 Literature review on mixed‐integer parametric programming techniques for static problems.

Table 2.6 Literature review on parametric programming/sensitivity analysis in dynamic optimization.

Table 2.7 Relevant methods for designing robust model‐based controllers.

Chapter 03

Table 3.1 Calculation of patient‐specific tissue mass.

Table 3.2 Range and default values for PK and PD parameters and variables (partition coefficients at 37 °C for isoflurane).

Table 3.3 Summary of the cases for sensitivity analysis.

Table 3.4 Sobol’s sensitivity indices using GUI‐HDMR for Cases 1–4 given in Table 3.3 after 3.5 min and 20 min.

Table 3.5 Percentage of change of CE and BIS after 5, 20 and 60 min, compared to the output with default PK and PD variables and parameters.

Table 3.6 Correlation matrix C of C50, γ, ke0 and VL for the parameter estimation problem PKu and PKu; PKu above diagonal and PKl below diagonal.

Table 3.7 Correlation matrix of the PD parameters, entries for PKu above diagonal and PKl below diagonal, and estimated PD parameters for PKl and PKu.

Table 3.8 Patients’ characteristics, calculated values of the lung volume and cardiac output and estimated PD parameters.

Table 3A.1 Denotation of variables and parameters of the PBPK/PD model.

Table 3A.2 Denotation of subscripts in the PBPK/PD model.

Chapter 04

Table 4.1 Comparison of GMDH and HDMR at t = 14.

Table 4.2 Biometric values of the virtual patients.

Table 4.3 Hybrid model for intravenous anaesthesia.

Chapter 05-1

Table 5.a.1 Mathematical models of glucose–insulin system.

Table 5.a.2 Variables of glucose metabolism model.

Table 5.a.3 Variable subscript denotation.

Table 5.a.4 Ratio of cardiac output at rest.

Table 5.a.5 Ratio of glucose uptake.

Table 5.a.6 Ratio of capillary volume.

Table 5.a.7 Density of muscles and adipose tissue.

Table 5.a.8 Model equations of three proposed insulin kinetics models and a reference model; schematic representation of the models.

Table 5.a.9 Variable and parameter definition of Models 1, 2 and 3.

Table 5.a.10 Goodness of fit of proposed models and model selection.

Table 5.a.11 Optimal mean parameter estimates and standard deviations reported in parentheses.

Table 5.a.12 Parameter estimation results.

Table 5.a.13 Model parameters’ default values and range, and SIs for all parameters and for those related to intra‐patient variability calculated with the GUI‐HDMR toolbox.

Table 5.a.14 Optimal parameter estimates, presented as mean (lower‐upper) value for the 10 patients.

Table 5.a.15 Area under the curve (outside the normal range).

Chapter 05-2

Table 5.b.1 Selected clinical studies that evaluate MPC as a control strategy to regulate BG concentration in T1DM.

Table 5.b.2 Estimated parameters of linearized model for 10 adults.

Table 5.b.3 Meal disturbance types.

Table 5.b.4 Control designs.

Table 5.b.5 Prediction horizon for the 10 patients.

Table 5.b.6 Inequality constraints.

Table 5.b.7 Specifications of MPC 2 and the Kalman filter.

Table 5.b.8 CD3 (predefined meal plan).

Table 5.b.9 CD4 (unmeasured).

Chapter 07

Table 7.1 The phases of the cell cycle.

Table 7.2 Stress biomarkers for normal and abnormal HSCs.

Chapter 08

Table 8.1 PK models of cancer drugs.

Table 8.2 Formulas of PD models.

Table 8.3 Brief guide to model equations.

Table 8.4 Chemotherapy process optimisation algorithm.

Table 8.5 PK, PD and cell cycle parameters and inter‐individual ranges used for model sensitivity analysis and sensitivity index results.

Table 8.6 Cell cycle times fitted for the clinical data of 6 patients under LD and DA protocol (Appendix 8B).

Table 8.7 Leukaemic population of patient P016 based on simulation model results.

Table 8.8 Optimal schedule of the first chemotherapy cycle for Patient P016.

Table 8.9 Optimal LDAC induction treatment protocol for Patient P016.

Table 8.10 Leukaemic and normal cell populations for P016, over the simulation and optimisation induction treatment protocols.

List of Illustrations

Chapter 01

Figure 1.1 Mathematical representation of a drug delivery system.

Figure 1.2 Schematic of a two‐compartment pharmacokinetic model.

Figure 1.3 Schematic of a physiological pharmacokinetic model.

Figure 1.4 Illustration of a pharmacodynamic dose–response curve.

Figure 1.5 Framework towards optimal drug delivery systems.

Chapter 02

Figure 2.1 A framework for explicit/multiparametric model predictive control and moving horizon estimation.

Figure 2.2 Schematic representation of the MOR approximation procedure.

Figure 2.3 Concept of MHE.

Figure 2.4 A schematic representation of a binary search tree used in branch‐and‐bound methods for the solution of certain mp‐MIP problems.

Figure 2.5 A schematic representation of the comparison procedure employed in Acevedo and Pistikopoulos (1997). According to Equation (3.10), in case (a), ; in case (b), ; and in case (c), CRint is split into CR1 and CR2.

Figure 2.6 A schematic representation of different scenarios for a comparison procedure of objective functions featuring bilinear and/or quadratic terms, an issue considered in Axehill et al. (2011, 2014) and Oberdieck et al. (2014).

Figure 2.7 A schematic representation of two comparison procedures presented for the solution of mp‐MIQP problems: in case (a), McCormick relaxations (McCormick 1976) are used to divide CRint into three regions, one of which contains an envelope of solutions (grey area) (Oberdieck et al. 2014), while in case (b) the entire CRint is regarded as an envelope of solution (grey area) (Axehill et al. 2011, 2014).

Figure 2.8 The general framework for the solution of mp‐MIQP problems.

Figure 2.9 The three classifications of overlap between CRk and PPj.

Figure 2.10 A schematic representation for the exact comparison procedure for the solution of mp‐MIQP problems. In part (a), the quadratic boundary resulting from the exact use of Δz(θ) is combined with CRint to form a quadratically constrained critical region CR (part (b)). For this region, a polyhedral outer approximation is calculated such that (part [c]). In part (d), the corresponding mp‐QP problem is solved in , resulting in a partition of the parameter space. Each of these critical regions, CR¹ ‐ ³, is compared against the current upper bound, thus resulting in a new set of Δz(θ) (part [e]). Lastly, in part (f), the original quadratic constraints from CR are reintroduced, thus closing the loop.

Chapter 03

Figure 3.1 Structure of the physiologically based patient model. (a) Patient body; (b) fluxes in the lungs.

Figure 3.2 Structure of one tissue compartment.

Figure 3.3 BIS for PK (left) and PD (right) variability in Table 3.2. The solid line marks the BIS for the model adjusted to patient 1. The grey dots mark the measured BIS.

Figure 3.4 Time‐varying sensitivity indices (SI) for Cases 1–4. The three bottom plots denote a zoomed‐in scope for Case 1, Case 2 and Case 4.

Figure 3.5 BIS output for estimated PD parameters in Table 3.7 capturing PK variability

Figure 3.6 Inspired and expired isoflurane concentrations and BIS for patient characteristics and parameters given in Table 3.8.

Figure 3.7 Closed‐loop control design for volatile anaesthesia.

Figure 3.8 Control design for algebraic Hill equation.

Figure 3.9 Control design for linearized Hill equation.

Figure 3.10 Linearized Hill equation at BIS = 50. The dot marks the linearization point.

Figure 3.11 Piecewise linearization of the Hill equation. The dots mark the intersection of the linearization functions and the switching points of the controllers, respectively.

Figure 3.12 Closed‐loop control design for on‐line parameter estimation of C50.

Figure 3.13 Decision process of the on‐line parameter estimation bloc.

Figure 3.14 Estimated of for Patient 3.

Figure 3.15 Control input for Patient 3 of CD1 and .

Figure 3.16 and actual Ce for Patient 3 of CD1 and .

Figure 3.17 BISR and actual BIS for Patient 3 of CD1 and .

Figure 3.18 Control input for Patients 1–3 of .

Figure 3.19 and actual Ce for Patients 1–3 of .

Figure 3.20 BISR and actual BIS for Patients 1–3 of .

Figure 3.21 Estimated of CD for Patients 1–3.

Figure 3.22 Framework presented in this thesis for volatile anaesthesia.

Chapter 04

Figure 4.1 Compartmental model of the patient. PK = the pharmacokinetic model; PD = the pharmacodynamic model.

Figure 4.2 Schematic representation of the nonlinear SISO patient model for intravenous anaesthesia.

Figure 4.3 Evolution of the first‐order sensitivity indices.

Figure 4.4 Comparison GMDH‐HDMR for small data samples (N = 40), t = 14.

Figure 4.5 Controller design using local linearization.

Figure 4.6 Controller scheme using local linearization.

Figure 4.7 Controller scheme using exact linearization.

Figure 4.8 Controller scheme using exact linearization.

Figure 4.9 Control scheme development flowchart.

Figure 4.10 Case 1: EPSAC control scheme.

Figure 4.11 Case 2:mp‐MPC without nonlinearity compensation – control scheme.

Figure 4.12 Case 3:mp‐MPC with nonlinearity compensation – control scheme.

Figure 4.13 Case 4: mp‐MPC with nonlinearity compensation and estimator – control scheme.

Figure 4.14 BIS output for all 13 patients for Case 1.

Figure 4.15 Map of critical regions, Case 2.

Figure 4.16 BIS output for all 13 patients for Case 2.

Figure 4.17 Map of critical regions, Case 3 and Case 4.

Figure 4.18 BIS output for all 13 patients for Case 3.

Figure 4.19 BIS output for all 13 patients for Case 4.

Figure 4.20 BIS response for the four controllers for PaN.

Figure 4.21 Output for the four controllers for PaN.

Figure 4.22 BIS response for the four controllers for patient 9.

Figure 4.23 Output for the four controllers for patient 9.

Figure 4.24 The artificially generated disturbance signal.

Figure 4.25 BIS response for the four controllers for PaN with disturbance.

Figure 4.26 Output for the four controllers for PaN with disturbance.

Figure 4.27 BIS response for the four controllers for patient 9 with disturbance.

Figure 4.28 Output for the four controllers for patient 9 with disturbance.

Figure 4.29 Schematic of simultaneous mp‐MHE and mp‐MPC for intravenous anaesthesia.

Figure 4.30 Map of critical regions – mp‐MPC.

Figure 4.31 BIS response for all 13 patients in the induction phase – nominal mp‐MPC.

Figure 4.32 Propofol infusion rate for all 13 patients in the induction phase – nominal mp‐MPC.

Figure 4.33 BIS response for all 13 patients in the induction phase – simultaneous mp‐MPC and Kalman filter.

Figure 4.34 Propofol infusion rate for all 13 patients in the induction phase – simultaneous mp‐MPC and Kalman filter.

Figure 4.35 BIS response for all 13 patients in the induction phase – simultaneous mp‐MPC and mp‐MHE.

Figure 4.36 Propofol infusion rate for all 13 patients in the induction phase – simultaneous mp‐MHE and mp‐MPC.

Figure 4.37 BIS response of the three controllers for patient 9 in the induction phase without noise.

Figure 4.38 BIS response of the three controllers for patient 9 in the induction phase without noise – zoomed in.

Figure 4.39 Propofol infusion rate of the three controllers for patient 9 in the induction phase without noise.

Figure 4.40 BIS response of the three controllers for patient 9 in the maintenance phase without noise.

Figure 4.41 Propofol infusion rate of the three controllers for patient 9 in the maintenance phase without noise.

Figure 4.42 BIS response of the three controllers for patient 9 in the maintenance phase – the B–C–D–E interval – without noise.

Figure 4.43 Propofol infusion rate of the three controllers for patient 9 in the maintenance phase – the B–C–D–E interval – without noise.

Figure 4.44 The original Hill curve and a piecewise linearized version. The red dots denote the points around which the linearization was performed, while the purple arrows show the switching points λ1 and λ2, respectively.

Figure 4.45 Map of critical regions – mp‐hMPC.

Figure 4.46 Robust hybrid mp‐MPC control scheme.

Figure 4.47 BIS output for all 13 patients without offset correction – induction phase.

Figure 4.48 Drug infusion for all 13 patients without offset correction – induction phase.

Figure 4.49 BIS output for all 13 patients without offset correction – maintenance phase.

Figure 4.50 Drug infusion for all 13 patients without offset correction – maintenance phase.

Figure 4.51 BIS output for all 13 patients – strategy 2 – induction phase.

Figure 4.52 Drug infusion for all 13 patients – strategy 2 – induction phase.

Figure 4.53 BIS output for all 13 patients – strategy 2 – maintenance phase.

Figure 4.54 Drug infusion for all 13 patients – strategy 2 – maintenance phase.

Chapter 05-1

Figure 5.a.1 Incidence of type 1 diabetes mellitus (T1DM) worldwide.

Figure 5.a.2 The framework of an automated insulin delivery system.

Figure 5.a.3 Structure of the physiologically based compartmental model of glucose metabolism in T1DM.

Figure 5.a.4 Detailed glucose uptake in the periphery.

Figure 5.a.5 Comparison of Models 1, 2 and 3 and a reference model with experimental data.

Figure 5.a.6 Effect of subcutaneous insulin injection on endogenous glucose production.

Figure 5.a.7 Time‐varying SIs when all parameters are considered.

Figure 5.a.8 Time‐varying SIs when intra‐patient variability‐related parameters are considered.

Figure 5.a.9 Comparison of blood glucose concentration (mg/dL) as predicted from the proposed model with the Simulator, for the 10 adults when a meal plan of 45 g, 70 g and 70 g of carbs are considered at 420 min, 720 min and 1080 min, respectively. The insulin infusion (U) is shown at the right axis for every patient.

Figure 5.a.10 Delayed insulin effect.

Figure 5.a.11 Patient‐dependent time delay.

Figure 5.a.12 Time delay dependent on patient and bolus.

Figure 5.a.13 Optimization (grey line) and simulation (black line) glucose profiles.

Figure 5.a.14 Optimal glucose profiles when insulin is given as a bolus and as a piecewise constant infusion.

Chapter 05-2

Figure 5.b.1 Model‐based control structure.

Figure 5.b.2 Framework for MPC controller design.

Figure 5.b.3 Comparison of full‐state and reduced linearized model for patient 2.

Figure 5.b.4 Comparison of original model and linearized model when 50 g of carbs are consumed and a 5 U bolus is given to patient 2.

Figure 5.b.5 Basic scheme of discrete MPC.

Figure 5.b.6 Proposed control strategy to compensate for unknown meal disturbances consisting of two controllers: the reference control that regulates glucose for a reference meal plan, and the correction control that regulates the difference of the glucose between a real and reference meal plan.

Figure 5.b.7 MPC control for 10 adults of UVa/Padova Simulator for predefined (CD1) and announced meal disturbances (CD2). Upper graphs: blood glucose concentration (mg/dL) profiles; lower graphs: control action, insulin (U/min).

Figure 5.b.8 Comparison of glucose regulation with control designs 3 and 4 for adult 6. The meals are given at 420, 720 and 1080 min and contain 75, 100 and 90 g of carbohydrates, respectively.

Figure 5.b.9 Evaluation of CD3 when a meal of 50 g is given 30 min in advance, 30 min after and simultaneous with the reference meal of 30 g.

Figure 5.b.10 Multiparametric MPC.

Figure 5.b.11 Comparison of the original and state‐space model.

Figure 5.b.12 Critical regions for mp‐MPC.

Figure 5.b.13 Closed‐loop control performance.

Chapter 06

Figure 6.1 Towards optimisation/personalisation of chemotherapy for leukaemia treatment.

Figure 6.2 (a): Geometry of the 3D scaffolds; (b–c) scanning electron microscopy (SEM) images of the highly porous 3D scaffolds, including seeded leukaemic cells.

Figure 6.3 Mathematical optimisation of chemotherapy treatment for AML.

Chapter 07

Figure 7.1 The human haematopoietic system.

Figure 7.2 The cell cycle.

Figure 7.3 Cyclin expression throughout the cell cycle.

Figure 7.4 K‐562 growth (a,b) the 2D and (c,d) the 3D systems, at different oxygen levels: (a,c) 20% O2, and (b,d) 5% O2. Different colours represent different glucose levels: ( ) [CTR], ( ) [HIGH] and ( ) [LOW].

Figure 7.5 Evolution of glutamate [Glu] for all the environmental conditions under study. Different colours represent the two different culturing systems: ( ) 2D cultures and ( ) 3D scaffolds.

Figure 7.6 Evolution of lactate [Lac] for all the environmental conditions under study. Different colours represent the two different culturing systems: ( ) 2D cultures and ( ) 3D scaffolds.

Chapter 08

Figure 8.1 Schematic diagram of PK and PD: blue boxes are for the PK model, and they are connected to the red cycle that represents the PD part of drug action.

Figure 8.2 The process of drug delivery. Drug delivery is governed by four mechanisms: absorption, distribution, metabolism and excretion. Each of these mechanisms is deprived of further mechanisms. Inter‐ and intra‐patient variability in these mechanisms is the probable source of PK variability.

Figure 8.3 Framework for the derivation of an optimal personalised chemotherapy protocol.

Figure 8.4 Patient P016 behaviour over the first chemotherapy cycle (days 1–11) and the recovery period prior to the second chemotherapy cycle (days 11–67). The dashed line is for the leukaemic cell population over the optimised protocol; the straight black line is for the leukaemic cell over the simulation of the clinical applied protocol; the cycle signs are for the normal population at the start and end dates of the optimisation protocol; the x signs are for the normal population at the start and end dates of the simulation protocol; and the grey line represents BM hypoplasia objective.

Figure 8.5 Patient P016 behaviour over the second chemotherapy cycle (days 67–77) and the recovery period prior to the BM aspirate at treatment completion (days 77–100). The dashed line is for the leukaemic cell population over the optimised protocol; the straight black line is for the leukaemic cell over the simulation of the clinical applied protocol; the cycle signs are for the normal population at the start and end dates of the optimisation protocol; the x signs are for the normal population at the start and end dates of the simulation protocol; and the grey line represents BM hypoplasia objective.

Modelling Optimization and Control of Biomedical Systems

Edited by

Efstratios N. Pistikopoulos

Texas A&M University, USA

Ioana Naşcu

Texas A&M University, USA

Eirini G. Velliou

Department of Chemical and Process Engineering University of Surrey, UK

This edition first published 2018

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List of Contributors

Dr. Maria Fuentes‐Gari

Process Systems Enterprise (PSE)

London

UK

Professor Michael C. Georgiadis

Laboratory of Process Systems Engineering

School of Chemical Engineering

Aristotle University of Thesaloniki

Greece

Dr. Alexandra Krieger

Jacobs Consultancy

Kreisfreie Stadt Aachen Area

Germany

Dr. Romain Lambert

Department of Chemical Engineering

Imperial College London

UK

Professor Athanasios Mantalaris

Department of Chemical Engineering

Imperial College London

UK

Dr. Ruth Misener

Department of Computing

Imperial College London

UK

Dr. Ioana Naşcu

Artie McFerrin Department of Chemical Engineering

Texas A&M University

College Station

USA

Dr. Richard Oberdieck

DONG energy A/S

Gentofte

Denmark

Dr. Nicki Panoskaltsis

Department of Medicine

Imperial College London

UK

Dr. Eleni Pefani

Clinical Pharmacology Modelling and Simulation

GSK

UK

Professor Efstratios N. Pistikopoulos

Texas A&M Energy Institute

Artie McFerrin Department of Chemical Engineering

Texas A&M University

USA

Dr. Pedro Rivotti

Department of Chemical Engineering

Imperial College London

UK

Susana Brito dos Santos

Department of Chemical Engineering

Imperial College London

UK

Dr. Eirini G. Velliou

Department of Chemical and Process Engineering

Faculty of Engineering and Physical Sciences

University of Surrey

UK

Dr. Stamatina Zavitsanou

Paulson School of Engineering & Applied Sciences

Harvard University

USA

Preface

A great challenge when dealing with severe diseases, such as cancer or diabetes, is the implementation of an appropriate treatment. Design of treatment protocols is not a trivial issue, especially since nowadays there is significant evidence that the type of treatment depends on specific characteristics of individual patients.

In silico design of high‐fidelity mathematical models, which accurately describe a specific disease in terms of a well‐defined biomedical network, will allow the optimisation of treatment through an accurate control of drug dosage and delivery. Within this context, the aim of the Modelling, Control and Optimisation of Biomedical Systems (MOBILE) project is to derive intelligent computer model‐based systems for optimisation of biomedical drug delivery systems in the cases of diabetes, anaesthesia and blood cancer (i.e., leukaemia).

From a computational point of view, the newly developed algorithms will be able to be implemented on a single chip, which is ideal for biomedical applications that were previously off‐limits for model‐based control. Simpler hardware is adequate for the reduced on‐line computational requirements, which will lead to lower costs and almost eliminate the software costs (e.g., licensed numerical solvers). Additionally, there is increased control power, since the new MPC approach can accommodate much larger – and more accurate – biomedical system models (the computational burden is shifted off‐line).

From a practical point of view, the absence of complex software makes the implementation of the controller much easier, therefore allowing its usage as a diagnostic tool directly in the clinic by doctors, clinicians as well as patients without the requirement of specialised engineers, therefore progressively enhancing the confidence of medical teams and patients to use computer‐aided practices. Additionally, the designed biomedical controllers increase treatment safety and efficiency, by carefully applying a what‐if prior analysis that is tailored to the individual patient’s needs and characteristics, therefore reducing treatment side effects and optimising the drug infusion rates. Flexibility of the device to adapt to changing patient characteristics and incorporation of the physician’s performance criteria are additional great advantages.

There were several highly significant achievements of the project for all different diseases and biomedical cases under study (i.e., diabetes, leukaemia and anaesthesia). From a computational point of view, achievements include the construction of high‐fidelity mathematical models as well as novel algorithm derivations. The methodology followed for the model design includes the following steps: (a) the derivation of a high‐fidelity model, (b) the conduction of sensitivity analysis, (c) the application of parameter estimation techniques on the derived model in order to identify and estimate the sensitive model parameters and variables and (d) the conduction of extensive validation studies based on patient and clinical data. The validated model is then reduced to an approximate model suitable for optimisation and control via model reduction and/or system identification algorithms. The several theoretical (in silico) components are incorporated in a closed‐loop (in silico–in vitro) framework that will be evaluated with in vitro trials (i.e., through experimental evaluation of the control‐based optimised drug delivery). The outcome of the experiments will indicate the validity of the suggested closed‐loop delivery of anaesthetics, chemotherapy dosages for leukaemia and insulin delivery doses in diabetes. It should be mentioned that this is the first closed‐loop system including computational and experimental elements. The output of such a framework could be introduced, at a second