Journal of Biomechanical Science and Engineering

Transcription

1 Science and Engineering Development of the Transfemoral Prosthesis for Swimming Focused on Ankle Joint Motion* Motomu NAKASHIMA**, Shingo SUZUKI***, Ayako ONO** and Takashi NAKAMURA**** **Graduate School of, Tokyo Institute of Technology Oookayama, Meguro-ku, Tokyo , Japan ***Graduate School of Information, Tokyo Institute of Technology ****Research Institute, National Rehabilitation Center for Persons with Disabilities Abstract The objective of this study was to develop a prototype of transfemoral prosthesis for swimming focused on the ankle joint motion. This prosthesis has (i) an ankle joint which provides appropriate foot motion, (ii) the capability of walking on land by the poolside, (iii) and a foot whose appearance is sufficiently similar to an actual one. In order to confirm the validity of the developed prosthesis, a swimming experiment, in which a subject swimmer swam in a pool with the developed prosthesis attached, was conducted. The joint angles of the lower limbs were measured and an evaluation with questionnaires was performed. The validity of the proposed prosthesis was experimentally confirmed since the movable ankle joint with an appropriate spring brought a large foot motion, yielding a better swimming performance and more comfort to the swimmer. In addition to the experiment, the simulation of the swimming movement with the prosthesis was conducted. Through the simulation, the general validity of the developed prosthesis was confirmed since the simulation s result exhibited the same tendency as the experiment, in which a spring constant that was too large for the extension spring brought worse swimming performance. Key words: Swimming, Prosthesis, Welfare Engineering, Biomechanics, Simulation 1. Introduction *Received 28 Jan., 2013 (No ) [DOI: /jbse.8.79] Copyright 2013 by JSME For people with disabilities, recreational activities such as sports are important to improve the quality of life (QOL) from the physical, mental and social aspects. Among the sports for disabled persons, swimming is widely accepted especially by persons with lower limb amputation (1)(2). One possible reason for this is that persons with lower limb amputation can be released from the gravity, which heavily burdens them in their daily life. Another possible reason is that they can start swimming relatively easily compared to other sports because of many chances to observe and participate. Indeed, swimming is a sport suitable for rehabilitation since it is an effectively aerobic and full body exercise. From these backgrounds, swimming is becoming more popular as a sport and rehabilitation for the health enhancement of the persons with lower limb amputation. The persons with lower limb amputation usually swim without their prosthesis. However, several problems related to swimming without the prosthesis have been pointed out by the actual persons with lower limb amputation. For example, balance during swimming is not good, the amputated part is exposed to other people, and movement on land is difficult. In order to solve these problems, a prosthesis for swimming will be 79

2 necessary. Few developments of the prosthesis for swimming have already been reported. Hashizume et al. (3)(4) developed a transtibial prosthesis for swimming. This prosthesis had an appearance sufficiently similar to a real foot, and walking on land was possible. However, the ankle was fixed at the plantar-flexed position during swimming. In the actual flutter kick, the feet should take the plantar-flexed position during the downbeat (in the direction of hip flexion) in order to obtain the thrust. However, during the upbeat (in the direction of hip extension), the feet should not take the plantar-flexed position but should hang loosely from the ankles so that they do not prevent the propulsion (5). Therefore, in order to realize comfortable swimming, an ankle joint which provides appropriate foot motion is necessary. In addition, a prosthetic fin was developed for persons with transtibial amputation (6). Although this fin had beautiful industrial design and an excellent function in which the rigidity of the fin was adjustable, it did not aim to reproduce the appearance of the real foot, and walking on land was difficult. The objective of this study was to develop a prototype of transfemoral prosthesis for swimming focused on the ankle joint motion. This prosthesis has (i) an ankle joint which provides appropriate foot motion, (ii) the capability of walking on land by the poolside, (iii) and a foot whose appearance is sufficiently similar to an actual one. The developed prosthesis is explained in 2. The swimming experiment using the developed prosthesis is shown in 3. The simulation to confirm the general validity of the developed prosthesis is described in 4. The main findings obtained in this study are summarized in Developed Prosthesis The photographs of the developed prosthesis are shown in Fig. 1. It has an extension spring at the front part of the ankle joint. When no load is applied to the foot, the ankle joint becomes fully dorsi-flexed, as shown in Fig. 1(a). When the fluid force is applied to the foot during the down flutter kick (in the direction of hip flexion), it becomes fully plantar-flexed, as shown in Fig. 1(b). Therefore, the toe never disturbs the ability to walk on land since it keeps the dorsi-flexed position. In the water, on the other hand, the foot can automatically take the plantar-flexed position during swimming. Due to this simple but effective structure, the user does not need any extra procedure, such as exchanging the foot part, when he/she goes into/out of the water. In addition, it is possible for the swimmer to adjust the feeling due to a change in the spring constant of the extension spring. Note that the ankle joint has two stoppers so that the foot does not flex more than the fully dorsi-flexed and plantar-flexed positions shown in Fig.1, that is, the range of motion of the ankle joint was limited between those two positions. For the shank part, a standard endoskeletal prosthesis was used. The type of socket was a silicone liner type with the pin lock system (Iceross transfemoral, Össur) and the outer thermoplastic socket was partially reinforced with carbon fiber. The knee joint was a conventional manual locking knee joint, which was locked in the fully extended position when swimming. The photographs of the ankle joint and foot of the developed prosthesis are shown in Fig. 2. The foot is made of silicone resin. The bolts at the connecting part to the shank do not protrude from the side surface in order to avoid the risk of injury to the user. The total mass of the prosthesis including the endoskeletal shank was 2.9kg. A photograph of a swimmer with the developed prosthesis attached is shown in Fig. 3. By wearing a long spats type of swimwear, a natural appearance can be realized. 80

3 (a) Dorsi-flexed (b) Plantar-flexed Fig. 1 Photographs of the developed transfemoral prosthesis Fig. 2 Photographs of the ankle joint and foot of the developed transfemoral prosthesis Fig. 3 Photograph of a swimmer with the developed prosthesis attached wearing a spats type of swimwear 3. Swimming Experiment Using Developed Prosthesis 3.1. Methods In the experiment, a subject swimmer swam with the developed prosthesis attached. The subject swimmer was a person with an acquired one-sided transfemoral amputation 81

4 (male, 42 years old, height: 1.73m and weight: 76kg). He swims frequently and is an experienced swimmer. Before the experiments, the objective and method of the experiments were fully explained to the subject, and his written and oral consent to the experiments were obtained. The experiments were approved by the ethics committee of the Graduate School of Information at the Tokyo Institute of Technology. In addition, the experiments were conducted in the presence of a prosthetist. A photograph of the subject swimmer with the developed prosthesis attached is shown in Fig. 4. The subject set the liner on the residual limb, and the liner was fixed to the socket of the prosthesis with the pin attached in the end of the liner. The thigh support bandage was used as an adjunct to keep the prosthesis fixed when swimming. Four types of the extension spring were prepared for the experiment, as shown in Table 1. In Type A, the foot part was fixed in the dorsi-flexed position by use of a rigid bar instead of a spring. Type B was the case of a small spring constant (0.5N/mm) while Type C was the case of a large one (2.5N/mm). Type D was the case of no spring, that is, the ankle joint was completely free within the range of motion. Two kinds of experiments were conducted in the present study. First, the subject swimmer performed the flutter kick for 10 seconds holding onto the side wall of the pool. The motion of the subject was recorded by an underwater video camera from both sides. The joint angles were computed assuming that the motion was in the sagittal plane. For this purpose, markers were attached to the subject and the prosthesis, as shown in Fig. 5. The attaching positions were at the waist, great trochanter (hip joint), knee joint, ankle joint and toe for each leg. Second, the subject swimmer performed a 25m crawl swimming twice. The time Fig. 4 Subject swimmer with the developed transfemoral prosthesis attached Table 1 Type Type A Type B Type C Type D Ankle joint conditions of prosthesis Ankle joint condition Dorsi-flexed / Fixed Spring constant Small (k = 0.5 N/mm) Spring constant Large (k = 2.5 N/mm) Free 82

5 Fig. 5 Markers attached to subject swimmer records for 25m were measured. Note that the subject swimmer was asked to swim with a constant effort as much as possible. In addition to those video and time recordings, questionnaires about comfort during swimming were asked in VAS (Visual Analogue Scale) for evaluation just after the flutter kick as well as the crawl swimming. For the flutter kick, balance between both legs and easiness to perform the six beat kick were asked as relative evaluations in which the scores were compared with that of Type A (Dorsi-flexed / Fixed). In these evaluations, the score of Type A was 0 (center of the scale), conceivably better was 50 (right end of the scale), and conceivably worse was 50 (left end of the scale). For the crawl swimming, a feeling of propulsion during kicking was additionally asked. In addition to these relative evaluations, reaction during kick was asked as an absolute evaluation both for the flutter kick and crawl swimming. In this evaluation, appropriate was 0 (center of the scale), too heavy was 50 (right end of the scale), and too light was 50 (left end of the scale) Results and discussion Firstly it should be noted that the remarkable change in the combination of the arm stroke and the flutter kick occurred in the experiment of the crawl stroke. Before the experiment, the subject swimmer usually swam the crawl stroke with an irregular two beat kick. In general, the crawl stroke accompanies two or six beat kicks during one stroke cycle which is defined as the time in which both the upper limbs pull and push the water once for each limb. Since the subject swimmer could not perform an effective kick with the amputated leg, he kicked twice in one stroke cycle with the non-amputated leg. However, immediately after attaching the developed prosthesis, he started swimming the crawl stroke with the normal six beat kick. Indeed, it was a surprise for the subject swimmer, himself. The last time he swam with the six beat kick was more than twenty five years ago, before the amputation. This fact suggests the effectiveness and possibilities of the prosthesis for swimming. In the present experiment, the subject swimmer swam the crawl stroke with the six beat kick from the beginning to the end. The results of questionnaires for the crawl swimming were shown in Fig. 6. In all the relative evaluations shown in Fig. 6(a), (b) and (c), Type B (small spring constant) and Type D (free) were significantly higher than the other two types. Type B was slightly higher than Type D, and Type C (large spring constant) was higher than Type A (fixed). From Fig. 6(d), it was found that the reaction during the kick in Types B and D was appropriate, and that of Types A and C was somewhat too heavy. This was the reason for the fact that Types B and D brought better results than Types A and C. The results of the questionnaire for the flutter kick were shown in Fig. 7. Contrary to 83

6 Fig. 6 Results of the questionnaire about comfort for crawl swimming Fig. 7 Results of the questionnaire about comfort for flutter kick the crawl swimming, the relative evaluation of Type D (free) shown in Fig. 7(a) and (b) was worse. The reason for this may be seen in Fig. 7(c). From this figure, it was found that the subject swimmer felt the reaction during kick of Type D to be too light. This feeling might affect those two relative evaluations. Indeed, in the experiment of the flutter kick, the 84

7 subject swimmer could easily concentrate on the feeling of the lower limb. However, in the crawl swimming, the subject swimmer s consciousness might go to the feeling of overall propulsion rather than to that of the reaction force acting on the lower limb. The results of time records for the 25m crawl swimming were shown in Table 2. The average swimming speeds were also shown in the table, which were simply calculated as the length that was swum (25m) divided by the time records. Similar to the questionnaires, Type C (large spring constant) brought worse results than Type B (small spring constant) and Type D (free), and Type A (fixed) brought the worst results. Note that the swimming speeds for the trials of the flutter kick were not available since the swimmer did not propel but held onto the side wall of the pool in those trials. An example of images captured by the underwater camera for the experiment of flutter Table 2 Time records and average swimming speeds Type Time record [s] Average swimming speed [m/s] Type A (fixed) Type B (small spring constant) Type C (large spring constant) Type D (free) /10 6/10 2/10 7/10 3/10 8/10 4/10 9/10 Fig. 8 5/10 10/10 Images captured by an underwater camera for the experiment of the flutter kick (Type B, amputated side) 85

8 kick (Type B, amputated side) is shown in Fig. 8. One kicking motion is divided into ten time frames in this figure. It can be seen that the ankle joint moves appropriately to kick the water, that is, planter-flexing motion during the time frames 1/10 to 5/10, as well as dorsi-flexing motion during 6/10 to 10/10. The joint angles of the hip, knee and ankle were computed by digitizing the marker points in these images. Examples of the computed joint angles are shown in Fig. 9. The results of the non-amputated side (left leg) are shown in Fig. 9(a), while those of amputated side (prosthesis side) are shown in Fig. 9(b), both for the case of Type B (small spring constant). The abscissas in these graphs are in a non-dimensional time, in which one corresponds to one stroke cycle (6 flutter kicks by both legs during 2 strokes by both arms) in the crawl swimming. From Fig. 9(a), it was found that the amplitude of the knee joint was the largest among the three joints. Indeed, the amplitude of the hip joint was very small. Therefore, it can be said that this subject swimmer performed the flutter kick mainly by the knee joint on the non-amputated side. From Fig. 9(b), on the other hand, it was found that the flutter kick on the amputated side was performed mainly by the hip joint. This was because the knee joint of the prosthesis was completely fixed. It was also found that the amplitude of the ankle joint was much larger than that in the non-amputated side in this case. The results of the comparison among four types of the prosthesis for the ankle joint angles of the amputated side are shown in Fig. 10. In the case of Type A (fixed), the ankle joint became almost constant at the dorsi-flexed position. The small fluctuation was caused by the measurement error. In the case of Type C (large spring constant), it was found that the angle displaced into the plantar-flexed direction since the fluid force rotated the foot part in that direction. In the case of Type B (small spring constant), the angle almost reached zero (fully plantar-flexed). In the case of Type D (free), the angle also reached zero. However, since no restoring torque acted on the foot part, the angle did not reach 90 degrees (fully dorsi-flexed). All values of the amplitudes are shown in Table 3. As a result, the amplitude of the joint angle became largest in the case of Type B. To summarize the experimental results, the validity of our proposed prosthesis was Fig. 9 Joint angles for the experiment of the flutter kick (Type B) 86

9 Fig. 10 Comparison among four types of prosthesis for the ankle joint angles of the amputated side Table 3 Results of the amplitudes of the ankle joint angle (peak-to-peak) Type Amplitude [degree] Type A (fixed) N/A Type B (small spring constant) 85.0 Type C (large spring constant) 65.2 Type D (free) 75.1 confirmed since the movable ankle joint with an appropriate spring brought larger foot motion, yielding a better swimming performance and more comfort to the swimmer. 4. Simulation to Confirm General Validity of Developed Prosthesis 4.1. Objective of simulation As described in the previous section, the validity of the proposed prosthesis was experimentally confirmed. However, it was difficult to prove the validity statistically since it was difficult to recruit many subject swimmers for the experiment. Therefore, in this study, the general validity of the proposed prosthesis was examined by simulation Simulation method For the simulation, the swimming human simulation model SWUM was employed. SWUM was developed for the mechanical analysis of human swimming (7). In SWUM, the swimmer s body is represented as a series of 21 truncated elliptic cones. The fluid forces acting on the swimmer are assumed to be computable from the local motion of the swimmer s body. By inputting the body geometry and joint motion, the equations of motion of the swimmer as one rigid body are solved by means of the time-marching method. As a result, the user can obtain the fluid forces acting on the swimmer and the resultant swimming movement, such as swimming speed. Various studies by means of SWUM including its validations have already been conducted (8)-(15). For the simulation of the present study, SWUM was extended to calculate the swimmer with a prosthesis. The geometry of the right lower limb was modified to represent the prosthesis, as shown in Fig. 11. The prosthetic foot part was represented as one rigid body separated from the swimmer and was again connected by the virtual springs and dampers, as schematically shown in Fig. 12(a). Since this connection restricted only the relative translational movement at the connecting point, it enabled the free rotation at the ankle joint. The stiffness of the virtual spring was determined as a sufficiently large value so that the relative displacement between the working part and foot part at the connecting point 87

10 Journal of Biomechanical Fig. 11 Modified geometry of right lower limb in the simulation model (a) Connection by virtual springs and dampers (b) Representation of extension spring Fig. 12 Representation of the ankle joint in the simulation model became sufficiently small. In addition to this connection, the extension spring of the actual prosthesis was also represented in the simulation model, as shown in Fig. 12(b). The actual geometrical relationship of the attaching points of the spring to the working and foot parts were reproduced in the simulation model. In order to reproduce the stopper in the actual prosthesis, the spring stiffness was assumed to become sufficiently large when the angle of the ankle joint exceeds the range of motion. With respect to the analysis conditions, the standard model parameters which were used in the previous studies (7)(8), such as the body geometry except for the prosthesis part, joint motion of the crawl stroke, stroke cycle (1.96s), and the coefficients in the fluid force model, were used in the present simulation Simulation of flutter kick Analysis conditions In order to reproduce the experiment of the flutter kick, the simulation of the flutter kick was carried out. In this simulation, the absolute movement of the swimmer was not solved by the time-marching method but given as the input, since the swimmer did not 88

11 propel in the experiment. Among the six degrees-of-freedom of the absolute movements of the swimmer, the translational movements in the three directions were assumed to be zero and the rotational movements in two directions except for the roll movement were assumed to be zero as well. For the roll movement, the roll angle measured in the experiment was input into the simulation. Since the motion of the upper limbs was unnecessary for this simulation, the upper limbs were fixed in a straightly stretched position. Five stroke cycles were simulated in order to eliminate the effect of the initial condition Results and discussion The swimming motion of the flutter kick in the case of Type B (small spring constant) was shown in Fig. 13. The symbol t * represents the non-dimensional time normalized by the stroke cycle (1.96s). Since the motion was the six beat crawl, one leg beat three times in one stroke cycle. Therefore, only one-third of the fifth cycle is shown in Fig. 13. The fifth cycle starts at t * = 4.0 and ends at t * = 5.0. In order to compare with the experimental results shown in Fig. 8, the period of t * = 4.2 ~ 4.5 is shown in Fig. 13 since the down kick followed by the up kick of the right (prosthetic) lower limb was performed in this period, as the same as shown in Fig. 8. The prosthetic foot is shown in green. The red lines from the swimmer s body represent the point of applications, directions and magnitudes of the fluid forces acting on the swimmer s body. From the figure, it can be seen that the prosthetic foot moves from the plantar-flexed position to the dorsi-flexed position, and vice versa. The t * = t * = t * = t * = t * = t * = t * = t * = t * = t * = Fig. 13 Swimming motion of the flutter kick (Type B) 89

12 Ankle joint angle [deg] Type A Type B Type C Type D Non-dimensional time Dorsi-flexion Planter-flexion Fig. 14 Results of the simulation for the ankle joint angles of the amputated side Table 4 Results of the amplitudes of the ankle joint angle (peak-to-peak) Type Amplitude [degree] Type A (fixed) N/A Type B (small spring constant) 83.8 Type C (large spring constant) 63.9 Type D (free) 80.3 results of simulation for the ankle joint angles of the amputated side are shown in Fig. 14. By comparing these results with Fig. 10, it was found that the overall tendency in the simulation was very similar to that in the experiment. Type A (fixed) was almost always 90 degrees. Type D (free) reached the fully plantar-flexed position and almost reached the fully dorsi-flexed position. With the spring, Type B and Type C (large spring constant) almost reached the fully dorsi-flexed position. Type B also reached the fully planter-flexed position while Type C did not. These are the same tendencies as in the experiment. The amplitudes of the ankle joint angles are shown in Table 4. The order of the amplitude was B > D > C > A, which was the same as the one in the experiment shown in Table Simulation of crawl stroke Analysis conditions In order to reproduce the experiment of the crawl stroke, the simulation of the crawl stroke was carried out. In this simulation, the six degrees-of-freedom movement of the swimmer was fully calculated. In addition, in order to prevent sinking of the lower half of the swimmer s body, the amplitudes of the flexion/extension at the hip joint were set to 1.5 times that of the standard value for both lower limbs. The amplitudes of the knee and ankle joints in the non-amputated side were also set to 1.5 times. Ten stroke cycles were simulated in order to eliminate the effect of the initial condition Results and discussion The swimming motion of the crawl stroke in the case of Type B (small spring constant) was shown in Fig. 15. Similarly to the same as the case of the flutter kick, it can be seen that the prosthetic foot moves from the plantar-flexed position to the dorsi-flexed position, and vice versa. The results of the swimming speed and propulsive efficiency are shown in Table 5. The propulsive efficiency η is an index which is generally used in the mechanics of swimming, and defined as: UD η = (1) P 90

13 t * = 9.0 t * = 9.5 t * = 9.1 t * = 9.6 t * = 9.2 t * = 9.7 t * = 9.3 t * = 9.8 t * = 9.4 t * = 9.9 Fig. 15 Swimming motion of the crawl stroke (Type B) Table 5 Results of crawl stroke simulation Type Swimming speed [m/s] Propulsive efficiency Type A (fixed) Type B (small spring constant) Type C (large spring constant) Type D (free) where U, D and P respectively represent the time-averaged swimming speed, the whole drag acting on the swimmer when the swimmer takes a gliding position, and the time-averaged power consumed by the swimmer. As shown in Table 5, the values of Type B (small spring constant) and Type D (free) became almost equal. Compared to Type B and D, Type C (large spring constant) brought worse result, and Type A (fixed) brought the worst result. This tendency was consistent with that in the experiment. Therefore, the general validity of the developed prosthesis was confirmed. 5. Conclusion The transfemoral prosthesis for swimming focused on the ankle joint motion was developed in the present study. A swimming experiment, in which a subject swimmer with 91

14 the developed prosthesis attached swam in a pool, was conducted. The joint angles of the lower limbs were measured and the evaluation by questionnaires was performed. The validity of the proposed prosthesis was experimentally confirmed since the movable ankle joint with an appropriate spring brought larger foot motion, yielding a better swimming performance and more comfort to the swimmer. In addition to the experiment, the simulation of the swimming movement with the prosthesis was conducted. By the simulation, the general validity of the developed prosthesis was confirmed since the simulation result exhibited the same tendency as the experiment, in which too large of a spring constant for the extension spring brought worse swimming performance. As a future task, more detailed simulation study should be conducted in order to clarify the optimal spring constant and its dependency on the motion speed as well as the physique of the swimmer. As another future task, it will be useful to employ the movable knee joint for more natural movement and better swimming performance. Acknowledgments The authors wish to thank the subject swimmer for his cooperation in the experiment. References (1) Kegel, B., Carpenter, M.L. and Burgess, E.M. A Survey of Lower-Limb Amputees: Prosthesis, Phantom Sensations, and Psychosocial Aspects, Bulletin of Prosthetics Research, Vol. 10, No. 27, (1977), pp (2) Kegel, B., Webster J.C. and Burgess, E.M. Recreational Activities of Lower Extremity Amputees: A Survey, Archives of Physical Medicine and Rehabilitation, Vol. 61, No. 6, (1980), pp (3) Hashizume, T. Below-Knee Prosthesis for Sports (in Japanese), Bulletin of the Japanese Society of Prosthetic and Orthotic Education, Research and Development, Vol. 7, No. 2, (1991), pp (4) Betto, A., Hashizume, T., Kubo, S., Hirose, I., Hayashi, T., Oshima, T., Honjo, Y., Takahashi, R. and Matsubara, M. Sports and Prosthesis. Joint of an Artificial Leg for Swimming., Journal of the Japanese Academy of Prosthetist and Orthotist, Vol. 6, No. 3, (1998), pp (5) Maglischo, E.W., Swimming Fastest, (2003), p.86, Human Kinetics. (6) Aguilar, M., Design: Prosthetic Flippers Could Help Amputees Swim Again. WIRED. (online), available from < (accessed ). (7) Nakashima, M., Miura, Y. and Satou, K. Development of Swimming Human Simulation Model Considering Rigid Body Dynamics and Unsteady Fluid Force for Whole Body, Journal of Fluid Science and Technology, Vol. 2, No. 1, (2007), pp (8) Nakashima, M. Mechanical Study of Standard Six Beat Front Crawl Swimming by Using Swimming Human Simulation Model, Journal of Fluid Science and Technology, Vol. 2, No. 1, (2007), pp (9) Nakashima, M. Analysis of Breast, Back, and Butterfly Strokes By The Swimming Human Simulation Model SWUM, Bio-mechanisms of Swimming and Flying - Fluid Dynamics, Biomimetic Robots, and Sports Science - (eds. Naomi Kato and Shinji Kamimura), Springer, Tokyo, (2007), pp (10) Nakashima, M. Simulation Analysis of the Effect of Trunk Undulation on Swimming Performance in Underwater Dolphin Kick of Human, Journal of Biomechanical, Vol. 4, No. 1, (2009), pp (11) Kiuchi, H., Nakashima, M., Cheng, K.B. and Hubbard, M. Modeling Fluid Forces in the Dive Start of Competitive Swimming, Journal of Biomechanical Science and Engineering, Vol.5, No.4, (2010), pp (12) Nakashima, M., Kiuchi, H. and Nakajima, K. Multi Agent/Object Simulation in Human Swimming, Journal of Biomechanical, Vol. 5, No. 4, (2010), pp

15 (13) Nakashima, M., Suzuki, S. and Nakajima, K. Development of a Simulation Model for Monofin Swimming, Journal of Biomechanical, Vol. 5, No. 4, (2010), pp (14) Nakashima, M. Modeling and Simulation of Human Swimming, Journal of Aero Aqua Bio-mechanisms, Vol.1, No.1, (2010), pp (15) Nakashima, M., Maeda, S., Miwa, T. and Ichikawa, H. Optimizing Simulation of the Arm Stroke in Crawl Swimming Considering Muscle Strength Characteristics of Athlete Swimmers, Journal of Biomechanical, Vol. 7, No. 2, (2012), pp