# Validation of a Biomechanical Injury and Disease Assessment Platform Applying an Inertial-Based Biosensor and Axis Vector Computation

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Inertial Measurement Unit Device and Model Foundation

- X positive to the East (E).
- Y positive to the North (N).
- Z positive when pointing Up (U)

**Figure 2.**The local sensor coordinate system (SCS) is associated with the sensor as indicated by the (x, y, z) cartesian coordinate system, while the global reference coordinate system (GRCS) is matched to the elbow joint and anatomic orientation as indicated by the (X, Y, Z) cartesian coordinate system. Since the SCS is not aligned with the GRCS in this anatomic configuration, the data measured by the SCS is transformed through vector algebra by applying the unit quaternion $\left[\mathrm{c}\mathrm{o}\mathrm{s}\frac{\pi}{4},0,0,\mathrm{s}\mathrm{i}\mathrm{n}\frac{\pi}{4}\right]$, which rotates data in SCS by 90 degrees about the Z axis.

^{2}) and angular velocity (units of ◦/s) as provided in the SCS. These IMU-based sensors output angular velocities as a direct measurement from the internal gyroscopes. The 3D orientation output takes the quotient of the axis vectors as unit quaternions. The orientation can be represented by a normalized quaternion, q = [W X Y Z], with W being the real component and X, Y, Z as the imaginary global coordinate components. This sensor output is within the ENU localized global reference coordinate system. The output IMU measurement vector ${S}_{raw}$ contains the individual measurements stacked together as ten state variables:

#### 2.2. Inverse Kinematic Solutions Using Quaternions

#### 2.3. Biomechanical Orientation Tracking with Quaternions

#### 2.4. Instantaneous Axis Angle Origin Location Algorithm

## 3. Results

## 4. Discussion

- Global Description: Axis-angle representations allow for a global description of rigid body motion without suffering from singularities due to local coordinates. Unlike traditional Euler angles, which can result in singularities and ambiguities, axis-angle representations provide a more robust and accurate representation of limb kinematics.
- Geometric Description: Axis-angle representations provide a geometric description of rigid motion, simplifying biomechanical analysis and facilitating the understanding of kinesthesis (the feeling of movement) in skeletal and muscle structures. This geometric description is useful for applications such as computer-aided graphics, vision, and virtual reality.
- Quaternion Operations: Axis-angle representations can be easily converted to quaternion representations, which have well-defined operations for vector addition, multiplication, and interpolation. Quaternions offer a more efficient and accurate way to represent rotations compared to other methods.
- Simplified Biomechanics Analysis: Axis-angle representations simplify the analysis of joint biomechanics by providing a clear and intuitive representation of joint function and ligament health. They can be used to study the instantaneous axis of rotation, which plays a crucial role in joint functionality and overall locomotion perception and motor control.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Lapresa, M.; Tamantini, C.; di Luzio, F.S.; Ferlazzo, M.; Sorrenti, G.; Corpina, F.; Zollo, L. Validation of Magneto-Inertial Measurement Units for Upper-Limb Motion Analysis Through an Anthropomorphic Robot. IEEE Sens. J.
**2022**, 22, 16920–16928. [Google Scholar] [CrossRef] - Białecka, M.; Gruszczyński, K.; Cisowski, P.; Kaszyński, J.; Baka, C.; Lubiatowski, P. Shoulder Range of Motion Measurement Using Inertial Measurement Unit—Validation with a Robot Arm. Sensors
**2023**, 23, 5364. [Google Scholar] [CrossRef] [PubMed] - Pérez-Sanpablo, A.I.; Quinzaños-Fresnedo, J.; Romero-Ixtla, M.; Aguirre-Güemez, A.V.; Rodríguez-Reyes, G.; Pérez-Zavala, R.; Barrera-Ortiz, A.; Quijano-González, Y. Validation of inertial measurement units for the assessment of trunk control in subjects with spinal cord injury. J. Spinal Cord. Med.
**2023**, 46, 154–163. [Google Scholar] [CrossRef] [PubMed] - Riek, P.M.; Best, A.N.; Wu, A.R. Validation of inertial sensors to evaluate gait stability. Sensors
**2023**, 23, 1547. [Google Scholar] [CrossRef] [PubMed] - Gu, C.; Lin, W.; He, X.; Zhang, L.; Zhang, M. IMU-based Mocap system for rehabilitation applications: A systematic review. Biomim. Intell. Robot.
**2023**, 3, 100097. [Google Scholar] - González-Alonso, J.; Oviedo-Pastor, D.; Aguado, H.J.; Díaz-Pernas, F.J.; González-Ortega, D.; Martínez-Zarzuela, M. Custom IMU-based wearable system for robust 2.4 GHz wireless human body parts orientation tracking and 3D movement visualization on an avatar. Sensors
**2021**, 21, 6642. [Google Scholar] [CrossRef] [PubMed] - D’Amore, N.; Ciarleglio, C.; Akin, D.L. Imu-based manipulator kinematic identification. In Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA, 26–30 May 2015; pp. 1437–1441. [Google Scholar]
- Kim, W.; Veloso, A.P.; Araújo, D.; Vleck, V.; João, F. An informational framework to predict reaction of constraints using a reciprocally connected knee model. Comput. Methods Biomech. Biomed. Eng.
**2013**, 18, 78–89. [Google Scholar] [CrossRef] [PubMed] - Kim, W.; Vela, E.A. Freedom in Osteoarthritis of the Knee. Appl. Sci.
**2022**, 12, 839. [Google Scholar] [CrossRef] - Kim, W.; Araujo, D.; Kohles, S.S.; Kim, S.-G.; Alvarez Sanchez, H.H. Affordance-Based Surgical Design Methods Considering Biomechanical Artifacts. Ecol. Psychol.
**2020**, 33, 57–71. [Google Scholar] [CrossRef] [PubMed] - Fregly, B.; D’Lima, D.; Besier, T.; Delp, S.; Lloyd, D.; Banks, S.; Pandy, M. Grand challenge competition to predict in vivo knee loads. J. Orthop. Res.
**2011**, 30, 503–513. [Google Scholar] [CrossRef] - Ancillao, A.; Vochten, M.; Aertbeliën, E.; Decré, W.; De Schutter, J. Estimating the instantaneous screw axis and the screw axis invariant descriptor of motion by means of inertial sensors: An experimental study with a mechanical hinge joint and comparison to the optoelectronic system. Sensors
**2019**, 20, 49. [Google Scholar] [CrossRef] - Kim, W. The Knee Proprioception as Patient-Dependent Outcome Measures within Surgical and Non-Surgical Interventions. In Proprioception; IntechOpen: London, UK, 2020. [Google Scholar]
- Schumacher, A. Integration of a Gps Aided Strapdown Inertial Navigation System for Land Vehicles. Master’s Thesis, KTH Electrical Engineering, Stockholm, Sweden, 2006. [Google Scholar]
- Li, Y.; Liu, C.; Zou, H.; Che, L.; Sun, P.; Yan, J.; Liu, W.; Xu, Z.; Yang, W.; Dong, L. Integrated wearable smart sensor system for real-time multi-parameter respiration health monitoring. Cell Rep. Phys. Sci.
**2023**, 4, 101191. [Google Scholar] [CrossRef] - Trujullo, D.M.; Busby, H.R. Practical Inverse Anlaysis in Engineering; CRC Press: Boca Raton, FL, USA, 1997. [Google Scholar]
- Ancillao, A.; Vochten, M.; Verduyn, A.; De Schutter, J.; Aertbeliën, E. An optimal method for calculating an average screw axis for a joint, with improved sensitivity to noise and providing an analysis of the dispersion of the instantaneous axes. PLoS ONE
**2022**, 17, e0275218. [Google Scholar] - Kim, W.; Tretheway, D.C.; Kohles, S.S. An inverse method for predicting tissue-level mechanics from cellular mechanical input. J. Biomech.
**2009**, 42, 395–399. [Google Scholar] [CrossRef] [PubMed] - Kim, W.; Kim, Y.-H.; Veloso, A.P.; Kohles, S.S. Tracking knee joint functional axes through Tikhonov filtering and Plűcker coordinates. J. Nov. Physiother.
**2013**, 4, 11732. [Google Scholar] [CrossRef] - Tincknell, M. Quaternion. MATLAB Central File Exchange. 2023. Available online: https://www.mathworks.com/matlabcentral/fileexchange/33341-quaternion (accessed on 29 April 2023).
- Kuipers, J.B. Quaternions and Rotation Sequences; Princeton University Press: Princeton, NJ, USA, 1999. [Google Scholar]
- Gibson, J.J. The Ecological Approach to Visual Perception; Houghton Mifflin: Boston, MA, USA, 1979. [Google Scholar]
- Ball, R. A Treatise on the Theory of Screws; Cambridge University Press: Cambridge, UK, 1900. [Google Scholar]
- Kim, W.; Veloso, A.P.; Vleck, V.E.; Andrade, C.; Kohles, S.S. The stationary configuration of the knee. J. Am. Podiatr. Med. Assoc.
**2013**, 103, 126–135. [Google Scholar] - Den Hartog, D.; van der Krogt, M.M.; van der Burg, S.; Aleo, I.; Gijsbers, J.; Bonouvrié, L.A.; Harlaar, J.; Buizer, A.I.; Haberfehlner, H. Home-based measurements of dystonia in cerebral palsy using smartphone-coupled inertial sensor technology and machine learning: A proof-of-concept study. Sensors
**2022**, 22, 4386. [Google Scholar] [CrossRef] [PubMed] - Mittag, C.; Waldheim, V.; Krause, A.; Seel, T. Using a single inertial sensor to control exergames for children with cerebral palsy. In Current Directions in Biomedical Engineering; De Gruyter: Berlin, Germany, 2022; pp. 431–434. [Google Scholar]
- Van Meulen, F.B.; van Beijnum, B.-J.F.; Buurke, J.H.; Veltink, P.H. Assessment of lower arm movements using one inertial sensor. In Proceedings of the 2017 International Conference on Rehabilitation Robotics (ICORR), London, UK, 17–20 July 2017; IEEE: Piscataway, NJ, USA; pp. 1407–1412. [Google Scholar]
- Mendoza, M.J.; Gollob, S.D.; Lavado, D.; Koo, B.H.B.; Cruz, S.; Roche, E.T.; Vela, E.A. A Vacuum-Powered Artificial Muscle Designed for Infant Rehabilitation. Micromachines
**2021**, 12, 971. [Google Scholar] [CrossRef] [PubMed] - Mannel, H.; Marin, F.; Claes, L.; Durselen, L. Establishment of a knee-joint coordinate system from helical axes analysis-a kinematic approach without anatomical referencing. IEEE Trans. Biomed. Eng.
**2004**, 51, 1341–1347. [Google Scholar] [CrossRef] - Kim, W.; Espanha, M.; Veloso, A.; Araújo, D.; João, F. An Informational Algorithm as the Basis for Perception-Action Control of the Instantaneous Axes of the Knee. J. Nov. Physiother.
**2013**, 3, 2. [Google Scholar] [CrossRef] - Kim, W.; Veloso, A.; Araújo, D.; Machado, M.; Vleck, V.; Aguiar, L.; Cabral, S.; Vieira, F. Haptic perception-action coupling manifold of effective golf swing. Int. J. Golf Sci.
**2013**, 2, 10–32. [Google Scholar] - Kim, W.; Vela, E.A. A Tensional Network in the Knee. Biomed. J. Sci. Tech. Res.
**2021**, 40, 32073–32078. [Google Scholar] - Kohles, S.S.; Gregorczyk, K.N.; Phillips, T.C.; Brody, L.T.; Orwin, I.F.; Vanderby, R., Jr. Concentric and eccentric shoulder rehabilitation biomechanics. Proc. Inst. Mech. Eng. H
**2007**, 221, 237–249. [Google Scholar] [PubMed] - Kohles, S.S.; McClaren, J.W. A stochastic model validated with human test data causally associating target vehicle Delta V, occupant cervicocranial biomechanics, and injury during rear-impact crashes. J. Forensic Leg. Med.
**2022**, 91, 102431. [Google Scholar] [PubMed]

**Figure 3.**Graphical axis-angle representation for vector rotations. The approach described here uses a normalized quaternion q around which the rotation is defined by four kinematic variables instead of three. Applications include computer-aided graphics, vision, and virtual reality computation.

**Figure 4.**A simplified upper limb with point P is identified at the palmar surface of the hand with rotation about the shoulder joint and free accelerations, referred to as the RC frame [25]. Depending upon the limb’s orientation, the local acceleration due to gravity is subtracted directly from the IMU reading measured in the SC frame.

**Figure 5.**An infant dummy was used for the experimental validation test with vacuum-powered artificial muscles.

**Figure 6.**Comparison of trajectories between the quaternion model (blue, sampling rate 60 Hz) and determined data (red, sampling rate 10 Hz) for the dummy model.

**Figure 8.**A sequence of IAAs from the single human subject elbow is represented relative to the origin of the global frame to show that IAAs occupy different colors of lines (units in meters, m).

**Figure 9.**The elbow IAA trajectories as viewed at the oblique angle (

**a**) and the sagittal plane containing the motion of flexion and extension (

**b**). (units in meters, m).

**Figure 10.**Experimental procedure for angle measurements in two dimensions compared with the angles obtained from the IMU system. The vertical arm of the compass (in white) was fixed onto the lateral side of the upper arm. In contrast, the horizontal arm was mobile to perform accurate 180° amplitude rotations between two segment movements. IMUs and goniometer system coordinates are presented in red and dark grey, respectively. The errors between the two systems are a range of 5% errors.

**Figure 11.**The resulting angle differed by approximately 11% on average versus measurements taken by compass (circle).

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**MDPI and ACS Style**

Kim, W.; Vela, E.A.; Kohles, S.S.; Huayamave, V.; Gonzalez, O.
Validation of a Biomechanical Injury and Disease Assessment Platform Applying an Inertial-Based Biosensor and Axis Vector Computation. *Electronics* **2023**, *12*, 3694.
https://doi.org/10.3390/electronics12173694

**AMA Style**

Kim W, Vela EA, Kohles SS, Huayamave V, Gonzalez O.
Validation of a Biomechanical Injury and Disease Assessment Platform Applying an Inertial-Based Biosensor and Axis Vector Computation. *Electronics*. 2023; 12(17):3694.
https://doi.org/10.3390/electronics12173694

**Chicago/Turabian Style**

Kim, Wangdo, Emir A. Vela, Sean S. Kohles, Victor Huayamave, and Oscar Gonzalez.
2023. "Validation of a Biomechanical Injury and Disease Assessment Platform Applying an Inertial-Based Biosensor and Axis Vector Computation" *Electronics* 12, no. 17: 3694.
https://doi.org/10.3390/electronics12173694