Measurement and Geometric Modelling of Human Spine Posture for Medical Rehabilitation Purposes Using a Wearable Monitoring System Based on Inertial Sensors
Abstract
:1. Introduction
2. Materials and Methods
2.1. Measurement System
2.2. Mathematical Model of the Spine
- A mathematical model based on polynomial functions: a 7th grade polynomial is required that is not time and computational efficient.
- A mathematical model based on spline functions: cubic functions for each segment. In this case, we ended with a nonlinear sistem of equations that we found to be difficult to use.
- A mathematical model based on circle arcs (Figure 4): the equations needed to calculate the radius and the coordinates of the imu sensors are only first grade relations. Thus, we get to a linear system of equations that is easier and faster to resolve.
- The wearable monitoring system provides orientation in 3-axis, but we are only using one axis (using all the axes is the subject of another research article).
- The proposed mathematical model is based on the approximation of the real curves with circle arcs and geometrical functions.
- The inputs of the model are the distances measured between the sensors on the flexible frame. The orientation angles are provided by the inertial sensors.
- The segments formed between two sensors are approximated with arcs of length l1, l2, l3, l4 and radius R1, R2, R3, R4. The circle arcs can have different radius, which in the common point have the same tangent to the slope that is equal with the measured value from the inertial sensors.
- The circle arcs will be tangent to each other and a smooth curve will be obtained.
- Determine the length of the circle arcs generated between two successive sensors: l1, l2, l3 and l4 based on radius (R1, R2, R3, R4) and measured angles (p1, p2, p3, p4, p5);
- Calculate the distances on X and Y axis for each sensor, except for the first, which is considered a reference: (d1x, d1y), (d2x, d2y), (d3x, d3y), (d4x, d4y), (d5x, d5y);
- Solve the linear system of 14 equations (Equations (1)–(7) from Table 1) with 14 unknowns (R1, R2, R3, R4, d1x, d1y, d2x, d2y, d3x, d3y, d4x, d4y, d5x, d5y);
- Calculate the (X, Y) coordinates for each sensor (x2, y2), (x3, y3), (x4, y4) and (x5, y5) and for maximum point (Xmax, Ymax);
- Calculate the coordinates of the circle center corresponding to the four arcs (see Table 1).
- The distance between the inertial sensors must be equal (and known), depending on the length of the spine;
- The position of the first sensor to be at the C7 vertebrae, which in general can be easily palpated;
- The prototype must be in contact with the skin. In the lumbar area of the spine, where there is a more pronounced curve, a flexible strap with a soft material can be used to push the sensing array closer to the spine.
2.3. Simulation of Mathematical Model
2.4. Hardware Equipment Analysis
2.4.1. Testing the Acquisition Board
2.4.2. Testing the Sensors
2.4.3. Testing the Wireless Communication
2.4.4. Testing the Local Data Storage
2.5. Measurement Protocol
2.6. Testing Methodology and Results
2.6.1. C2 Posture
2.6.2. A4 Posture
2.7. Visual Representation of Obtained Measurements
Error assessment
- The spine monitoring system is positioned in a C and S-shape corresponding to models A4 and C2;
- The orientation angles from the inertial sensors are given to the simulation software in which the mathematical model is implemented;
- The mathematical model calculates the coordinates of the sensors;
- The real coordinates of the sensors are manually measured on the testing table;
- We analyze the results from the simulation software with the manually measured distances.
3. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A
Name | Criteria | Results |
---|---|---|
A1 | Max point between P2 and P3; p1 > p2, p2 < p3, p3 < p4, p4 < p5. | |
A2 | Max point between P3 and P4; p1 > p2, p2 > p3, p3 < p4, p4 < p5. | |
A3 | Max point between P1 and P2; p1 > p2, p2 < p3, p3 < p4, p4 < p5. | |
A4 | Max point between P4 and P5; p1 > p2, p2 > p3, p3 > p4, p4 < p5. | |
B1 | Max point between P2 and P3; p1 > p2, p2 < p3, p3 < p4, p4 < p5. | |
B2 | Max point between P3 and P4; p1 > p2, p2 > p3, p3 < p4, p4 < p5. | |
B3 | Max point between P1 and P2; p1 > p2, p2 < p3, p3 < p4, p4 < p5. | |
B4 | Max point between P4 and P5; p1 > p2, p2 > p3, p3 > p4, p4 < p5. | |
C1 | Max point between P1-P2 and P3-P4; p1 > p2, p2 < p3, p3 > p4, p4 < p5. | |
C2 | Max point between P2-P3 and P4-P5; p1 > p2, p2 < p3, p3 > p4, p4 < p5. | |
C3 | Max point between P1-P2 and P3-P4; p1 > p2, p2 < p3, p3 > p4, p4 < p5. | |
D1 | Max point between P1-P2 and P3-P4; p1 > p2, p2 < p3, p3 > p4, p4 < p5. | |
D2 | Max point between P2-P3 and P4-P5; p1 > p2, p2 < p3, p3 > p4, p4 < p5. | |
D3 | Max point between P1-P2 and P3-P4; p1 > p2, p2 < p3, p3 > p4, p4 < p5. | |
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Single Max Point Curve (“C” Shape) | Double Max Point Curve (“S” Shape) | Equation Number |
---|---|---|
(1) | ||
(2) | ||
(3) | ||
(4) | ||
(5) | ||
(6) | ||
(7) | ||
(8) | ||
(9) | ||
(10) | ||
(11) | ||
(12) | ||
(13) | ||
(14) | ||
(15) | ||
(16) | ||
(17) |
Name | Criteria | Results |
---|---|---|
A4 | Max point between P4 and P5; p1 > p2, p2 > p3, p3 > p4, p4 < p5. | |
C2 | Max point between P2-P3 and P4-P5; p1 > p2, p2 < p3, p3 > p4, p4 < p5. | |
Characteristic | Bosch BNO055 | MPU 9150 | Flora LSM9DS0 | AltIMU 10 v.4 | MinIMU 9 V3 |
---|---|---|---|---|---|
Accelerometer | |||||
Measurement range | ±2 g to ±16 g | ±2 g to ±16 g | ±2 g to ±16 g | ±2 g to ±16 g | ±2 g to ±16 g |
Sensitivity | 1 LSB/g | 2 LSB/g | 0.732 LSB/g | 0.732 LSB/g | 0.732 LSB/g |
Gyroscope | |||||
Measurement range | ±125°/s to ±2000°/s | ±250°/s to ±2000°/s | ±245°/s to ±2000°/s | ±245°/s to ±2000°/s | ±245°/s to ±2000°/s |
Sensitivity | 16 LSB/°/s | 16.4 LSB/°/s | 70 LSB/°/s | 70 LSB/°/s | 70 LSB/°/s |
Magnetometer | |||||
Measurement range | ±1300 μT (x-, y-axis); ±2500 μT (z-axis) | ±1200 µT | 200 µT to 1200 µT | 200 µT to 1200 µT | 200 µT to 1200 µT |
Resolution | 0.3 μT | 0.3 μT | 0.48 μT | 0.47 μT | 0.47 μT |
Temperature sensor | Yes | Yes | Yes | No, includes a 24 bits barometer | No |
Size (mm) | 20 × 27 × 4 | 15.5 × 29 × 4 | Diameter of 16 mm, Width 0.8 mm | 25.4 × 12.7 × 2.54 | 20 × 13 × 3 |
Communication | HID-I2C/I2C/UART | I2C | SPI/I2C | I2C | I2C |
Supply voltage | 2.4 V to 3.6 V | 2.4 V to 3.46 V | 2.4 V to 3.6 V | 2.5 V to 5.5 V | 2.5 V to 5.5 V |
Power management | Yes, with three modes | No | Yes | No | No |
Statistic | Z1 | Z2 | Z3 | Z4 | Z5 |
---|---|---|---|---|---|
Nbr. of observations | 10 | 10 | 10 | 10 | 10 |
Minimum | 23.460 | 6.470 | −35.110 | −0.980 | 25.140 |
Maximum | 24.130 | 8.170 | −33.090 | 0.340 | 31.440 |
1st Quartile | 23.620 | 7.253 | −34.423 | −0.878 | 28.123 |
Median | 23.755 | 7.660 | −34.285 | −0.500 | 28.790 |
3rd Quartile | 23.900 | 8.028 | −33.865 | −0.215 | 30.638 |
Mean | 23.762 | 7.550 | −34.134 | −0.477 | 28.962 |
Variance (n − 1) | 0.050 | 0.371 | 0.369 | 0.192 | 3.796 |
Standard deviation (n − 1) | 0.223 | 0.609 | 0.607 | 0.438 | 1.948 |
Statistic | Z1 | Z2 | Z3 | Z4 | Z5 |
---|---|---|---|---|---|
Nbr. of observations | 10 | 10 | 10 | 10 | 10 |
Minimum | 24.060 | 23.120 | 16.400 | 2.680 | −14.160 |
Maximum | 25.550 | 23.920 | 17.280 | 4.000 | −12.740 |
1st Quartile | 24.475 | 23.265 | 16.750 | 2.870 | −13.908 |
Median | 24.930 | 23.345 | 16.955 | 3.130 | −13.510 |
3rd Quartile | 25.430 | 23.488 | 17.210 | 3.463 | −13.263 |
Mean | 24.889 | 23.401 | 16.948 | 3.238 | −13.536 |
Variance (n − 1) | 0.334 | 0.05 | 0.084 | 0.211 | 0.188 |
Standard deviation (n − 1) | 0.578 | 0.223 | 0.290 | 0.460 | 0.434 |
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Voinea, G.-D.; Butnariu, S.; Mogan, G. Measurement and Geometric Modelling of Human Spine Posture for Medical Rehabilitation Purposes Using a Wearable Monitoring System Based on Inertial Sensors. Sensors 2017, 17, 3. https://doi.org/10.3390/s17010003
Voinea G-D, Butnariu S, Mogan G. Measurement and Geometric Modelling of Human Spine Posture for Medical Rehabilitation Purposes Using a Wearable Monitoring System Based on Inertial Sensors. Sensors. 2017; 17(1):3. https://doi.org/10.3390/s17010003
Chicago/Turabian StyleVoinea, Gheorghe-Daniel, Silviu Butnariu, and Gheorghe Mogan. 2017. "Measurement and Geometric Modelling of Human Spine Posture for Medical Rehabilitation Purposes Using a Wearable Monitoring System Based on Inertial Sensors" Sensors 17, no. 1: 3. https://doi.org/10.3390/s17010003