Dynamic analysis of disease progression in Alzheimer’s disease under the influence of hybrid synapse and spatially correlated noise
Introduction
Alzheimer’s disease (AD), as a neurodegenerative disease, has caused great damage to the health of patients [1]. To address this problem and boost people’s happiness, researchers have made some achievements in the early prediction of AD by using machine learning[2], [3], [4], [5]. The main approach is to classify the images by extracting the features in the functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG) of the patients, and then to determine the stage of the patients’ disease. Due to the complexity of the pathogenesis of AD and the inability to conduct experiments on human brains, the pathogenesis of AD is still not clear [6]. It has become a feasible way to prevent and treat AD to explore the pathogenesis of AD and seek treatment by using kinetic method.
As a clinical feature of AD patients, cognitive impairment includes the decline of learning and memory ability [7], [8]. As a kind of memory ability of human brain, associative memory can be divided into self-associative, heteroassociative and multidirectional associative memory. Self-associative memory ability can restore impaired memory patterns, while heterassociative memory ability establishes the correlation between two memory patterns. Multidirectional associative memory ability is an extension of heterassociative memory ability, and establishes the correlation between multiple memory patterns. The disease stage of AD can be judged by analyzing the strength of association ability. From the last century to present, various neural network structures such as HNNs(Hopfield neural networks) [9], BAMNNs(Bidirectional Associative Memory Neural Networks) [10] and MAMNNs(Multidirectional Associative Memory Neural Networks) [11] have been proposed to analyze the associative memory ability of human brain. However, the research on the above three networks is mainly focused on the stability analysis of the neural network, pattern recognition, image encryption and other applications [12], [13], [14], and rarely applied in the field of disease. Therefore, this paper analyzes the association memory as the disease characteristics of AD, and in order to complete the simulation of different stages of AD, we successively builds a neural network model with self-associative, heteroassociative and multidirectional associative memory ability respectively to simulate the brain’s various associative memory abilities.
Synaptic plasticity refers to the characteristic or phenomenon that the morphology and function of synapses can be changed permanently. Synapses will be strengthened and weakened with the strengthening and weakening of their own activities, corresponding to the increase or decrease of the weight of synapses in the artificial neural network. We will discuss the loss and compensatory behavior of synapses. Synaptic loss is the main neurobiological basis of neurodegenerative diseases such as AD, epilepsy and schizophrenia. Therefore, it is now a hot research direction to determine the key brain regions related to the disease according to the condition of synaptic loss in the affected individuals, and then to clarify the relationship between synaptic loss and the degree of disease. At present, there are two mainstream research methods. One is to extract the changes of synaptic proteins in brain regions of subjects for analysis. For example, Emanuele selected a case-control study of schizophrenia to quantify the levels of synaptic proteins and mRNA in brain tissues and analyze the differences between cases and the control group [15]. Another approach is to use positron emission tomography to determine where synaptic loss occurs in the brain. Bastin used positron emission tomography to compare the imaging of patients with mild cognitive impairment and AD [16]. Due to the specificity of individual disease and the occult nature of pre-AD disease, the rules obtained from the above research results have certain applicability within the range of samples selected, but the corresponding relationship between synaptic loss and the degree of AD disease has not been solved. Therefore, from the perspective of dynamics, we built a synaptic loss model to establish the corresponding relationship between associative memory ability and synaptic loss phenomenon in the degree of disease.
Clinically, a number of experimental studies have found that the cognitive decline of AD is accompanied by the occurrence of synaptic compensation. During cognitive impairment, synapses can also compensate for their function and metabolism by increasing their own volume [17], [18], [19]. From the neurobiological point of view, neuroinflammatory hyperplasia, increased neurogenetic processes, and increased expression of postsynaptic proteins PSD-95 and apolipoprotein D may lead to synaptic compensations [20]. Based on the above synaptic activities, we establish a synaptic loss model and a synaptic compensation model to analyze the decreased associative memory ability caused by the decrease in the strength of synaptic connections, so as to quantify the strength of associative memory ability at various stages of the disease and make an accurate judgment of the stage of the disease.
Many experiments have demonstrated that hybrid synapses, both electrical and chemical, coexist in most living organisms and brain structures [21], [22], [23]. Researchers have investigated the diversity of electrical and chemical synaptic connections in neural activity in networks of varying complexity. Autapse is a synaptic connection formed between the axons of human brain neurons and their own dendrites or cell bodies, which can have a variety of firing patterns [24], [25], [26]. It has been found in cerebellum, hippocampus, cerebral cortex and other brain regions, and plays an important role in regulating the signal processing of neurons [27], [28], [29]. In order to simulate the complex human brain environment, hybrid synapses and autapses will be considered in this paper to build a more biointerpretable neural network model and analyze the performance of the neural network under a certain intensity of noise.
Previous studies have shown that synchronous oscillation is a common phenomenon in the nervous system and it is the basis of the brain’s attention and memory [30]. Gamma oscillation (30–100 Hz) is widespread in all kinds of organisms and is closely related to the learning and memory abilities of human brain. In 2020, Sitong Wang proposed that neural oscillation analysis plays an important role in the early diagnosis of AD [31]. Therefore, the associative memory ability of the network can be judged by analyzing the law of gamma synchronous oscillation in the neural network, and the application of the judgment results to the pathological analysis of AD becomes a feasible way to predict the stage of AD.
On the basis of previous work, we use dynamic modeling method to create synaptic loss and synaptic compensation models, analyze the effects of hybrid synapses and autapse currents on the associative memory ability of neural networks, and study the effects of synaptic loss and compensation on associative memory ability through synchronous oscillation of neurons.
The main contents of this paper are summarized as follows.
- 1.
Considering hybrid synapses and autapses, a neural network model with multiple associative memory abilities was established to test the degree of cognitive decline in the human brain.
- 2.
Considering the influence of the external environment of the nervous system. The spatial correlated noise is added to analyze the influence of the external environment of the nervous system on associative memory ability.
- 3.
Synaptic loss and synaptic compensation models are established to analyze the associative memory ability of neural networks under different levels of loss and compensation.
Section snippets
Neural network model construction
We propose a simplified three-layer neural network model with multiple associative memory abilities, composing of 260 neurons with 80, 100 and 80 respectively in the first, second and third layer, as an imitation of its three-layer neural network structure. Among them, each layer of neurons are fully interconnected, and each layer of neurons is not interconnected. The neuron model and synaptic model of the neural network are as follows.
Model simulation
In order to establish the relationship between synaptic loss and the deterioration of associative memory ability, and to further study the relationship with the prediction of AD disease stage, we combine the neural network model established in the previous section to simulate the associative memory ability of the neural network under the three conditions of normal, synaptic loss and synaptic compensation. Table 1 indicates the specific meanings and values of the parameters in the simulation
Conclusion
It is known that Alzheimer’s disease is associated with a marked loss of associative memory, therefore, to further explore the pathogenesis of Alzheimer’s disease and solve the problem of no specific drug treatment, we set up a neural network model with multiple associative memory abilities to simulate Alzheimer’s disease with different degrees from the perspective of the degeneration of associative memory caused by Alzheimer’s disease. Considering that synaptic loss is the cause of the decline
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grant 81961138010, U1803263, 11931015 and Grant U1836106, in part by the Fundamental Research Funds for the Central Universities under Grant FRF-TP-19-005A3, QNXM20210036, and Grant FRF-IDRY-20-022, in part by the Technological Innovation Foundation of Shunde Graduate School, USTB, under Grant BK19BF006 and Grant BK20BF010, in part by National Natural Science Foundation for Distinguished Young Scholars
Weiping Wang received the Ph.D. degree in telecommunications physics electronics from Beijing University of Posts and Telecommunications, Beijing, China, in 2015. She is currently an Associate Professor with the Department of Computer and Communication Engineering, University of Science and Technology Beijing. She received the National Natural Science Foundation of China, the Postdoctoral fund, and the basic scientific research project. Her current research interests include brain-like
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Weiping Wang received the Ph.D. degree in telecommunications physics electronics from Beijing University of Posts and Telecommunications, Beijing, China, in 2015. She is currently an Associate Professor with the Department of Computer and Communication Engineering, University of Science and Technology Beijing. She received the National Natural Science Foundation of China, the Postdoctoral fund, and the basic scientific research project. Her current research interests include brain-like computing, memrisitive neural network, associative memory awareness simulation, complex network, network security and image encryption.
Chang He received the bachelor’s degree in Tianjin University of Science and Technology, China, in 2020, where she is currently pursuing the M.E. degree from University of Science and Technology Beijing, Beijing, China. Her current research interests is associative memory neural network.
Zhen Wang received the Ph.D. degree from Hong 1287 Kong Baptist University, Hong Kong, in 2014. From 2014 to 2016, he was a JSPS Senior Researcher with the Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka, Japan. Since 2017, he has been a Full Professor with Northwestern Polytechnical University, Xian, China. His current research interests include complex networks, complex system, big data, evolutionary game theory, behavioral economic, and brain science. Thus far, he has published more than 100 scientific papers, his total citations is around 6,000 times and H-index is 40. Dr. Wang was a recipient of the 1000 National Talent Plan Program of China.
Jun Cheng received the B.S. degree in mathematics and applied mathematics from the Hubei University for Nationalities, Enshi, China, in 2010, and the Ph.D. degree in instrumentation science and technology from the University of Electronic Science and Technology of China, Chengdu, China, in 2015. From 2013 to 2014, he was a Visiting Scholar with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore. From 2016 to 2018, he was a Visiting Scholar with the Department of Electrical Engineering, Yeungnam University, Gyeongsan, South Korea. He is currently with the Qingdao university of Scinence and Technology, Qingdao, China, and the Hubei university for Nationalities. His current research interests include analysis and synthesis for stochastic hybrid systems, networked control systems, robust control, and nonlinear systems.
Xishuo Mo is currently an undergraduate student at the University of Science and Technology Beijing, Beijing, China.
Kuo Tian is currently an undergraduate student at the University of Science and Technology Beijing, Beijing, China.
Denggui Fan received the Ph.D. degree in Beihang University in 2016, his current research interests include neurodynamics and brain-like computation.
Xiong Luo received the Ph.D degree in computer applied technology from Central South University, Changsha, China, in 2004. He is currently a Professor with the School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing, China. His current research interests include neural networks, machine learning, and computational intelligence. He has published extensively in his areas of interest in several journals, such as IEEE ACCESS, Future Generation Computer Systems, and Personal and Ubiquitous Computing.
Manman Yuan received the Ph.D. degree in University of Science and Technology Beijing, Beijing, China, in 2020. She is currently a postdoctoral fellow with the Department of Computer and Communication Engineering, University of Science and Technology Beijing. Her current research interests include memristive neural networks, brain computing, and machine learning.
Jürgen Kurths studied mathematics with the University of Rostock and received the Ph.D. degree from the GDR Academy of Sciences in 1983. He was a Full Professor with the University of Potsdam from 1994 to 2008. He has been a Professor of nonlinear dynamics with Humboldt University, Berlin, and the Chair of the research domain transdisciplinary concepts of the Potsdam Institute for Climate Impact Research since 2008 and a Sixth-Century Chair of Aberdeen University, U.K., since 2009. He has authored over 500 papers that are cited over 18000 times (h-factor: 57). His primary research interests include synchronization, complex networks, and time series analysis and their applications. He is a fellow of the American Physical Society. He became a member of the Academia Europaea in 2010 and the Macedonian Academy of Sciences and Arts in 2012. He received the Alexander von Humboldt Research Award from CSIR, India, in 2005, and an Honorary Doctorate from the Lobachevsky University Nizhny Novgorod in 2008 and one from the State University Saratov in 2012. He is an Editor of journals, such as PLoS ONE, the Philosophical Transaction of the Royal Society A, the Journal of Nonlinear Science, and Chaos.