# Estimation of the Abduction/Adduction Movement of the Metacarpophalangeal Joint of the Thumb
## 4 Discussion  
In this study, the correlation between thumb joints during grasps was explored, and a prediction model was obtained that allows the thumb MCP abduction/adduction angle to be estimated from the other joint motions of the thumb during grasp postures and free movements. Several correlations between thumb joints were found, in which MCP abduction/adduction presented the highest values: high correlation with CMC abduction/adduction (0.68), correlation with MCP flexion/extension (0.27), as well as negative correlation with CMC flexion/extension angles (\(-\)0.30). The results are in accordance with the previous literature. CMC-MCP correlation was previously derived analytically, since abductor/adductor muscles for the CMC joints are also abductors/adductors for the MCP joint [4]. The CMC-IP joint coordination is also present in previous studies [8] and reflects the fact that grasping, in general, requires flexing the joints to place the tip of the thumb in the grasping position. MCP flexion/extension appears poorly coordinated with the rest of the thumb joints. This result is novel with respect to the literature, in which it usually appears highly correlated with CMC flexion/extension movement during free actions such as circumduction and opposition movements [8]. These differences could be due to the fact that the activities used in our study are postures and not free movements, and therefore the coordination observed may be more linked to the object to be grasped (shape, weight, rigidity, etc.). Figure 8: Recorded MCP abduction/adduction (MCPA) angles versus the estimated MCPA angles during all the recorded frames/postures from set 1 (**b**) and set 2 (**a**). Subjects are presented in different colors. The model used to estimate the abduction/adduction of the thumb MCP joint obtained low estimation error (6.29 degrees), with no significant differences between grasps. In our model, MCP abduction/adduction movement is expressed mainly from CMC joint movements, which is in accordance with the literature. Due to the action of the muscles that act on these joints, the thumb MCP joint is closely linked to the movements of the thumb CMC joint [4,8]. The interaction between CMC joint movements also has a physiological meaning [18]: depending on the thumb position (more/less flexed or more/less abducted), thumb ligaments are distended or not, thereby allowing or blocking the MCP abduction/adduction movement. To the best of our knowledge, no previous studies have been conducted to obtain a prediction model for the MCP abduction/adduction joint movement as obtained herein. The model has been validated with other kinematic data with different grasp postures as well as during free movement (reach-to-grasp), with low estimation errors being obtained (ranging from 4.91 degrees to 5.58 degrees). The results could benefit many fields such as virtual reality or teleoperation, where many devices used to measure the kinematics of the hand (such as instrumented gloves) [19] do not typically include this joint movement. Since independent control of thumb joint motions affects the overall performance of the hand, synergistic approaches can provide viable solutions to simplify thumb models and for the design of prostheses and exoskeletons [7]. In this sense, biomechanical models, prostheses and exoskeletons may also benefit from it, by providing more accurate thumb joint positioning that it is important to incorporate for accurate thumb-tip force reproduction [7]. [PERSON]-[PERSON] and [PERSON] conceived the study, designed the experiments and contributed to the writing phase. [PERSON] performed the experiments and data analysis, as well as the writing phase. All authors have read and agreed to the published version of the manuscript. This research was funded by the project PGC2018-095606-B-C21 (MCIU/AEI/FEDER, UE). The study was conducted in accordance with the guidelines of the Declaration of Helsinki, and approved by the Ethics Committee of Universitat Jaume I (CD/31/2019, 6 th June 2019).