Development of 3D reaching model for upper limb rehabilitation

다국어 초록 (Multilingual Abstract)

Upper limb impairment following neurological injuries such as stroke significantly limits independence in Activities of Daily Living (ADLs). In robot-assisted rehabilitation, reaching to spatial targets is widely used for high-dosage, task-specific training and quantitative assessment. However, clinical practice typically favors self-selected (comfortable) speed over maximum-speed instructions to ensure safety, increasing trial-to-trial variability in Movement Time (MT). Under these conditions, Fitts-based models that rely only on distance and target size may lose predictive power, and existing kinematic-based models with speed-related terms often fail to capture target-size effects and direction-dependent variability. Accordingly, this study proposed and validated a 3D reaching model that satisfies three requirements: (1) robustness to MT variability under self-selected speeds, (2) coverage of various target sizes, and (3) incorporation of direction-dependent MT variability in 3D reaching. Twenty healthy right-handed adults participated, and 3D hand trajectories were recorded using an optical motion capture system (250 Hz). Participants performed discrete pointto-point reaching to targets on a vertical panel. Data were collected from 72 conditions combining 3 movement distances (38.59, 42.01, 45.59 cm), 3 target widths (6, 9, 13 cm), and 8 movement directions, with 5 repetitions each (360 trials per participant). Compared with baseline models (3D Fitts and the Normal Reaching Model), the proposed model achieved the best performance (mean Adjusted R2 = 0.78, RMSE=80.60 ms) and maintained a stable quantile-based error of approximately 4–6%, reducing instability due to speed variation. The target-width term consistently reflected the speed–accuracy trade-off, and significance tests showed the target-width term was significant in 20/20 participants, the maximum-velocity term in 19/20, and the directional term in 14/20. Overall, the proposed model provides a robust baseline for predicting movement time in rehabilitation tasks with varying target sizes and 3D directions, supporting personalized difficulty scheduling and generalization to ADL-like tasks.

국문 초록 (Abstract)

뇌졸중 등 신경계 손상 이후 상지 기능 저하는 일상생활동작(Activities of Daily Living, ADL) 수행의 독립성을 크게 제한한다. 로봇 보조 재활에서는 목표 지점으로의 도달운동 (reaching)이 고반복 · 과제특이 훈련 및 정량평가를 위한 핵심 과제로 널리 활용된다. 그러나 임상 재활 환경에서는 안전성과 운동질을 고려하여 최대 속도 지시(as fast as possible)보다 편안한 자기선택 속도 수행이 일반적이며, 이로 인해 운동시간(Movement Time, MT)의 시 행 간 변동성이 커진다. 이러한 조건에서는 거리와 목표물 크기만으로 운동시간을 설명하는 기하학 기반 모델의 예측력이 저하될 수 있고, 속도 관련 항을 포함하는 기존 운동학 기반 모델도 목표물 크기 변화 및 3차원 공간에서의 중력에 따른 방향성 효과를 충분히 반영하지 못한다. 이에 본 연구는 (1) 자기선택 속도에서 발생하는 운동시간 변동성에 대한 강건성, (2) 다 양한 목표물 크기에 대한 포괄성, (3) 3차원 도달운동의 방향에 따른 도달운동 시간 변동성 반영이라는 세 요구조건을 동시에 만족하는 3차원 도달운동 모델을 제안하고 검증하였다. 실험은 건강한 오른손잡이 성인 20명을 대상으로 수행되었으며, Vicon 기반 모션캡처 (250 Hz)를 통해 손의 3차원 궤적을 측정하였다. 과제는 수직 패널 상의 목표물을 향한 단일 도달운동으로 구성하였다. 이동 거리 3수준(38.59–45.59 cm), 목표물 폭 3수준(6, 9, 13 cm), 이동 방향 8수준을 조합한 72조건을 각 5회 반복하여(총 360 trials/인) 데이터를 수집 · 분석 하였다. 비교 모델(3D Fitts, NRM) 대비 제안 모델은 평균 Adjusted R2=0.78 및 RMSE=80.60 ms로 가장 높은 예측 성능을 보였고, 운동시간 분위별 오차 분석에서도 약 4–6% 수준의 안 정적인 오차 분포를 유지하여 속도 변화에 따른 불안정성을 완화하였다. 또한 목표물 크기 항은 모든 참가자에서 일관되게 속도-정확도 상충 관계를 반영하는 방향으로 나타났으며, 항의 유의성 검정 결과는 목표물 크기 20/20, 최대 속도 19/20, 방향성 항 14/20 참가자에서 유의하였다. 본 연구의 통합 모델은 다양한 목표물 크기와 3차원 방향 조건을 포함하는 재활 과제에 서 운동시간을 강건하게 예측할 수 있는 기준선을 제공한다. 이는 향후 로봇 상지 재활에서 개인맞춤 난이도 조절, ADL 유사 과제에 대한 일반화에 활용될 수 있다.

목차 (Table of Contents)

• 1 Background 1
• 1.1 Stroke and Upper-Limb Motor Rehabilitation 1
• 1.1.1 Post-Stroke Upper Limb Motor Impairment and ADL Limitations 3
• 1.1.2 Neuroplasticity and Principles of High-Dosage, Task-Specific Training 3
• 1.2 Robot-Assisted Upper-Limb Rehabilitation 4
• 1.2.1 Robotic Systems as High-Dosage, Task-Specific Trainers 4
• 1.2.2 Reaching as a Prerequisite for Independence in ADLs 6
• 1.2.3 Planar Rehabilitation Robots and Limitations of 2D Workspaces 6
• 1.2.4 3D Rehabilitation Robots and ADL-Like Workspaces 8
• 1.2.5 Robotic Systems as Objective, High-Resolution Measurement Devices 9
• 1.2.6 Movement Time as an Upper-Limb Kinematic Measure 10
• 1.2.7 Limitations of Movement Time 12
• 1.2.8 Why Reaching Models Are Needed for Rehabilitation 13
• 1.3 Model-Based Evaluation of Reaching 14
• 1.3.1 Fitts' Law 14
• 1.3.2 Kinematic-Based Reaching Models 19
• 1.3.3 Importance of Target Width in Rehabilitation 24
• 1.4 Requirements for a 3D Reaching Model for Rehabilitation 25
• 1.4.1 Robustness to Movement Time Variability 26
• 1.4.2 Coverage of Various Target Widths (Accuracy Demands) 26
• 1.4.3 Addressing Spatial Complexity and Direction-Dependent Dynamics 26
• 1.5 Study Goal 27
• 2 Materials and Methods 29
• 2.1 Experimental Methods 29
• 2.1.1 Participants and Ethical Approval 29
• 2.1.2 Apparatus 31
• 2.1.3 Task and Experimental Protocol 35
• 2.1.4 Session Workflow and Calibration 36
• 2.2 Data Acquisition and Processing 37
• 2.2.1 Data Acquisition Pipeline 38
• 2.2.2 Pre-processing 40
• 2.3 Model Development: Term Selection and Formulation 41
• 2.3.1 Multiple Linear Regression Framework 42
• 2.3.2 Selection of the Representative Kinematic Term 44
• 2.3.3 Multicollinearity and Mathematical Coupling Checks 45
• 2.3.4 Modeling Distance and Target Width 48
• 2.3.5 Angular Term and Directional Effects in 3D 49
• 2.3.6 Proposed Model Formulation 50
• 2.4 Baseline Models and Statistical Analysis 51
• 2.4.1 Baseline Models and Proposed Model 51
• 2.4.2 Statistical Analysis 53
• 3 Results 57
• 3.1 Movement Time Characteristics 57
• 3.1.1 Directional Profile of Movement Time 58
• 3.1.2 Inter-Subject Variability 59
• 3.2 Detailed Coefficient Analysis of the Proposed Model 59
• 3.3 Overall Model Performance 61
• 3.3.1 Model Formulations for Comparison 61
• 3.3.2 Performance Evaluation 62
• 3.4 Requirement 1: Robustness to Movement Time Variability 63
• 3.4.1 Baseline Comparison for Kinematic Contribution 63
• 3.4.2 Overall Goodness-of-Fit Comparison 64
• 3.4.3 Quantile-wise Error Analysis (MAPE) 64
• 3.4.4 Verification of Robustness to MT Variability 65
• 3.5 Requirement 2: Coverage of Various Target Sizes 65
• 3.5.1 Overall Performance Comparison 66
• 3.5.2 Verification of Coverage for Various Target Sizes 66
• 3.6 Requirement 3: Addressing Spatial Complexity in 3D Reaching 67
• 3.6.1 Nested Model Comparison 67
• 3.6.2 Statistical Significance of Model Terms 68
• 3.6.3 Verification of Modeling 3D Spatial Complexity 69
• 3.7 Comparison by Shared Information Source 69
• 4 Discussion 71
• 4.1 Biomechanical Interpretation of Directional Constraints 71
• 4.1.1 Gravitational Constraints and Motor Compensation 72
• 4.1.2 Horizontal Anisotropy and Kinematic Redundancy 73
• 4.2 Implications for Clinical Application 76
• 4.2.1 Performance Gap in Pooled Fitting 76
• 4.2.2 Apparent Improvement and Practical Limitations 77
• 4.2.3 Generalization to Continuous ADL Tasks 79
• 5 Conclusion 81
• 5.1 Research Contributions 81
• 5.2 Limitations 82
• 5.3 Future Works 83
• References 85
• 초 록 93