Giuseppe De Nicolao

Predictive Pharmacokinetic-Pharmacodynamic Modeling of Tumor Growth Kinetics in Xenograft Models after Administration of Anticancer Agents

The available mathematical models describing tumor growth and the effect of anticancer treatments on tumors in animals are of limited use within the drug industry. A simple and effective model would allow applying quantitative thinking to the preclinical development of oncology drugs. In this article, a minimal pharmacokinetic-pharmacodynamic model is presented, based on a system of ordinary differential equations that link the dosing regimen of a compound to the tumor growth in animal models. The growth of tumors in nontreated animals is described by an exponential growth followed by a linear growth. In treated animals, the tumor growth rate is decreased by a factor proportional to both drug concentration and number of proliferating tumor cells. A transit compartmental system is used to model the process of cell death, which occurs at later times. The parameters of the pharmacodynamic model are related to the growth characteristics of the tumor, to the drug potency, and to the kinetics of the tumor cell death. Therefore, such parameters can be used for ranking compounds based on their potency and for evaluating potential differences in the tumor cell death process. The model was extensively tested on discovery candidates and known anticancer drugs. It fitted well the experimental data, providing reliable parameter estimates. On the basis of the parameters estimated in a first experiment, the model successfully predicted the response of tumors exposed to drugs given at different dose levels and/or schedules. It is, thus, possible to use the model prospectively, optimizing the design of new experiments.

Model Predictive Control of Type 1 Diabetes: An in Silico Trial:

Background: The development of artificial pancreas has received a new impulse from recent technological advancements in subcutaneous continuous glucose monitoring and subcutaneous insulin pump delivery systems. However, the availability of innovative sensors and actuators, although essential, does not guarantee optimal glycemic regulation. Closed-loop control of blood glucose levels still poses technological challenges to the automatic control expert, most notable of which are the inevitable time delays between glucose sensing and insulin actuation. Methods: A new in silico model is exploited for both design and validation of a linear model predictive control (MPC) glucose control system. The starting point is a recently developed meal glucose-insulin model in health, which is modified to describe the metabolic dynamics of a person with type 1 diabetes mellitus. The population distribution of the model parameters originally obtained in healthy 204 patients is modified to describe diabetic patients. Individual models of virtual patients are extracted from this distribution. A discrete-time MPC is designed for all the virtual patients from a unique input-output-linearized approximation of the full model based on the average population values of the parameters. The in silico trial simulates 4 consecutive days, during which the patient receives breakfast, lunch, and dinner each day. Results: Provided that the regulator undergoes some individual tuning, satisfactory results are obtained even if the control design relies solely on the average patient model. Only the weight on the glucose concentration error needs to be tuned in a quite straightforward and intuitive way. The ability of the MPC to take advantage of meal announcement information is demonstrated. Imperfect knowledge of the amount of ingested glucose causes only marginal deterioration of performance. In general, MPC results in better regulation than proportional integral derivative, limiting significantly the oscillation of glucose levels. Conclusions: The proposed in silico trial shows the potential of MPC for artificial pancreas design. The main features are a capability to consider meal announcement information, delay compensation, and simplicity of tuning and implementation.

Fully Integrated Artificial Pancreas in Type 1 Diabetes: Modular Closed-Loop Glucose Control Maintains Near Normoglycemia

Integrated closed-loop control (CLC), combining continuous glucose monitoring (CGM) with insulin pump (continuous subcutaneous insulin infusion [CSII]), known as artificial pancreas, can help optimize glycemic control in diabetes. We present a fundamental modular concept for CLC design, illustrated by clinical studies involving 11 adolescents and 27 adults at the Universities of Virginia, Padova, and Montpellier. We tested two modular CLC constructs: standard control to range (sCTR), designed to augment pump plus CGM by preventing extreme glucose excursions; and enhanced control to range (eCTR), designed to truly optimize control within near normoglycemia of 3.9–10 mmol/L. The CLC system was fully integrated using automated data transfer CGM→algorithm→CSII. All studies used randomized crossover design comparing CSII versus CLC during identical 22-h hospitalizations including meals, overnight rest, and 30-min exercise. sCTR increased significantly the time in near normoglycemia from 61 to 74%, simultaneously reducing hypoglycemia 2.7-fold. eCTR improved mean blood glucose from 7.73 to 6.68 mmol/L without increasing hypoglycemia, achieved 97% in near normoglycemia and 77% in tight glycemic control, and reduced variability overnight. In conclusion, sCTR and eCTR represent sequential steps toward automated CLC, preventing extremes (sCTR) and further optimizing control (eCTR). This approach inspires compelling new concepts: modular assembly, sequential deployment, testing, and clinical acceptance of custom-built CLC systems tailored to individual patient needs.

A new kernel-based approach for linear system identification

This paper describes a new kernel-based approach for linear system identification of stable systems. We model the impulse response as the realization of a Gaussian process whose statistics, differently from previously adopted priors, include information not only on smoothness but also on BIBO-stability. The associated autocovariance defines what we call a stable spline kernel. The corresponding minimum variance estimate belongs to a reproducing kernel Hilbert space which is spectrally characterized. Compared to parametric identification techniques, the impulse response of the system is searched for within an infinite-dimensional space, dense in the space of continuous functions. Overparametrization is avoided by tuning few hyperparameters via marginal likelihood maximization. The proposed approach may prove particularly useful in the context of robust identification in order to obtain reduced order models by exploiting a two-step procedure that projects the nonparametric estimate onto the space of nominal models. The continuous-time derivation immediately extends to the discrete-time case. On several continuous- and discrete-time benchmarks taken from the literature the proposed approach compares very favorably with the existing parametric and nonparametric techniques.

Survey Kernel methods in system identification, machine learning and function estimation: A survey

Most of the currently used techniques for linear system identification are based on classical estimation paradigms coming from mathematical statistics. In particular, maximum likelihood and prediction error methods represent the mainstream approaches to identification of linear dynamic systems, with a long history of theoretical and algorithmic contributions. Parallel to this, in the machine learning community alternative techniques have been developed. Until recently, there has been little contact between these two worlds. The first aim of this survey is to make accessible to the control community the key mathematical tools and concepts as well as the computational aspects underpinning these learning techniques. In particular, we focus on kernel-based regularization and its connections with reproducing kernel Hilbert spaces and Bayesian estimation of Gaussian processes. The second aim is to demonstrate that learning techniques tailored to the specific features of dynamic systems may outperform conventional parametric approaches for identification of stable linear systems.

Multinational Study of Subcutaneous Model-Predictive Closed-Loop Control in Type 1 Diabetes Mellitus: Summary of the Results

Background: In 2008–2009, the first multinational study was completed comparing closed-loop control (artificial pancreas) to state-of-the-art open-loop therapy in adults with type 1 diabetes mellitus (T1DM). Methods: The design of the control algorithm was done entirely in silico, i.e., using computer simulation experiments with N = 300 synthetic “subjects” with T1DM instead of traditional animal trials. The clinical experiments recruited 20 adults with T1DM at the Universities of Virginia (11); Padova, Italy (6); and Montpellier, France (3). Open-loop and closed-loop admission was scheduled 3–4 weeks apart, continued for 22 h (14.5 h of which were in closed loop), and used a continuous glucose monitor and an insulin pump. The only difference between the two sessions was that insulin dosing was performed by the patient under a physicians supervision during open loop, whereas insulin dosing was performed by a control algorithm during closed loop. Results: In silico design resulted in rapid (less than 6 months compared to years of animal trials) and cost-effective system development, testing, and regulatory approvals in the United States, Italy, and France. In the clinic, compared to open-loop, closed-loop control reduced nocturnal hypoglycemia (blood glucose below 3.9 mmol/liter) from 23 to 5 episodes (p < .01) and increased the amount of time spent overnight within the target range (3.9 to 7.8 mmol/liter) from 64% to 78% (p = .03). Conclusions: In silico experiments can be used as viable alternatives to animal trials for the preclinical testing of insulin treatment strategies. Compared to open-loop treatment under identical conditions, closed-loop control improves the overnight regulation of diabetes.

Nonparametric input estimation in physiological systems: problems, methods, and case studies

Input estimation from output data is an important problem in the analysis of physiological systems, because many signals of interest are not directly accessible to measurement. When the system is time-invariant, this problem is often referred to as deconvolution. Three representative physiological problems, regarding hormone secretion, insulin dynamics, and hepatic glucose production, are used to illustrate the major challenges: ill-conditioning, confidence intervals assessment, infrequent and nonuniform sampling, nonnegativity constraints, and computational efficiency. The paper provides a critical overview of the existing techniques, focusing on regularization theory and Bayesian estimation. In order to overcome some inadequacies of the existing methods, some new results are derived. In particular, the connection between the maximum-likelihood estimate of the regularization parameter and the notion of equivalent degree of freedom is studied. Moreover, a fast SVD-based numerical algorithm is developed that includes the optimization of the regularization parameter, and the computation of confidence intervals. The proposed techniques are validated on a benchmark problem and are shown to provide effective solutions to the three physiological case studies.

The Periodic Riccati Equation

The history of the time-varying Riccati equation can be traced back to Riccati’s original manuscripts of 1715–1725. Indeed, the major concern of Count Riccati was to study the problem of the separation of variables in quadratic and time-varying scalar differential equations [1]. The equation has been the subject of several contributions in the subsequent centuries. In recent times, the importance of the Riccati equation in Control, Systems, and Signals has led to the development of a considerable research activity on the subject, see e.g., [2], [3], [4] for the time-varying matrix Riccati equation.

Prediction error identification of linear systems: A nonparametric Gaussian regression approach

A novel Bayesian paradigm for the identification of output error models has recently been proposed in which, in place of postulating finite-dimensional models of the system transfer function, the system impulse response is searched for within an infinite-dimensional space. In this paper, such a nonparametric approach is applied to the design of optimal predictors and discrete-time models based on prediction error minimization by interpreting the predictor impulse responses as realizations of Gaussian processes. The proposed scheme describes the predictor impulse responses as the convolution of an infinite-dimensional response with a low-dimensional parametric response that captures possible high-frequency dynamics. Overparameterization is avoided because the model involves only a few hyperparameters that are tuned via marginal likelihood maximization. Numerical experiments, with data generated by ARMAX and infinite-dimensional models, show the definite advantages of the new approach over standard parametric prediction error techniques and subspace methods both in terms of predictive capability on new data and accuracy in reconstruction of system impulse responses.

Evaluating the Efficacy of Closed-Loop Glucose Regulation via Control-Variability Grid Analysis

Background: Advancements in subcutaneous continuous glucose monitoring and subcutaneous insulin delivery are stimulating the development of a minimally invasive artificial pancreas that facilitates optimal glycemic regulation in diabetes. The key component of such a system is the blood glucose controller for which different design strategies have been investigated in the literature. In order to evaluate and compare the efficacy of the various algorithms, several performance indices have been proposed. Methods: A new tool—control-variability grid analysis (CVGA)—for measuring the quality of closed-loop glucose control on a group of subjects is introduced. It is a method for visualization of the extreme glucose excursions caused by a control algorithm in a group of subjects, with each subject presented by one data point for any given observation period. A numeric assessment of the overall level of glucose regulation in the population is given by the summary outcome of the CVGA. Results: It has been shown that CVGA has multiple uses: Comparison of different patients over a given time period, of the same patient over different time periods, of different control laws, and of different tuning of the same controller on the same population. Conclusions: Control-variability grid analysis provides a summary of the quality of glycemic regulation for a population of subjects and is complementary to measures such as area under the curve or low/high blood glucose indices, which characterize a single glucose trajectory for a single subject.