Mechanical Science and Engineering, Graduate School of Engineering, Nagoya University, Furo-cho,Chikusa-ku, Nagoya, Japan.

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1 4B4 Copyright C 2018 一般社団法人日本機械学会 Estimation of Intervertebral Joint Location for Improving the Accuracy of Compressive Force on Lumbar Spine Siryou Tou* 1, Yoji Yamada 1, Xiaohan Xiang 1 and Naoki Kudo 2 1 Mechanical Science and Engineering, Graduate School of Engineering, Nagoya University, Furo-cho,Chikusa-ku, Nagoya, Japan. 2 Kawasaki Heavy Industries, Ltd, 1-1,kawasaki-cho, Akashi, Japan. The study aims to develop a non-invasive method to estimate the location of intervertebral joint from L1 though S1. Due to a lack of validation test methodology, robotic care devices are not validated to be safe in their use. Validation requires calculation of the load of stress on lumbar spine since the compressive force on the Lumbar spine is one cause of low back pain. In our research, we choose the Non- Invasive method to estimate the force on lumbar spine by using the 3D motion capture system. For enhancing the accuracy of evaluating, we make an area-constant hypothesis to verify the method for estimating the distance between the back surface and the intervertebral joint and estimate the location of intervertebral joint. Key Words : Lumbar spine; CS; location of L1-S1; low back pain; area-constant model Introduction * Correspondence: tao.ziliang@c.mbox.nagoya-u.ac.jp 1 Mechanical Science and Engineering, Graduate School of Engineering, Nagoya University, Furo-cho,Chikusa-ku, Nagoya, Japan [No.18-3] 第 23 回ロボティクスシンポジア講演論文集 , 焼津 Background Many care workers have low back pain (LBP) due to heavy load of transferring tasks. While the need for care giving is increasing with the background of Japanese super aging society. According to the literatures, we know that there are two types of low back pains (LBPs) acute and chronic low back pains. (1) The biggest reason causing a chronic low back pain is disc degeneration. (2) Since too much load on the disc may cause its degeneration, we need to measure the compressive force existing on the disc so that we could reduce the risk of causing LBP. 1 2 Previous work Invasive method Nachemson et al. measured the load on lumbar disks in different positions of the body by using a membrane-covered needle which was connected to a pressure transducer on autopsy to verify the hydrostatic properties of the nucleus pulposus. This needle can be performed in the living man. The measuring needle is inserted from behind at an angle of 45 degree to the sagittal plane at the level of the disk to be test. (3) Wilke et al. measured intradiscal pressure to complement earlier data from Nachemson with dynamic and long-term measurements over a broad range of activities. He also used a pressure transducer with diameter of 1.5mm and implanted the pressure transducer in the nucleus pulposus of nondegenerated L4-5 disc of a volunteer. Pressure was determined during exercise while standing, lifting activities, sitting unsupported on a stool or an ergonomic sitting ball, sitting in different postures and others. Good correlation was found with Nachemson's data during many exercises, but there were still a little different in the results of standing posture and sitting posture between two groups, these differences may be explained by the different transducers used. (4) Kazuaki Takahashi also did the experiment with a pressure transducer. The different point was he only measured the pressures during bending and standing up back. The subjects in this experiment need to bend about 30 degree in 10s, and hold the posture in 20s then stand up in 10s. (5) These researchers implanted pressure transducers which is shown in Figure 1 into the disc of volunteers. And the compressive force was determined during the exercise. Among the three exercise, the experiment of Takahasi is the simplest one to reproduce for us Non-invasive method In Kudo and Honjou's experiment the subjects were asked to do the same action as Takahasi's experiments. The researchers measure the body position data of the subjects by using a 100 Hz's motion capture system (6) because the invasive method is harmful to the human body. For accurately estimating the force exerted on the lumbar spine, they set up two model after analyzing the data. The L5/S1 is on the back surface directly and the L5/S1 is in vivo. The error of two models is mainly 0.32KN.For example when the subject bent to 20 degree with 10kg load,

2 the computed result is about 2.93KN in model 1and 2.61KN in model 2 (7). 2 1 Measurement of the distance. We define ' li as the distance from back surface to the vertebral body in each level of lumbar spine, and divide it to two parts li and ', the distance from vertebral body to spine process and the distance from spine process to back surface. Figure 3 shows the definition of the 3 parameters in the level. Fig. 1 Pressure transducer. (5) This is the pressure transducer used in Nachemson s experiment. By comparing with the results of invasive methods, they found that the model 2 is more accurate and for estimating the compressive force on lumbar spine, the accurate locations of the lumbar body are needed. Though the results of the invasive method are more accurate, it is harmful for the volunteer. For this reason, we decide to use the non-invasive method. Fig. 3 The distance from back surface to vertebral body. ' li is the distance from back surface to vertebral body in each level, li is the distance from vertebral body to spinous process in each level, ' is the distance from back surface to spinous process. So the distance ' li will be Fig. 2 Two model simulated by using the data from Motion capture. The location of L5/S1 is on the back surface in model1, and the L5/S1 is in vivo with a short distance from back surface in model2. (7) 1 3 Objective According to the results of the two models, we can consider that the distance from back surface to the lumbar spine which is defined as shown in Figure 2 is needed to calculate the compressive force accurately., llll =, + llll (1) It is easy for us to find that li is constant, so we can compute ' li by calculating '. 2 2 Calculation of ' Firstly, we set several assumptions: The area (S) between the skin and spinous process is constant, and ' is same in each part of lumbar spine. Fit the curve which is composed of all points, and obtain the following polynomial function. Figure 4 shows the model of this method. ff(xx) = aaxx 3 + bbxx 2 + cccc + dd (2) According to the ff(xx), we can obtain the first derivative ff (xx) = 3aaxx 2 + 2bbxx + cc (3) and the second derivative ff (xx) = 6aaxx + 2bb (4) Method for estimating the distance

3 ss(ii) = ββ(ii) 2222,22 + αα(ii) ππ, rr(ii) (9) If it is not convex, but concave, the area of the arch will be ss(ii) = αα(ii) 2222 {[rr(ii) +, ] 22 rr 22 (ii)} = αα(ii) 2222 [, , rr(ii)] (10) And in this condition I define ββ(ii) = αα(ii) so the area will be Fig. 4 Calculation of '. The green points are the locations of markers which are attached on L1-S1 (without L5). The yellow points are the location of each spinous process we estimated. S is the area in each two markers and two spinous process αα is the central angle of the arc which fitted by two markers Using the ff (xx) to obtain the central angle αα(ii) = (11,ff (xx ii )) (11,ff (xxii+11 )) 11,ff (xx ii ) 11,ff (xx ii+11 ) Using the ff (xx) and ff (xx) to obtain the radius of curvature of each point 11 = ff (xx ii ) ρρ(xx ii ) [11+ ff (xx ii ) ] 22 (5) (6) ss(ii) = ββ(ii) 2222 The total area (s) is,22 + αα(ii) ππ, rr(ii) (11) 55 SS = ii=11 ss(ii) (12) Finally, we can obtain the following function 55 ( ββ(ii) 2222 ii=11 ), [ αα(ii) ii=11 rr(ii) ], SS = 00 (13) The value of S is calculated by use of MR images. Figure 5 shows the distance from back surface to each vertebral body and spinous process. After the calculation of S, we can obtain,. ππ Assume that there is an arc between each two points on the back surface. And the radius of this arc rr(ii) = ρρ(xx ii )+ρρ(xx ii+11) 22 (7) Then, check each arc if it is convex or not. If it is convex, the area of the arch will be ss(ii) = αα(ii) 2222 {rr22 (ii) [rr(ii), ] 22 } = αα(ii) 2222 [, , rr(ii)] (8) In this condition, I define ββ(ii) = αα(ii), so the area will be Fig. 5 MR image in upright standing posture. The MR image was obtained after the experimental design and was

4 approved by the ethical committee in the school of engineering, Nagoya University. Experiment bending task In order to calculate the value of,, we need to estimate the back surface curve which is shown in (2) and Figure 4. For fitting this curve, the locations of each green points in different posture are needed. So we do the bending experiment. In this experiments, the subject is a 24-year old, 167cm high, 57kg weigh, healthy man. There were 6 markers attached on his back surface. Figure 6 shows where and how the markers are attached along the lumbar line. The subject is asked to stand in an upright posture and perform a forward bending operation after a signal to start the operation. The subject is instructed bend forward in 10 seconds from upright standing to the greatest flexion position, and recovery to upright posture in another 10 seconds. And the subject repeat the experiment 20 times. In order to capture the position data of each part of the body, measurement was made with a 100 Hz three-dimensional motion capture system (Motion Analysis MAC3D System, manufactured by Motion Analysis Corporation). And then, we calculate the angle θθ between the trunk and vertical direction in each time. We define this angle θθ as the bending one. Figure 7 is the bending progress in 20 trails. It shows the motion of the subject who starts the experiment at about 3s to 4s, bends to the greatest flexion posture, 60 to 70 degree, at 10s to 12s and then recovers to the upright posture. Fig. 7 Bending angles during the experiments. 4 2 Results of, in 20 trails of experiment The blue points in Figure 8 are the calculated results of, in different postures. Figure 8 shows the calculated results of, during 20 trails of the experiment. Fig.6 Marker locations for experiment estimating the intervertebral joint location Fig. 8 The calculated results of, during the 20 trails of experiment. Results 4 1 Results of the movements We fit the line of trunk which contains all points in the lumbar area, and obtain the following formula ll(xx) = kkkk + bb (14), ranges from 10.8mm to 10.0mm which means in the standing posture the distance from back surface to spinal process is almost largest and it decreases along the flexion motion of the subject and turn to the smallest value when the subject flexion to the deepest. We can find that there are roughly two fluxes of the results in Figure 8. One flux is the results during the bending process, and the other is the standing up process. One reason causing this is due to the fact that after a

5 flexion motion reaches the deepest, the tape has stretched to the longest. When the subject stands up, there will be a small gap between the marker and his skin since the skin quivers. Furthermore, muscles are stretching, during flexion motion, while, muscles are contracting during standing up, and the shape of muscles are not necessarily the same. Based upon the results of the bending angle obtained in Figure 7, we can find that there are some small fluctuations during the experiment meaning the trunk of the subject quivers. This kind of quivers is considered to influence the distance between back surface and spine process. We can obtain that when the bending angle is closed to 0 degree where the subject is in the upright standing posture, the value of, is in the range of 10.5mm to 10.8mm. Compared with the MR image shown in Figure 5, we consider the results are basically reliable. In order to analyze the relationship easily, we simulate the calculated results shown in Figure 8 and apply the regression curve shown in Figure 9., = θθ θθ θθ ) According to this function we can easily obtain the value of, in different postures. Fig. 10 Distance from back surface to each vertebral body in each level. 5. Discussion There are some points which should be improved. First, the computed results are not smoothly varying. This was because there is no marker on the 5th lumbar in the experiment. It was too difficult for us to obtain the data on L5 since it is very close to S1 and L4 in the upright standing posture. And the motion capture is not able to catch the location of L5 if the markers are very close to each other. And in some postures, the concave and convex of the curve changes at L5 like the posture shown in Figure 11. So the curve which fits these data (without L5) are not accurate enough. If we can add the marker on L5 in the future, the area (S) of L4-L5 and L5-S part can be computed separately, and the results may be smooth and more accurately. Fig. 9 Relationship between bending angle and distance from back surface to spine process 4 3 Distance from back surface to each vertebral body in each level. Using the MR image, we can obtain the distance between the vertebral body and the spine process. By applying this distance to the function above, we can compute the final results of the distance from the back surface to each level of the vertebral bodies as Figure 10 shows. Fig. 11 Curve with and without the L5 (8)

6 Secondly it is difficult to measure the distance in the MR image, since the image is not clear enough, which influences the result of area. Thirdly, the range of calculated results is small, so the results in the deepest bending angle is not so accurately. We will find another method to calculate the distance in this posture and compare the results with it. 6. Conclusions By reviewing the previous work, we obtained that for enhancing the accuracy of estimation of the compressive force on the lumbar spine, the locations of lumbar spine are needed. For obtaining the locations, we need the distance between back surface and vertebral body in each level. By building a new kind areaconstant model, we obtained the distances from back surface to each spinous processes in different posture (bending angle). The calculated results in upright standing posture ranges from 10.0mm to 10.5mm. Compared with the MR image, we consider the results are basically reliable. Using the MR image, we measured the distances between spinous process and vertebral body. According to these results, we are able to obtain the distance from back surface to vertebral body and simulate the location of each vertebral (L1- S1). As the ongoing work, we are building a new model to calculate the distance from back surface to spinous process. The new model also use area-constant hypothesis. In the new model, the curve of back surface is divided into more than 1000 parts evenly. We calculate the area between each part and the spinous process, and add them together as the total area between back surface to spinous process. And the value of this area should equal to the area calculated from the MR image. 2. Gallagher, S., Mayton, A.: Mining Engineering, vol.59,. no.12, pp (2007). 3. Nachemson, AL., The Lumbar Spine An Orthopaedic Challenge. spine vol.1,no.1, pp (1976). 4. Wilke, H.J., Neef, P., Caimi, M., Hoogland, T., Claes, L.E: New in vivo measurements of pressures in the intervertebral disc in daily life. spine vol.1,no.1,vol.24,no (1999) 5. Kazuaki Takahashi, Shoichi Kikuchi,, Naoto Sato,: Relationship between mechanical load on the lumbar and trunk muscle activity during forward bending of the trunk. Clinical Orthopedic Surgery, vol.41, no (2006) 6. Naoki KUDO. : A Study on Lumbar Burden Evaluation with Lifting Operations 7. Akihiko HONJOU: Estimation of Intervertebral Joint Location for Enhancing the Accuracy of Evaluating of Lumbar Load by Use of a Non-invasive Motion Capture System 8. IStokes,AF, Bevinsi,TM, Lunn,RA.: Back surface curvature and measurement of lumbar spinal motion.. Spine (1987) 7. Acknowledgements The authors would like to thank Dr. Atsuchi Fukuyama for providing the MR image, and the support of the ethical committee in the school of engineering, Nagoya University. 8. References 1. Tatsuro Yamamoto, (ed.): Science of low back pain (Science Practice of pain). Bunkado, (in Japanese) (2014)