The method for the evaluation of spinal column posture.

Vacarescu, Valeria ; Lovasz, Erwin Christian ; Vacarescu, Cella Flavia 等

1. INTRODUCTION

A fundamental issue related to our research is scoliosis. Scoliosis is defined as abnormal lateral curvature of the human spine. It is usually considered as a three dimensional deformity, because axial rotation will always accompany the lateral curvature. Severe scoliosis curves may alter balance and coordination, interfere with the function of internal organs, determines premature degeneration of the spinal column, and cause deterioration of neurological function. To understand the disease and to document the morphology of the scoliotic spine, actual studies (Boisvert et al., 2006) were made about the positions and orientation of the vertebrae in scoliotic patients, using a set of rigid inter-vertebral transforms on the radiographic imaging. (Ghanem et.al.,1997) uses the optic measurements, during surgery, to determine the vertebrae position. (Chi et al., 2006) presents a new method for measuring axial rotation of vertebra. (Bronzino et al, 2000) makes the gait evaluation by comparing the technical reference system attached to a cluster with 3 markers, with an anatomical reference system with z axis along each foot bone. In [5], (Vacarescu et al,. 1998), applies the rigid transforms between reference systems for analyzing the robots errors, respectively for their calibration. Based on the above mentioned, the authors of this paper propose the application of the methods used in analyzing the robots errors for evaluating the correction of the spine's position. In this paper, the evaluation of spinal column posture is made with the 3D Measuring Module with ultrasounds. It is assumed that every vertebra is associated with a precision point on the crest of the vertebrae. It is established the position and orientation matrix of spinal column and correction matrix of spinal column, correction which resulted from medical therapy. So, it can be evaluated the efficiency and evolution in the treatment of the spine posture.

2. MATRIX OF HUMAN SPINE POSTURE

The report of measurements shows the spinal crest line in sagittal, frontal and transversal projections. This is subdivided automatically into the number of vertebrae. The rotation angles are shown in addition to the representation in sagittal and frontal projections (angles [phi] and [psi]). The angles in transversal projection may be determined for each vertebrae (angle [theta]); the coordinates [x.sub.i]; [y.sub.i]; [z.sub.i] of the vertebrae "i" are shown in the measurements report. For analyzing the 3D human spine scoliotic deformations, this paper proposes the use of rigid transforms between references systems (figure 1). For this purpose, reference [O.sub.0] [x.sub.0] [y.sub.0] [z.sub.0] , having the [O.sub.0] [y.sub.0] axis in vertical position, will be attached to the reference marker (fixed on the patient's body). Each vertebrae "i" will have attached a reference system [O.sub.i] [x.sub.i] [y.sub.i] [z.sub.i], having the [O.sub.i] [y.sub.i] axis in direction i, i-1 (figure 1). The position of [O.sub.i] [x.sub.i] [y.sub.i] [z.sub.i] reference system, reporting to the [O.sub.0] [x.sub.0] [y.sub.0] [z.sub.0] reference, is defined by the following transform:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Shown through the relation:

[sup.0][T.sub.i] = Transl([X.sub.i],[y.sub.i],[Z.sub.i]) x RPY([phi], [theta], [psi]) (1)

[FIGURE 1 OMITTED]

3. CORRECTION MATRIX

In relation (1), the [x.sub.i], [y.sub.i], [z.sub.i], [phi], [psi], [theta] parameters are determined by measurements using the Measuring Module in examining the human spine posture of patient "x". In order to estimate the human spine correction, obtained by applying the therapeutic techniques, are compared two series of measurements, obtained after the human spine posture investigation of the patient "x" before and after applying the therapy (figure2). In the figure 2, the [O.sub.i] [x.sub.i] [y.sub.i] [z.sub.i] reference system defines the vertebrae "i" position, reporting to the O0 x0 y0 z0 reference marker, corresponding to the first investigation. The [O.sub.c] [x.sub.c] [y.sub.c] [z.sub.c] reference system defines the corrected vertebrae "[i.sub.c]" position and orientation), corresponding to the human spine investigation after applying the medical therapy. The position of corrected "[i.sub.c]" vertebrae, defined by the [O.sub.c] [x.sub.c] [y.sub.c] [z.sub.c] reference is described by the following transforms:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[FIGURE 2 OMITTED]

The [sup.i][T.sub.c] transform expresses the size of the position and orientation correction of "[i.sub.c]" vertebrae, resulted after the rehabilitation therapy. The [sup.i][T.sub.i] transform expresses the corrected "[i.sub.c]" vertebrae position and orientation, reported to the [O.sub.0] [x.sub.0] [y.sub.0] [z.sub.0] reference:

[sup.i][T.sub.c] = Transl ([x.sub.c],[y.sub.c],[z.sub.c]) x RPY ([[phi].sub.c],[[theta].sub.c],[[psi].sub.c]) (2)

[sup.i][T.sub.c] = Transl ([x.sub.ic],[y.sub.ic],[z.sub.ic]) x RPY ([[phi].sub.ic],[[theta].sub.ic],[[psi].sub.ic]) (3)

In the figure 2:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

In the relations (2), (3), (4):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

in which:

[sup.i][R.sub.c]--is the correction matrix of the orientation of "i" vertebrae;

[sup.i][p.sub.c]--is the correction matrix of the position of "i" vertebrae.

4. CASE STUDY

The described method was applied to a group of 15 scoliotic patients from the City Hospital of Timisoara, partner of the Politehnica University of Timisoara, in the Research Project CEEX 88/2006. For one of the patients in the group, the initial geometrical parameters of spine position and orientation were measured with the Measuring Module and are presented in figure 3. It can be observed a small scoliosis deviation to the 6th vertebrae, T6 (fig. 3). The shape and the position geometrical parameters of the correction spine, resulted from the application of the therapeutic procedures, are presented in the fig. 4. It can be observed the T6 position's correction. The measured dates were processed in Matlab. Comparing the values from fig. 3 with the values from fig. 4, for the T6 vertebrae, results:

[x.sub.ic]=0.640038; [y.sub.ic]=0.409; [z.sub.ic]=1.02709; [[psi].sub.ic]=2.8; [[phi].sub.ic]=-1.3; [[theta].sub.ic]=0 The spine correction matrix of the T6 vertebrae is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

5. CONCLUSION

The obtained data was used to estimate the size of the spine's correction for the patients included in the project and which benefited of medical rehabilitation therapy.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The proposed method offers relevant information about the variability of the human spine, using rigid transforms. In the future research, we will use the proposed method for the situations presented below:

--for an initial analysis, comparing the geometrical parameters of the patient's spine obtained by measurements with geometrical parameters of the "ideal" spine of the same patient, having as a result the maximum values of correction needed by the patient;

--for analyzing the efficiency of the therapeutic technique applied in order to correct the posture of the spine, comparing the geometrical parameters of patient's spine before and after the therapy;

--for the improvement of the intelligent brace developed in the research project, by using the proposed method in programming its control system, in order to have progressive adjustments of the spine, proposed by the medical specialist.

6. REFERENCE

Bronzino, J.(2000). The biomedical engineering handbook, CRC Press, IEEE Press, IEEE Order No: PC5788, USA

Boisvert, J. et al. (2006). 3D anatomical variability assessment of the scoliotic spine using statistics on Lie groups, Proc. 3rd IEEE International Symposium, pp.750-753, ISBN: 0-7803-9576-X, USA

Chi, W.M. et al (2006). Vertebral axial rotation measurement method, Computer methods and programs in biomedicine, vol. 81, no1, pp . 8-17 , ISSN 016(922607, Elsevier Science, Ireland

Ganem, I.P et. al (1997). Intraoperative optoelectronic analysis of three-dimensional vertebral displacement after Cotrel-Dubousset rod rotation, Journal Spine, vol. 22, no16, pp. 1913-1921, ISSN 0362-2436, USA

Vacarescu, V.; Vacarescu, I.N.(1998). Industrial robots: performances and testing, Mirton Publisher, ISBN: 973-578-590-0, Timisoara, Romania