Physics-informed neural networks for physiological signal processing and modeling: a narrative review

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Physics-informed neural networks for physiological signal processing and modeling: a narrative review

Abstract

Physics-informed neural networks represent a transformative approach to data models by incorporating known physical laws into neural network training, thereby improving model generalizability, reducing data dependency, and enhancing interpretability. Like many other fields in engineering and science, the analysis of physiological signals has been influenced by physics-informed neural networks in recent years. This manuscript provides a comprehensive overview of physics-informed neural networks from various perspectives in the physiological signal analysis domain. After exploring the literature and screening the search results, more than forty key studies in the related domain are selected and categorized based on both practically and theoretically significant perspectives, including input data types, applications, physics-informed models, and neural network architectures. While the advantages of physics-informed neural networks in tackling forward and inverse problems in physiological signal contexts are highlighted, challenges such as noisy inputs, computational complexity, loss function types, and overall model configuration are discussed, providing insights into future research directions and improvements. This work can serve as a guiding resource for researchers exploring physics-informed neural networks in biomedical and physiological signal processing, paving the way for more precise, data-efficient, and clinically relevant solutions.

One. Introduction

Physics-informed neural networks are a class of neural networks that incorporate physical laws directly into the learning process. The idea is to use established scientific principles, often explicitly expressed in ordinary differential equations or partial differential equations, as a part of the neural network's training, guiding the model to solutions that inherently satisfy these physical laws. In conventional neural networks, the model is purely data-driven. Therefore, their performance decreases with limited data or in the presence of noise, distortion, and missing values. Physics-informed neural networks, on the other hand, balance both data and prior knowledge of physics-based constraints. This trade-off allows physics-informed neural networks to capture complex patterns in data without drastic deviation from the known physics of the phenomena.

The idea of integrating physical prior knowledge into a neural network framework dates back to nineteen ninety-four, when Dissanayake and Phan-Thien introduced a numerical universal approximator, based on neural networks to solve partial differential equations. Afterward, the concept of physics-informed neural networks has been utilized in different areas with known physics laws and shallow neural networks.

Thanks to computing hardware advancements in subsequent decades, the use of deep neural networks with numerous adjustable parameters has become prevalent, which could facilitate leveraging physics-informed neural networks to solve more detailed and complicated problems. Nowadays, physics-informed neural networks-based solutions can be seen across various fields of science and engineering, including (but are not limited to) optics, electromagnetism, aerodynamics, petroleum engineering, etc.

In medicine, the analysis of physiological data presents some of the most suitable problems for modeling with ordinary differential equations or partial differential equations and solving with physics-informed neural networks. Figure one shows the growing trend of publications in this field in recent years, serving as an indicator of the increasing importance and potential of this method. Among the various types of problems, the study of electrical signals propagation (electrophysiology) and blood flow in cardiovascular system (hemodynamics) are the two most remarkable fields in the literature in which physics-informed neural networks are deployed, as shown in figure two.

However, to the best of our knowledge, a comprehensive review of physics-informed neural networks methods, particularly their applications in solving physiological and biomedical problems, is lacking in the literature. While individual studies have explored specific implementations, a review that systematically categorizes their methodologies, governing ordinary differential equations or partial differential equations, neural network architectures, and objectives across different domains remains largely unexplored.

In this study, we review the literature on the application of physics-informed neural networks in biomedical and physiological data analysis from April twenty nineteen to December twenty twenty-four. The selected papers were sourced from various databases and digital libraries, including Google Scholar, PubMed, and IEEE Xplore, using a combination of targeted keywords to maximize the retrieval of relevant studies. The keywords used in the various research engines are listed as follows:

The following is a sample query utilized to filter the search results:

A flowchart is shown in figure three to demonstrate the search strategy for this paper. Articles on biomedical imaging are excluded to maintain focus on studies utilizing physics-informed neural networks for physiological signal processing and modeling. Additional characteristics, including the application fields, ordinary differential equations or partial differential equations properties, and neural network architectures, are identified by manual inspection and detailed analysis of the articles.

The next sections are organized as follows: section two explores the architecture of physics-informed neural networks framework, structure of embedded neural networks, and the associated loss functions. Section three describes the prevalent partial differential equations and ordinary differential equations used in the application of physics-informed neural networks to physiological signal processing and modeling. Section four summarizes the objectives, key characteristics, and performance metrics of physics-informed neural networks in various areas. In section five, the general aims and findings of the study are discussed. Finally, section six concludes the paper.

Two. Framework of physics-informed neural networks in physiological signal

Two point two. Loss function

Two point three. Overview of PINNs frameworks

Three. Physics models and prior information

Three point one. Electrophysiological models

Three point one point one. Eikonal model

Three point one point two. State-space model

Three point one point three. Aliev-Panfilov model

Three point one point four. Fenton-Karma model

Three point one point five. Mitchell-Schaeffer model

Three point one point six. Hodgkin-Huxley model

Three point one point seven. FitzHugh-Nagumo model

Three point two. Muscle electromechanical models

Three point two point one. Hill-type model

Three point two point two. Twitch force model

Three point three. Hemodynamic models

Three point three point one. Navier-Stokes equations

Three point three point two. Linearized Navier-Stokes equations

Three point three point three. Burger equations

Three point four. Other fields

Three point five. Conventional numerical methods

Four. Overview of characteristics and metrics

Five. Discussion

Objective

Six. Conclusion

Data availability statement

Overview

This narrative review discusses the role of physics-informed neural networks in analyzing physiological signals, emphasizing their ability to integrate physical laws with data-driven methods. The work provides a comprehensive overview of key studies, methodologies, and identified challenges in the field.

Key Points

1Physics-informed neural networks enhance model generalizability by incorporating physical laws
2The review highlights over forty significant studies on physiology-related applications of PINNs
3Challenges like noisy inputs and computational complexity are discussed
4The study serves as a resource for researchers interested in data-efficient physiological modeling
5Insights into the future research directions for improving PINNs in biomedical contexts are provided

Details

Authors: Anni Zhao, Davood Fattahi, Xiao Hu
Category: Health and Medicine

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