# Dynamic Observation of the Effect of L-Theanine on Cerebral Ischemia-Reperfusion Injury Using Magnetic Resonance Imaging under Mathematical Model Analysis

Authors: Hui Ye; Zaiming Liu; Long Zhou; Qiang Cai
Journal: Journal of Healthcare Engineering
 (2021)

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## Abstract

This study was to use the partial differential mathematical model to analyze the magnetic resonance imaging (MRI) images of cerebral ischemia-reperfusion injury (CIRI) and to dynamically observe the role of L-theanine in CIRI based on this. 30 patients with cerebral ischemia in a hospital in a certain area were selected and divided into a cerebral ischemia group and a L-theanine treatment group. The two groups of patients were examined by MRI within 48 hours, and the relative apparent diffusion coefficient (rADC) of the cerebral ischemic part of the patients was determined. The partial differential mathematical model was used for data processing to obtain the function of cerebral ischemia time and infarct area, and the data of patients in the cerebral ischemia group and L-theanine treatment group were compared and analyzed. The results showed that the partial differential mathematical model could effectively analyze the linear relationship between the rADC value and time in the treatment of CIRI using L-theanine. The rADC values of the four points of interest in the L-theanine treatment group all increased with time, and there was a positive correlation between the variablesX and Y. In observing the efficacy indicators of L-theanine, the L-theanine treatment group showed a significant advantage in the neurospecific enolase (NSE) content compared with the cerebral ischemia group (P<0.01), and the neurological function score of the L-theanine treatment group gradually decreased and showed a statistically obvious difference on the 7th day of treatment (P<0.05). In summary, it was verified in this study that the role of L-theanine in the treatment of CIRI was of a great and positive significance for the subsequent treatment of patients with cerebral ischemia, providing reliable theoretical basis and data basis for clinical treatment of CIRI.


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## Body

## 1. Introduction

The brain part of the human body is the most sensitive to hypoxia among all parts and organs. When the brain tissue is ischemic, it will cause serious damage to the function of the local brain tissue. Cerebral ischemia is a relatively broad term in nature. Clinically related diseases include but are not limited to transient ischemic attack, ischemic stroke, and chronic cerebral insufficiency [1]. The degree of brain damage depends on the length of the ischemia time and the amount of residual blood flow. When incomplete short-term ischemia occurs, the damage to the brain tissue is reversible at this time [2] However, if the brain tissue is completely and severely ischemia for a long time, it will cause irreversible damage to the brain tissue, such as infarction and death [3]. The most obvious change is the change in tissue, which may cause hypoxic necrosis of brain tissue, and a series of neurological deficit syndromes may appear [4, 5]. There are generally many pathophysiological mechanisms of cerebral ischemia, including free radicals and cerebral ischemia-reperfusion injury (CIRI) damage, calcium overload and CIRI damage, excitatory amino acids and CIRI damage, NO and CIRI damage, inflammatory response and CIRI damage, and cell apoptosis [6–8].In addition to brain damage caused by simple cerebral ischemia, CIRI can also cause serious damage to brain function [9, 10]. When cerebral ischemia occurs, the bioelectricity of brain cells in the brain will change to a certain extent, followed by pathological slow waves. When the brain is reperfused after a period of ischemia, the pathological slow wave of the brain will continue and aggravate at this time, and the neurotransmitter amino acid metabolism in the temporal lobe tissue will be greatly changed. The longer the ischemia-reperfusion injury time, the lower the content of excitatory transmitters and the more obvious the changes in the ultrastructure of brain tissue at this time.There are many possible causes of cerebral ischemia. The more common ones are stroke and ischemic stroke. These diseases are important causes of death and paralysis in the elderly, and most of the strokes are ischemic strokes. The reason is that the internal arteries in the brain tissue have been irreversibly damaged. Because this type of disease has a very high disability and fatality rate, it has brought heavy economic pressure and serious impact to the social family. Therefore, the prevention and treatment of cerebral hemorrhage and reperfusion need to be further explored. At present, there are many types of drugs for the treatment of cerebral ischemia, including neuroprotection, anticoagulation, and antiplatelet aggregation. Many neuroprotective agents have had very good effects in animal experiments, but they have not achieved the corresponding curative effect in clinical application. In addition, it has been found that these neuroprotective agents can also bring a certain degree of side effects in clinical application [11]. As a neuroprotective agent with almost no toxic side effects, L-theanine has gradually entered the field of clinical research [12].To study the actual effect of L-theanine on cerebral ischemia, it is necessary to dynamically observe the area of cerebral ischemia. MRI is a new medical imaging technology that uses the principle of MRI. It shows excellent diagnostic effects on the brain, thyroid, liver, gallbladder, spleen, kidney, pancreas, adrenal glands, uterus, ovaries, prostate, and other physical organs, as well as the heart and large blood vessels. Compared with other auxiliary examination methods, MRI shows the advantages of multiple imaging parameters, fast scanning speed, high tissue resolution, and clearer images. It has become a powerful tool for early screening of tumors, heart diseases, and cerebrovascular diseases. MRI data cannot directly reflect the therapeutic effect of drugs on CIRI. Therefore, the partial differential mathematical model was adopted in this study to analyze the data to further explore the effect of drugs on cerebral ischemia area and its changing law.


## 2. Methods

### 2.1. Research Objects

30 patients aged 25–75 who were diagnosed with cerebral ischemia in a hospital in a certain area for two years were selected, including 20 male patients and 10 female patients. All patients had no other diseases or tumors in their brains. 30 patients were divided into a cerebral ischemia group and a L-theanine treatment group. MRI examinations were performed on two groups of patients within 48 hours, and the relative apparent diffusion coefficient (rADC) of the cerebral ischemic part of the patients was measured.The inclusion criteria were defined as follows: patients with cerebral ischemia sites measurable by MRI images, patients with no major organ failure, patients whose survival time was expected to be greater than three months, and patients who had signed the informed consent of L-theanine treatment.The exclusion criteria were defined as follows: those who had allergic reactions to L-theanine drugs, those who had the history of mental illness, those who had no measurable lesions on MRI scans, and those who had dysfunction of vital organs.


### 2.2. MRI Scanning Parameters

The GE Discovery MR750w HD 3.0T MRI with an 18-channel body coil was adopted to scan the patient. The patient was required to stay supine on the examination table, the head and neck joint coil was adopted to fix the patient’s head, and the coronal 3D TRICKS scan was performed. After the image was obtained, four points of interest were selected on the image. After 1 hour of continuous 18 F-FDG scanning, the data were divided into 5 seconds × 4 frames, 10 seconds × 4 frames, 30 seconds × 2 frames, 60 seconds × 8 frames, and 300 seconds × 10 frames for dynamic reconstruction. The thoracic aorta is extracted as the blood pool input function for brain dynamic parameter imaging analysis. In order to avoid the difference of the brain infarct position of patients from affecting the experimental results, the ratio of the diseased side to the normal side in the MRI data, which was the rADC value, was calculated in this study. The main observation indicator was the rADC value of patients in different time points and different regions of interest (ROI).


### 2.3. Establishment of Mathematical Models of Differential Equations to Analyze Data

The mathematical model of differential equations has a wide range of applications in the diffusion of matter [13]. It plays an important role in the field of natural sciences such as nerve conduction and the distribution and diffusion of drugs in the human body. The calculation is relatively simple, which is related to the reaction diffusion area generally, and can be solved quantitatively or qualitatively by establishing mathematical models through linear or nonlinear partial differential equations.It was assumed that the mathematical model to be established wasF = R∪E, and the cost function of the data to be analyzed could be expressed as follows:(1)Tf=∫fr∇fdxdy.In the data that needed to be calculated hierarchically, there was an impact function ∇_f. At this time, the standby function had to satisfy the following equation:(2)∫fr∇fdxdy<∞.In the mathematical model established by the differential equation algorithm,r (|∇_f|) = |∇_f|; then, the function at this time was expressed as follows:(3)Tf=∫f∇fdxdy.If invalid data were proposed in the process of establishing a mathematical model to analyze the target data, the following conditions had to be met:(4)δ2=1sEE∫Ef−f02dxdy.In the above equation,δ^2 represents the variance of Gaussian noise, s (E) represents the image data of the undamaged part, f represents the result of removing invalid data, and f_0 represents to the original image data with invalid data. The overall energy functional function could be obtained by combining equations (3) and (4):(5)Gλf=∫f∇fdxdy+λ2∫Ef−f02dxdy.In equation (5) above, λ represents the Lagrange multiplier. Next, the minimum value of the energy functional function of this model can be solved with the following equation:(6)Ef=∫wDx,y,f,ϕfϕx,Φfϕydxdy.If the minimum value ofE (f) was required, the following equation had to be met:(7)Df−ϕϕJCDfx−ϕϕyDfy=0.In the mathematical model established by the differential algorithm equation, the following condition can be found.(8)Dx,y,f,ϕxϕn,ϕyϕn=φfφx2+φfφy2λ2f−f02.It can obtain the minimum energy functional equation of the mathematical model by combining equations (8) and (7) as follows:(9)−∇⋅∇f∇f+λf−f0=0.For a certain pointz = (x, y) ∈ ω in the target image data, the Lagrange multiplier in equation (9) satisfied the following equation:(10)λ=λ,z∈E,O,z∈D.


### 2.4. Observation Indicators of the Curative Effect of L-Theanine on Two Groups of Patients

The jugular venous blood was drawn from selected patients with cerebral ischemia, and 3 mL of blood was drawn at four time points after the ischemia-reperfusion. The time points were 1 h, 2 h, 4 h, and 6 h. The obtained blood sample was centrifuged at 2000 r/min for 10 minutes, and then, serum was obtained. The serum was placed in a refrigerator at −70°C for later use. After all preparations were made, the serum was tested for neurospecific enolase (NSE) according to the enzyme-linked immunosorbent assay (ELISA) method.After the selected patients with cerebral ischemia were treated with L-theanine, the neurological improvement scores of the two groups of patients were scored using Bederson’s scoring criteria [14]. A person with no behavioral impairment scored 0 points, a person who cannot fully extend the forelimbs scored as 1 point, a drop in thrust against the contralateral side scored as 2 points, and 3 points were scored for a circle to the opposite side. Based on Bederson’s scoring criteria, the behavioral function scores of patients in the cerebral ischemia group and the L-theanine treatment group were performed within 21 days, and the behavioral function status of the two groups of patients over time was counted.


### 2.5. Statistical Analysis

The SPSS19.0 software was adopted for statistical analysis. Measurement data conforming to normal distribution were expressed as mean ± standard deviation, and comparisons between groups were analyzed by the independent samplet-test. The measurement data not conforming to the normal distribution were represented by the median value and the four-point position, and the comparison of differences between groups was analyzed by the nonparametric rank sum test. Enumeration data were expressed by n (%), and the comparison of differences between groups was analyzed by the chi-square test. The test standard considered that P<0.05 and a = 0.05 were statistically different.


## 2.1. Research Objects

30 patients aged 25–75 who were diagnosed with cerebral ischemia in a hospital in a certain area for two years were selected, including 20 male patients and 10 female patients. All patients had no other diseases or tumors in their brains. 30 patients were divided into a cerebral ischemia group and a L-theanine treatment group. MRI examinations were performed on two groups of patients within 48 hours, and the relative apparent diffusion coefficient (rADC) of the cerebral ischemic part of the patients was measured.The inclusion criteria were defined as follows: patients with cerebral ischemia sites measurable by MRI images, patients with no major organ failure, patients whose survival time was expected to be greater than three months, and patients who had signed the informed consent of L-theanine treatment.The exclusion criteria were defined as follows: those who had allergic reactions to L-theanine drugs, those who had the history of mental illness, those who had no measurable lesions on MRI scans, and those who had dysfunction of vital organs.


## 2.2. MRI Scanning Parameters

The GE Discovery MR750w HD 3.0T MRI with an 18-channel body coil was adopted to scan the patient. The patient was required to stay supine on the examination table, the head and neck joint coil was adopted to fix the patient’s head, and the coronal 3D TRICKS scan was performed. After the image was obtained, four points of interest were selected on the image. After 1 hour of continuous 18 F-FDG scanning, the data were divided into 5 seconds × 4 frames, 10 seconds × 4 frames, 30 seconds × 2 frames, 60 seconds × 8 frames, and 300 seconds × 10 frames for dynamic reconstruction. The thoracic aorta is extracted as the blood pool input function for brain dynamic parameter imaging analysis. In order to avoid the difference of the brain infarct position of patients from affecting the experimental results, the ratio of the diseased side to the normal side in the MRI data, which was the rADC value, was calculated in this study. The main observation indicator was the rADC value of patients in different time points and different regions of interest (ROI).


## 2.3. Establishment of Mathematical Models of Differential Equations to Analyze Data

The mathematical model of differential equations has a wide range of applications in the diffusion of matter [13]. It plays an important role in the field of natural sciences such as nerve conduction and the distribution and diffusion of drugs in the human body. The calculation is relatively simple, which is related to the reaction diffusion area generally, and can be solved quantitatively or qualitatively by establishing mathematical models through linear or nonlinear partial differential equations.It was assumed that the mathematical model to be established wasF = R∪E, and the cost function of the data to be analyzed could be expressed as follows:(1)Tf=∫fr∇fdxdy.In the data that needed to be calculated hierarchically, there was an impact function ∇_f. At this time, the standby function had to satisfy the following equation:(2)∫fr∇fdxdy<∞.In the mathematical model established by the differential equation algorithm,r (|∇_f|) = |∇_f|; then, the function at this time was expressed as follows:(3)Tf=∫f∇fdxdy.If invalid data were proposed in the process of establishing a mathematical model to analyze the target data, the following conditions had to be met:(4)δ2=1sEE∫Ef−f02dxdy.In the above equation,δ^2 represents the variance of Gaussian noise, s (E) represents the image data of the undamaged part, f represents the result of removing invalid data, and f_0 represents to the original image data with invalid data. The overall energy functional function could be obtained by combining equations (3) and (4):(5)Gλf=∫f∇fdxdy+λ2∫Ef−f02dxdy.In equation (5) above, λ represents the Lagrange multiplier. Next, the minimum value of the energy functional function of this model can be solved with the following equation:(6)Ef=∫wDx,y,f,ϕfϕx,Φfϕydxdy.If the minimum value ofE (f) was required, the following equation had to be met:(7)Df−ϕϕJCDfx−ϕϕyDfy=0.In the mathematical model established by the differential algorithm equation, the following condition can be found.(8)Dx,y,f,ϕxϕn,ϕyϕn=φfφx2+φfφy2λ2f−f02.It can obtain the minimum energy functional equation of the mathematical model by combining equations (8) and (7) as follows:(9)−∇⋅∇f∇f+λf−f0=0.For a certain pointz = (x, y) ∈ ω in the target image data, the Lagrange multiplier in equation (9) satisfied the following equation:(10)λ=λ,z∈E,O,z∈D.


## 2.4. Observation Indicators of the Curative Effect of L-Theanine on Two Groups of Patients

The jugular venous blood was drawn from selected patients with cerebral ischemia, and 3 mL of blood was drawn at four time points after the ischemia-reperfusion. The time points were 1 h, 2 h, 4 h, and 6 h. The obtained blood sample was centrifuged at 2000 r/min for 10 minutes, and then, serum was obtained. The serum was placed in a refrigerator at −70°C for later use. After all preparations were made, the serum was tested for neurospecific enolase (NSE) according to the enzyme-linked immunosorbent assay (ELISA) method.After the selected patients with cerebral ischemia were treated with L-theanine, the neurological improvement scores of the two groups of patients were scored using Bederson’s scoring criteria [14]. A person with no behavioral impairment scored 0 points, a person who cannot fully extend the forelimbs scored as 1 point, a drop in thrust against the contralateral side scored as 2 points, and 3 points were scored for a circle to the opposite side. Based on Bederson’s scoring criteria, the behavioral function scores of patients in the cerebral ischemia group and the L-theanine treatment group were performed within 21 days, and the behavioral function status of the two groups of patients over time was counted.


## 2.5. Statistical Analysis

The SPSS19.0 software was adopted for statistical analysis. Measurement data conforming to normal distribution were expressed as mean ± standard deviation, and comparisons between groups were analyzed by the independent samplet-test. The measurement data not conforming to the normal distribution were represented by the median value and the four-point position, and the comparison of differences between groups was analyzed by the nonparametric rank sum test. Enumeration data were expressed by n (%), and the comparison of differences between groups was analyzed by the chi-square test. The test standard considered that P<0.05 and a = 0.05 were statistically different.


## 3. Results

### 3.1. MRI Scanning Results

MRI scans were performed on 30 patients diagnosed with cerebral ischemia in a selected hospital, and the fuzzy and noisy sample data were removed. A total of 47 MRI scan images were obtained. Based on the obtained MRI scan images, the patient was further diagnosed with cerebral ischemia. Figure1 shows two samples of the images.Figure 1
MRI scanning results of patients.


### 3.2. Analysis Results of rADC Data of the Two Groups of Patients

Table1 provides the rADC values based on mathematical model analysis in the cerebral ischemia group at different time points. There was a negative correlation between the variables X and Y (P<0.05 and a = 0.05). At this time, the linear relationship between the two variables was more obvious. As shown in Figure 2, at 9–12 h, the correlation coefficient of point 2 in the ROI met r < 0, the variables X and Y were negatively correlated at this time, and the linear regression equation was Y = 1.497–0.038X (P>0.05 and a = 0.05). There was no obvious linear relationship between the two variables at this time. At 9–12 h, the correlation coefficient of point 4 in the ROI met r < 0, the variable X and Y presented a negative correlation at this time, and the linear regression equation was Y = 1.462–0.044X (P<0.05 and a = 0.05). There was a more obvious linear relationship between the two variables.Table 1
Comparison on rADC values in different ROIs at different time points for patients in the cerebral ischemia group.
rADCInfarct time (h)1359121521Point 10.740.410.580.850.620.790.49Point 20.870.510.620.930.680.820.53Point 30.940.560.711.080.890.820.55Point 40.990.630.791.230.931.060.74Figure 2
Linear relationship between variablesX and Y in the cerebral ischemia group.Table2 provides the rADC values based on mathematical model analysis in the L-theanine treatment group at different time points. There was a positive correlation between variables X and Y (P<0.05 and a = 0.05), and the linear relationship between the two variables was more obvious. As given in Table 2, at 9–12 h, the correlation coefficient of point 3 in the ROI met r > 0, and the variables X and Y were positively correlated at this time (P>0.05 and a = 0.05). There was an obvious linear relationship between the two variables at this time. As shown in Figure 3, at 1–6 h, the correlation coefficient of point 2 in the ROI met r > 0, and the variables X and Y presented a positive correlation at this time (P<0.05 and a = 0.05). There was a more obvious linear relationship between the two variables. The linear regression equation was Y = 0.802 + 0.721X. Therefore, it was found that within 48 hours of measuring the rADC value of the L-theanine treatment group, the rADC values of the four points of interest all increase with time, and the variables X and Y were positively correlated with each other.Table 2
Comparison on rADC values in the L-theanine treatment group at different time points.
rADCInfarct time (h)134562448Point 10.740.811.011.030.980.790.86Point 20.830.941.141.171.150.880.99Point 30.871.021.211.231.170.951.03Point 40.941.181.361.371.281.061.16Figure 3
Linear relationship between variablesX and Y in the L-theanine treatment group.


### 3.3. Serum NSE Measurement Results of the Two Groups of Patients

Serum NSE was measured for the two groups of patients. The NSE content of the cerebral ischemia group was greatly lower than that of the L-theanine treatment group (P<0.05), and the results were statistically and obviously different. When CIRI appeared in the two groups of patients, the serum NSE was measured again. At this time, the NSE content of the L-theanine treatment group continued to increase, which showed obvious advantages compared with the NSE content of the cerebral ischemia group (P<0.01). The results were statistically and remarkably different in the L-theanine treatment group. The specific data are shown in Figure 4.Figure 4
Comparison on serum NSE measurement results between the two groups of patients.


### 3.4. Results of Neurological Evaluation of the Two Groups of Patients

The neurological function of the patients was scored within 21 days. After statistics, the neurological score of the L-theanine treatment group after one day of treatment was 2.69 ± 0.34, and the neurological score of the patients in the cerebral ischemia group was 2.76 ± 0.61. With the gradual extension of time, the neurological function score of the L-theanine treatment group gradually decreased and the behavior function gradually improved. On the 7th day of treatment, the neurobehavioral scores of the two groups were statistically and observably different (P<0.05). The specific data are shown in Figure 5.Figure 5
Results of neurological evaluation of the two groups of patients.


## 3.1. MRI Scanning Results

MRI scans were performed on 30 patients diagnosed with cerebral ischemia in a selected hospital, and the fuzzy and noisy sample data were removed. A total of 47 MRI scan images were obtained. Based on the obtained MRI scan images, the patient was further diagnosed with cerebral ischemia. Figure1 shows two samples of the images.Figure 1
MRI scanning results of patients.


## 3.2. Analysis Results of rADC Data of the Two Groups of Patients

Table1 provides the rADC values based on mathematical model analysis in the cerebral ischemia group at different time points. There was a negative correlation between the variables X and Y (P<0.05 and a = 0.05). At this time, the linear relationship between the two variables was more obvious. As shown in Figure 2, at 9–12 h, the correlation coefficient of point 2 in the ROI met r < 0, the variables X and Y were negatively correlated at this time, and the linear regression equation was Y = 1.497–0.038X (P>0.05 and a = 0.05). There was no obvious linear relationship between the two variables at this time. At 9–12 h, the correlation coefficient of point 4 in the ROI met r < 0, the variable X and Y presented a negative correlation at this time, and the linear regression equation was Y = 1.462–0.044X (P<0.05 and a = 0.05). There was a more obvious linear relationship between the two variables.Table 1
Comparison on rADC values in different ROIs at different time points for patients in the cerebral ischemia group.
rADCInfarct time (h)1359121521Point 10.740.410.580.850.620.790.49Point 20.870.510.620.930.680.820.53Point 30.940.560.711.080.890.820.55Point 40.990.630.791.230.931.060.74Figure 2
Linear relationship between variablesX and Y in the cerebral ischemia group.Table2 provides the rADC values based on mathematical model analysis in the L-theanine treatment group at different time points. There was a positive correlation between variables X and Y (P<0.05 and a = 0.05), and the linear relationship between the two variables was more obvious. As given in Table 2, at 9–12 h, the correlation coefficient of point 3 in the ROI met r > 0, and the variables X and Y were positively correlated at this time (P>0.05 and a = 0.05). There was an obvious linear relationship between the two variables at this time. As shown in Figure 3, at 1–6 h, the correlation coefficient of point 2 in the ROI met r > 0, and the variables X and Y presented a positive correlation at this time (P<0.05 and a = 0.05). There was a more obvious linear relationship between the two variables. The linear regression equation was Y = 0.802 + 0.721X. Therefore, it was found that within 48 hours of measuring the rADC value of the L-theanine treatment group, the rADC values of the four points of interest all increase with time, and the variables X and Y were positively correlated with each other.Table 2
Comparison on rADC values in the L-theanine treatment group at different time points.
rADCInfarct time (h)134562448Point 10.740.811.011.030.980.790.86Point 20.830.941.141.171.150.880.99Point 30.871.021.211.231.170.951.03Point 40.941.181.361.371.281.061.16Figure 3
Linear relationship between variablesX and Y in the L-theanine treatment group.


## 3.3. Serum NSE Measurement Results of the Two Groups of Patients

Serum NSE was measured for the two groups of patients. The NSE content of the cerebral ischemia group was greatly lower than that of the L-theanine treatment group (P<0.05), and the results were statistically and obviously different. When CIRI appeared in the two groups of patients, the serum NSE was measured again. At this time, the NSE content of the L-theanine treatment group continued to increase, which showed obvious advantages compared with the NSE content of the cerebral ischemia group (P<0.01). The results were statistically and remarkably different in the L-theanine treatment group. The specific data are shown in Figure 4.Figure 4
Comparison on serum NSE measurement results between the two groups of patients.


## 3.4. Results of Neurological Evaluation of the Two Groups of Patients

The neurological function of the patients was scored within 21 days. After statistics, the neurological score of the L-theanine treatment group after one day of treatment was 2.69 ± 0.34, and the neurological score of the patients in the cerebral ischemia group was 2.76 ± 0.61. With the gradual extension of time, the neurological function score of the L-theanine treatment group gradually decreased and the behavior function gradually improved. On the 7th day of treatment, the neurobehavioral scores of the two groups were statistically and observably different (P<0.05). The specific data are shown in Figure 5.Figure 5
Results of neurological evaluation of the two groups of patients.


## 4. Discussion

With the further development of society, the aging of Chinese population has become inevitable, among which brain diseases among the elderly have gradually developed to the young. The sequelae of brain diseases such as stroke are more serious, causing serious economic burden and psychological pressure on the normal life of human beings. Among them, cerebral ischemia caused by stroke is more likely to cause death and disability.For patients with cerebral ischemia, clinical treatment methods are generally divided into stent therapy and drug therapy. Drug therapy includes thrombolytic therapy, neuroprotective agents, hyperbaric oxygen, and antioxygen free radicals. Thrombolytic therapy is currently the only therapeutic drug for cerebral ischemia approved by the U. S. Food and Drug Administration. Hypoxia in brain tissue may be caused by embolization of the internal carotid artery. Therefore, timely and effective thrombolytic therapy can recanalize the embolized blood vessel, thereby treating the ischemic penumbra in the brain tissue [15]. In current clinical practice, terephthalic acid (T-PA) is the only approved therapeutic drug for cerebral ischemia, which is used to dissolve embolism, but there are certain limitations in the use of T-PA. It is relatively safe to use within 4.5 h of cerebral ischemia. If it is used after more than 4.5 h, intracranial hemorrhagic transformation may occur due to the destruction of the blood-brain barrier and the neurotoxicity of the drug [16, 17]. Neuroprotective agents have been the research hotspots in clinical cerebral ischemia drug treatment in recent years and are usually divided into neurofactor superfamily, neurogenesis supercell family, and neurotrophic factor superfamily [18–20]. In addition to L-theanine selected in this study, mesencephalic astrocyte-derived neurotrophic factor (MANF) protein is also an effective neuroprotective agent, a class of neurotrophic factor family. Relevant studies have shown that under the conditions of endoplasmic reticulum stress, the expression of MANF protein may be upregulated to a certain extent. It is clinically found that MANF protein can effectively reduce the volume of patients with cerebral infarction and can improve the neurological score of patients. At the same time, it was found in in vitro experiments that these drugs also have a good protective effect on artificially cultured hippocampal neurons [21, 22]. In addition, related studies have shown that apigenin has a protective effect on the oxidative stress damage and apoptosis of PC12 cells induced by CoCl2. The IC50 of CoCl2 in PC12 cells is 1.2 mM, and the optimal effective concentration of apigenin is 10 μg·mL−1. The concentration at this time resulted in a reduction in the production of reactive oxygen species, inhibition of apoptosis, an increase in the number of viable cells, and improved matrix metalloproteinase (MMP) in PC12 cells that were damaged by CoCl2. These studies also proved that apigenin greatly improved the neurological deficit score of rats and reduced the infarct size. In conclusion, these results indicated that apigenin had great potential as a clinical therapeutic drug and may be helpful in the treatment of oxidative stress injury in CIRI.In this study, CIRI imaging was analyzed and researched based on mathematical model analysis, and the hidden laws behind MRI data were found using functional relations. But there were still some shortcomings in this study. The sample data based on mathematical model analysis were too small, resulting in the data credibility of the root model analysis not high enough. It was necessary to further expand the sample data and improve the establishment of the mathematical model to improve the credibility of the analysis data results. Further research on L-theanine neuroprotective agents was of great significance for the treatment of patients with cerebral ischemia, which was also an important work worth continuing to explore in the future.


## 5. Conclusion

This study was to use the partial differential mathematical model to analyze the magnetic resonance imaging (MRI) images of cerebral ischemia-reperfusion injury (CIRI) and to dynamically observe the role of L-theanine in CIRI based on this, aiming to further evaluate the value of L-theanine in the treatment of CIRI. The results showed that the partial differential mathematical model can effectively analyze the linear relationship between the rADC value and time of L-theanine in the treatment of CIRI. The cerebral ischemia group showed a negative correlation between the variablesX and Y at different time points (P<0.05 and a = 0.05). Within 48 hours of measuring the rADC value of the L-theanine treatment group, the rADC values of the four points of interest all increased with time, and there was a positive correlation between the variables X and Y. In observing the efficacy indicators of L-theanine, the L-theanine treatment group showed a significant advantage in the neurospecific enolase (NSE) content compared with the cerebral ischemia group (P<0.01). The neurological score of the L-theanine treatment group after one day of treatment was 2.69 ± 0.34, and the neurological score of the patients in the cerebral ischemia group was 2.76 ± 0.61 one day later. With the gradual extension of time, the neurological function score of the L-theanine treatment group gradually decreased, and the behavior function gradually improved.In this study, CIRI imaging was analyzed and researched based on mathematical model analysis, and the hidden laws behind MRI data were found using functional relations. But there were still some shortcomings in this study. The sample data based on mathematical model analysis was too small, resulting in the data credibility of the root model analysis not high enough. It was necessary to further expand the sample data and improve the establishment of the mathematical model to improve the credibility of the analysis data results. In addition, it verified the role of L-theanine in the treatment of CIRI, which was of a great effect and positive significance for the subsequent treatment of patients with cerebral ischemia, and also provided a reliable theoretical basis and data basis for the clinical treatment of CIRI.



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