Based on data released by the organizing committee of the 15th annual meeting of the Asian Society of Cardiovascular Surgery, we estimate there are currently 60 million potential heart disease patients in China, of which 8 million patients require cardiovascular surgery. We also surmise that globally two-thirds of heart attack patients can recover, but if ambulance service is not delivered in a timely or improper manner, the proportion of deaths will rise dramatically. In the United States, where medical resources are relatively abundant, the Institute of Medical Research's study of medical institutions in the past 40 years has demonstrated that 7% of patients have suffered as a result of serious medical errors. The World Health Organization reports that in countries such as Canada, New Zealand, and the United Kingdom, 10% of patients suffer from one medical adverse event every year [1]. The accuracy of the doctor's diagnosis, the implementation of ambulance service to patients, and a low error rate must be pursued. However, various errors frequently occur during medical treatment, which pose a threat to the life of patients [2].

As a country with relatively scarce medical resources, there are few theoretical and practical studies in the fields of medical quality and efficiency in China. The existing research focuses primarily on hospital management and the medical expert system. Current research on improving medical quality and reducing adverse events during medical treatment is typically based on the experiences of countries and regions with advanced medical and health management, such as the United States, Singapore, Taiwan, and Hong Kong. From the perspective of management science, the hospital is regarded as a service industry. From the perspective of patients, it is important to strengthen hospital management, improve the level and quality of physical therapy services, and reduce medical costs [3]. With the robustness of medical emergency decision making as the starting point, research on how to improve the quality and efficiency of the medical system is scarce. Existing research focuses mainly on the attitudes of ambulance personnel in the operating room and the development of personnel training models. From a medical perspective, the current diagnosis and treatment of cardiovascular diseases focus primarily on the development of medical technologies for specific diagnoses and treatments, while neglecting the study of models and systems, with even less research on medical process control.

The entire first aid process is a large complex system. The various data, information, and knowledge generated and used in it are employed as resources to support first aid decision making. They constitute a multilayer, heterogeneous, and massive complex information space. To represent this state, state space equations can be used, and subspaces can be transformed. A state space equation composed of matrices is a widely used form in subspace identification. Most of the subspace identification algorithms are carried out using subspaces and their mapping methods. In this paper, orthogonal projection is used to obtain the vector space for the state of first aid for heart disease [6].

The static structure (L) of the cardiac emergency decision-making system consists of the emergency information space M, the emergency reasoning space Q, and the emergency decision space D. The cardiac emergency information space is a vector space defined on a real or complex field F as M. It consists of dimension space, and dimension space contains collection space, and collection space contains attribute space. Therefore, M can be represented by the following quaternion:

Among them, Z, Se, and At represent dimension space, set space, and attribute space, respectively, and are composed of the emergency medical information vector. The dimension space constituting the emergency response decision M mainly includes the case dimension space Z_c of case-based reasoning (CBR), the rule dimension space Z_r of rule-based reasoning (RBR), the resource dimension space Z_e of decision reasoning, and the time dimension space Z_t of decision reasoning. The dimensional space is multidimensional, and the contained collection space or attribute space is heterogeneous. For example, the information in the vital sign collection Se_v in Z_c is different from the automatic control information in the medical emergency equipment collection Se_QU in Z_e. We introduce the definition of emergency reasoning space given in the cardiac emergency decision system below.

The knowledge structure composed of all the data, information, and knowledge of the subdecision process in the cardiac emergency information space is called the emergency reasoning space, which is represented by Q. Q can be expressed as a quaternion:

Among them, U represents the fusion first aid reasoning space metadata, A is the feature set of the first aid reasoning space; its feature value range is V, , where u_i is the feature value vector, and C is the solution of the first aid reasoning space. In Q, an inference information function is formed between C and U:

According to the properties of the corresponding space vector in the state space, the above relationship shows that Q can be divided into several subspaces. For Q, according to the definition of the state space for cardiac emergency, there are:

There is an invertible matrix S_i,I = 1,2,…,n such that A – BD^-1C = S_iA^-TS_i ^-1.

In space three, the information space for cardiac emergency decision making is constructed. The dimension is an item-level division of the entire cardiac emergency decision-making system, including case dimension (CBR), rule dimension (RBR), resource dimension, and time window. The concept of subsets is divided under the dimensions, and there is a corresponding subset under each dimension. The next level of attributes describes these subsets and their relationships in detail. Different subsets contain different attributes, and the subset attributes of different dimensions are described in different ways. This vector space system reflects the most important characteristics of cardiac rescue and is the core foundation for the establishment of a cardiac rescue model [7]. The ternary composition of M is a “dimension-subset-attribute” frame (digital subtraction angiography frame), which describes the entire dimension space of the first aid of the heart by constructing a dimensional matrix space. The concept of subset space is used to describe the content of each dimension space, and the attribute space is used to construct a local model frame in each subset space.

Dimension space (Z) is an 4D solid vector space structure model used to describe cardiac emergency information space. It mainly includes case-dimensional space, regular-dimensional space, resource-dimensional space and time-dimensional space. Z can be expressed as:

Among them, Z_c, Z_r, Z_e, and Z_t refer to the case dimension, rule dimension, resource dimension, and time dimension, respectively.

Subset space (Se) is a vector space structure model about a subset of features that exists in any dimension space in the 4D cardiac emergency information space. It can be seen that Z_c is a dimension space formed by and represents the richness of the emergency decision-making experience of the first-aid heart disease specialists. Attribute space (At) refers to the specific combination of attribute vectors that constitutes the space of each subset, and can be expressed as:

In the formula, at_di(se) represents the attribute component, subscript di represents the dimension, and se represents the subset component. Take the physical collection space Sev as an example to illustrate the correlation. Let body temperature, blood pressure, heart beat, and other attributes be denoted as a₁,a₂,a₃,…,at_CBR (Se_v), the attribute vector of the knife dimension, so at_CBR (Se_v) = {a₁,a₂,a₃,…,a_n}. The Dimension One Subset One Attribute framework of the cardiology emergency information space is shown in Figure 3. In Figure 3, a knowledge representation model of the state space for cardiac emergency response is constructed using the “dimensional-subset-attribute” framework [8].

The process of acquiring and transferring knowledge in the first aid reasoning space is complicated. In order to study the robustness of the first aid decision-making system, the dynamic performance of the first aid reasoning space needs to be studied. From these spaces containing decision-making reasoning information, a knowledge space (knowledge base) for decision-making processes is collected, extracted, and mapped from the cardiac emergency information subspace to the reasoning knowledge space. In the multidimensional cardiac emergency information space, the data sets required for decision-making reasoning are obtained and transmitted, and these data constitute heterogeneous knowledge of decision-making reasoning.

The neutron space of complex cardiac emergency decision making is recessive, random, or uncontrollable, and the information generated shows system characteristics such as multidimensional, dynamic, and uncertain. In terms of inference knowledge transfer, for all the attributes obtained in the decision-making process of cardiac emergency, using attribute reduction, the initial inference state space S formed, eliminating attribute redundancy and retaining the relevant attribute set of information, reasoning for t temporal. The space S is used for the information characterization of relationship mapping, the role of reasoning, or the influence of uncertain factors to obtain the t + Δt temporal reasoning state Sⁿ. In this way, the N_s step reasoning is performed, and finally, the emergency decision-making knowledge C is obtained, as shown in Figure 4 [9].

Regarding the state transition chain, for the two information state subspaces S = (U, AT, V, f) and S’ = (U’, AT’, V’, f’) of the state at any t and t + Δt in the emergency reasoning space Q, where AT, AT’ ⊂ A, S and S’ are the two reasoning state subspaces in Q.