## 2 Methodology
### Model Construction  
In the review of research on virtual reality (VR) technology for cognitive rehabilitation over the past decade, we have identified immersion and social interaction as two key factors influencing patient recovery outcomes. In terms of social interaction, VR applications for cognitive rehabilitation can be categorized into two broad types based on the number of participants: individual and multiplayer applications. Individual applications primarily serve a single patient [13], allowing them to engage in personalized cognitive training within a virtual environment through VR headsets or handheld devices, receiving immediate feedback, with a focus on providing a tailored rehabilitation experience. Multiplayer applications, on the other hand, involve interactions between patients, therapists, and other assistants. Multiple participants can engage in collaborative or competitive cognitive training within a shared virtual environment [14]. This not only enhances patients' cognitive abilities and response speed but also strengthens teamwork and social interaction among patients, thereby enhancing the overall effectiveness of cognitive rehabilitation.  
Furthermore, according to the level of immersion, VR technology applications can be classified into three types: non-immersive, semi-immersive, and fully immersive. Non-immersive virtual reality cognitive rehabilitation technology is suitable for patients with various cognitive impairments, providing personalized and controlled training environments to help them improve their cognitive functions [15]. For example, it can be used for patients with stroke, brain injury, Alzheimer's disease, and autism. In non-immersive settings, users are still aware of the real world's presence, usually interacting with the virtual environment through a computer screen or head-worn display. Semi-immersive virtual reality cognitive rehabilitation technology is appropriate for patients who require  
Figure 2: Trend in the number of relevant papers published per year from 2010 to 2023.  
both an immersive experience and a connection to the real world [16], such as those with Parkinson's disease, Alzheimer's disease, multiple sclerosis, and stroke. In semi-immersive environments, users partially perceive the real world while their senses are mostly engaged with the virtual environment, typically achieved through head-worn displays and surround sound. Fully immersive virtual reality cognitive rehabilitation technology is designed for patients who need deep immersion and full-body engagement [17], such as those with stroke, brain injury, Parkinson's disease, multiple sclerosis, and autism. In fully immersive settings, users are completely immersed in the virtual environment and are unaware of the real world's presence, usually experiencing the virtual environment through head-worn displays, panoramic projection, or panoramic display walls.  
By comprehensively considering both immersion and social interaction as key influencing factors, we have proposed a comprehensive multidimensional interactive system model (Figure 3)--the Multi-Dimensional VR Cognitive Rehabilitation Theory Model (MD-VRCRTM)--to better guide the practical application of VR technology in cognitive rehabilitation.