96 RESEARCH ON THE APPLICATION OF APPLIED MATHEMATICS IN THE ASSESSMENT OF THOUGHT DISORDERS IN SCHIZOPHRENIA PATIENTS

Abstract Background Schizophrenia patients often have thinking disorders, which not only affect the patients’ daily life, but also cause them great trouble in social interaction and cognitive function. The assessment of thinking disorders is an important basis for clinical diagnosis and treatment. However, traditional assessment methods often rely on subjective judgment and have certain limitations. With the gradual development of applied mathematical methods, the objective assessment of thinking disorders using mathematical modeling and data analysis techniques has become a new trend. By combining mathematical models with the characteristics of schizophrenia thinking disorders, the accuracy and objectivity of the assessment can be improved. Methods The study selected 60 patients with schizophrenia and compared them with 30 healthy controls. All participants were evaluated for symptoms using the standard Positive and Negative Syndrome Scale (PANSS), focusing on the manifestations of their thought disorders. Combined with mathematical modeling methods, the study constructed a graph-based thought disorder assessment model, which can quantify the degree of thought disorder by analyzing indicators such as the patient’s speech structure and thought fluency. The study quantitatively analyzed the language samples of patients and healthy controls, used the model to calculate the score of thought disorder, and then evaluated the severity of thought disorder. Results The results show that applying mathematical modeling methods can effectively quantify thought disorders in patients with schizophrenia and produce a significant positive correlation with traditional assessment methods. Specifically, the scores of patients in the experimental group in thinking fluency, language complexity, and information processing ability were significantly lower than those in the control group, and the difference was statistically significant (P < 0.05). In the graph theory model assessment, patients’ thought disorder scores averaged 72.5 ± 6.3, compared with 36.2 ± 4.1 in the control group, a significant difference (P < 0.01). In addition, the study also found a significant positive correlation between thought disorder scores and positive symptoms (r = 0.75) and cognitive impairment (r = 0.68) in PANSS, indicating that thought disorder is closely related to patients’ symptom presentation. Through mathematical modeling assessment, patients’ thinking deficiencies can be better quantified, thereby providing clinicians with more precise treatment directions. The mathematical model shows good discrimination ability among patients at different stages of the disease, especially in the assessment of thinking disorders in patients in the acute stage, and is more sensitive than the traditional scale assessment method. Discussion Studies have shown that the application of mathematical modeling methods, especially the thought disorder assessment model based on graph theory, can effectively quantify the degree of thought disorder in schizophrenia patients with high objectivity and accuracy. Compared with traditional assessment methods, mathematical models can provide more detailed assessments, especially in the clinical treatment process, which can help doctors better understand patients’ cognitive disorders and provide a theoretical basis for the development of personalized treatment plans. By further optimizing this mathematical model, new support can be provided for the early diagnosis and personalized treatment of schizophrenia in future clinical applications.