## 1 Introduction  
The increase in the number of aged in the Japanese population is faster than any other country and the elderly (aged 65 or over) comprised 27.3% in 2016 [1]. One critical issue accompanying aging is impairment of physical and cognitive abilities, with the decline in the ability to swallow particularly causing serious problems including aspiration pneumonia. Therefore, dysphagia difficulty with swallowing is a serious health concern in an aging society, and pneumonia has been the third most common cause of death in Japan from 2011 [2], with most of the pneumonia in the elderly ascribed to aspiration pneumonia caused by dysphagia [3; 4]. Disability in swallowing also increases the risks of suffocation, undernutrition, and dehydration, which have the potential to decrease the quality of life. Therefore, prevention and treatment of dysphagia are a social issue in an aging society with extended healthy life spans and social welfare concerns. Swallowing, or deglutition, is a coordinated and smoothly functioning process to propel food and drink from the mouth to the esophagus. Since it involves complex neuromuscular coordination [5], it is difficult to understand the physiological mechanisms. Videofluroscopic (VF) examination [6; 7] is commonly used in research and clinical settings as the preferred standard method for assessing swallowing function because of the comprehensive information it provides. This method allows anatomic and kinematic analysis such as the movement of food bolus and swallowing-related organs. Videoendoscopic (VE) examination [8; 9] is also widely used as a reliable and portable technique to observe the pharyngolaryngeal complex directly. However, the information on muscle activation patterns during swallowing cannot be obtained by these methods, though swallowing is controlled by the coordination of many muscles [5]. Surface electromyograms (sEMG) [10; 11] are the best way to estimate muscle activation patterns non-invasively so far, but the simultaneous measurement of swallowing-related muscles is limited. The main reason for this is that most swallowing-related muscles are located deep below the surface and overlap as if forming a layered structure. As a result, sEMG cannot avoid cross-talk problems in the simultaneous measurement of many muscles in swallowing. Therefore, conventional methods cannot provide information to quantify the sequential pattern of the muscles in swallowing. It is impossible to measure internal forces, such as joint contact forces and muscle strength, non-invasively with conventional techniques. Hence, biomechanical analysis using musculoskeletal models [12; 13; 14; 15] has been considered as an alternative technique to estimate such internal forces. For example, musculoskeletal models for the lower extremities were used to analyze complicated inter-muscle coordination in dynamic movement, such as in walking [16; 17], running [18], and jumping [19]. Upper extremity models [20; 21] were also developed for the biomechanical analysis of dynamic motion of the upper limbs, such as in throwing [22], propelling of wheelchair [23], and so forth. Presently, large-scale musculoskeletal analysis is readily conducted, as software for developing a complicated musculoskeletal model has become available commercially [12; 13] or as open-source software [14]. It may be expected that muscle activity during swallowing can be estimated in a similar manner as dynamic body movements even though most of the muscle activity involved in swallowing cannot be determined in vivo. However, there are few studies reporting musculoskeletal models of swallowing [24; 25]. The authors have reported a musculoskeletal model of swallowing by analyzing normal swallowing motion considering muscle activity [26; 27], but an analysis of details of the muscle activity in swallowing is still difficult and challenging. Previous studies on computational biomechanical analysis of swallowing mainly focused on the interaction between the bolus and organs considering fluid dynamics [28; 29; 30].