Evaluation of respiratory properties by means of fractional order models

Combining Fractional Derivatives and Machine Learning: A Review

Fractional calculus has gained a lot of attention in the last couple of years. Researchers have discovered that processes in various fields follow fractional dynamics rather than ordinary integer-ordered dynamics, meaning that the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of which is that fractional derivatives inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It has provided many further insights and discoveries in various scientific disciplines. As these two modern-day topics hold a lot of potential for combined approaches in terms of describing complex dynamics, this article review combines approaches from fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there is already extensive literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning and fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools, and enhance their existing approaches.

A finite-time adaptive order estimation approach for non-integer order nonlinear systems

This paper proposes some methods for estimating the order of nonlinear systems having non-integer order. First, the stability of time-varying order systems is studied. Afterward, the multivariable systems with time-varying incommensurate order are studied and an estimation scheme is proposed to approximate the order. In the next step, considering the pseudo-states of a system to be unknown, an order/pseudo-state estimator is designed for a category of nonlinear systems. It is shown that the method is extendible to form order/pseudo-state estimators for other classes of nonlinear systems using other traditional nonlinear observers. One of the advantages of the proposed methods is that a compact time interval is enough to guarantee bounded estimation error.

Model Calibration of Pharmacokinetic-Pharmacodynamic Lung Tumour Dynamics for Anticancer Therapies

Individual curves for tumor growth can be expressed as mathematical models. Herein we exploited a pharmacokinetic-pharmacodynamic (PKPD) model to accurately predict the lung growth curves when using data from a clinical study. Our analysis included 19 patients with non-small cell lung cancer treated with specific hypofractionated regimens, defined as stereotactic body radiation therapy (SBRT). The results exhibited the utility of the PKPD model for testing growth hypotheses of the lung tumor against clinical data. The model fitted the observed progression behavior of the lung tumors expressed by measuring the tumor volume of the patients before and after treatment from CT screening. The changes in dynamics were best captured by the parameter identified as the patients’ response to treatment. Median follow-up times for the tumor volume after SBRT were 126 days. These results have proven the use of mathematical modeling in preclinical anticancer investigations as a potential prognostic tool.

Conditional GAN based augmentation for predictive modeling of respiratory signals

Respiratory illness is the primary cause of mortality and impairment in the life span of an individual in the current COVID-19 pandemic scenario. The inability to inhale and exhale is one of the difficult conditions for a person suffering from respiratory disorders. Unfortunately, the diagnosis of respiratory disorders with the presently available imaging and auditory screening modalities are sub-optimal and the accuracy of diagnosis varies with different medical experts. At present, deep neural nets demand a massive amount of data suitable for precise models. In reality, the respiratory data set is quite limited, and therefore, data augmentation (DA) is employed to enlarge the data set. In this study, conditional generative adversarial networks (cGAN) based DA is utilized for synthetic generation of signals. The publicly available repository such as ICBHI 2017 challenge, RALE and Think Labs Lung Sounds Library are considered for classifying the respiratory signals. To assess the efficacy of the artificially created signals by the DA approach, similarity measures are calculated between original and augmented signals. After that, to quantify the performance of augmentation in classification, scalogram representation of generated signals are fed as input to different pre-trained deep learning architectures viz Alexnet, GoogLeNet and ResNet-50. The experimental results are computed and performance results are compared with existing classical approaches of augmentation. The research findings conclude that the proposed cGAN method of augmentation provides better accuracy of 92.50% and 92.68%, respectively for both the two data sets using ResNet 50 model.

Tailored Pharmacokinetic model to predict drug trapping in long-term anesthesia

Introduction

In long-term induced general anesthesia cases such as those uniquely defined by the ongoing Covid-19 pandemic context, the clearance of hypnotic and analgesic drugs from the body follows anomalous diffusion with afferent drug trapping and escape rates in heterogeneous tissues. Evidence exists that drug molecules have a preference to accumulate in slow acting compartments such as muscle and fat mass volumes. Currently used patient dependent pharmacokinetic models do not take into account anomalous diffusion resulted from heterogeneous drug distribution in the body with time varying clearance rates.

Objectives

This paper proposes a mathematical framework for drug trapping estimation in PK models for estimating optimal drug infusion rates to maintain long-term anesthesia in Covid-19 patients. We also propose a protocol for measuring and calibrating PK models, along with a methodology to minimize blood sample collection.

Methods

We propose a framework enabling calibration of the models during the follow up of Covid-19 patients undergoing anesthesia during their treatment and recovery period in ICU. The proposed model can be easily updated with incoming information from clinical protocols on blood plasma drug concentration profiles. Already available pharmacokinetic and pharmacodynamic models can be then calibrated based on blood plasma concentration measurements.

Results

The proposed calibration methodology allow to minimize risk for potential over-dosing as clearance rates are updated based on direct measurements from the patient.

Conclusions

The proposed methodology will reduce the adverse effects related to over-dosing, which allow further increase of the success rate during the recovery period.

PVC arrhythmia classification based on fractional order system modeling

It is well known that many physiological phenomena are modeled accurately and effectively using fractional operators and systems. This type of modeling is due mainly to the dynamical link between fractional-order systems and the fractal structures of the physiological systems. The automatic characterization of the premature ventricular contraction (PVC) is very important for early diagnosis of patients with different life-threatening cardiac diseases. In this paper, a classification scheme of normal and PVC beats of the electrocardiogram (ECG) signal is proposed. The clustering features used for normal and PVC beats discrimination are the parameters of the commensurate order linear fractional model of the frequency content of the QRS complex of the ECG signal. A series of tests and comparisons have been performed to evaluate and validate the efficiency of the proposed PVC classification algorithm using the MIT-BIH arrhythmia database. The proposed PVC classification method has achieved an overall accuracy of 94.745%, a specificity of 95.178% and a sensitivity of 90.021% using all the 48 records of the database.

A Minimal PKPD Interaction Model for Evaluating Synergy Effects of Combined NSCLC Therapies

This paper introduces a mathematical compartmental formulation of dose-effect synergy modelling for multiple therapies in non small cell lung cancer (NSCLC): antiangiogenic, immuno- and radiotherapy. The model formulates the dose-effect relationship in a unified context, with tumor proliferating rates and necrotic tissue volume progression as a function of therapy management profiles. The model accounts for inter- and intra-response variability by using surface model response terms. Slow acting peripheral compartments such as fat and muscle for drug distribution are not modelled. This minimal pharmacokinetic-pharmacodynamic (PKPD) model is evaluated with reported data in mice from literature. A systematic analysis is performed by varying only radiotherapy profiles, while antiangiogenesis and immunotherapy are fixed to their initial profiles. Three radiotherapy protocols are selected from literature: (1) a single dose 5 Gy once weekly; (2) a dose of 5 Gy × 3 days followed by a 2 Gy × 3 days after two weeks and (3) a dose of 5 Gy + 2 × 0.075 Gy followed after two weeks by a 2 Gy + 2 × 0.075 Gy dose. A reduction of 28% in tumor end-volume after 30 days was observed in Protocol 2 when compared to Protocol 1. No changes in end-volume were observed between Protocol 2 and Protocol 3, this in agreement with other literature studies. Additional analysis on drug interaction suggested that higher synergy among drugs affects up to three-fold the tumor volume (increased synergy leads to significantly lower growth ratio and lower total tumor volume). Similarly, changes in patient response indicated that increased drug resistance leads to lower reduction rates of tumor volumes, with end-volume increased up to 25–30%. In conclusion, the proposed minimal PKPD model has physiological value and can be used to study therapy management protocols and is an aiding tool in the clinical decision making process. Although developed with data from mice studies, the model is scalable to NSCLC patients.

Implementation of a Fractional-Order Electronically Reconfigurable Lung Impedance Emulator of the Human Respiratory Tree

The fractional-order lung impedance model of the human respiratory tree is implemented in this paper, using Operational Transconductance Amplifiers. The employment of such active element offers electronic adjustment of the impedance characteristics in terms of both elements values and orders. As the MOS transistors in OTAs are biased in the weak inversion region, the power dissipation and the dc bias voltage of operation are also minimized. In addition, the partial fraction expansion tool has been utilized, in order to achieve reduction of the spread of the required time-constants and scaling factors. The performance of the proposed scheme has been evaluated, at post-layout level, using MOS transistors models provided by the 0.35 μ m Austria Mikro Systeme technology CMOS process, and the Cadence IC design suite.

A robust fixed point transformation-based approach for type 1 diabetes control

Modeling and control of diabetes mellitus (DM) are difficult due to the highly nonlinear attitude, time-delay effects, the impulse kind input signals and the lack of continuously available blood glucose (BG) level to be regulated. Regarding the mentioned problems, identification of DM model is crucial. Furthermore, due to the lack of information about the internal states (which cannot be measured in everyday life) and because the BG level is not available in every moment over time, adaptive robust control design method regardless exact model dependency would successfully handle these unfavorable effects without simplifications. The recently developed nonlinear robust fixed point transformation (RFPT)-based controller design method requires only a roughly approximate model in order to realize the controller structure. Moreover, parallel simulated approximate models-in order to provide additional internal information-can be used with the method. In this paper, the usability of the novel RFPT-based technique is demonstrated on the physiological problem of diabetes.