Description of fixation frame and fixation posture
Fixation posture G is derived from free standing posture, which is supplemented with further fixation in order to reduce postural sway and thus increase reliability of the spinal shape examination. A prototype of the fixation frame was designed and constructed for fixing the subject in the course of the spinal shape examination. The fixation frame (Figure 1) consists of a stepping platform, a support construction and five adjustable rests. Two rests support the front parts of the shoulders and are adjustable in all three directions (vertical, mediolateral and anterioposterior). One of the rests supports the root of the nose and is also adjustable in all three directions. The remaining two rests support the pelvis, fixing the front and rear parts respectively, and are adjustable in the vertical and anterioposterior directions. In order to construct a prototype of the fixation frame, we applied the MayTec modular elements (MayTec, Dachau, Germany). Construction works, based on our requirements, were carried out by the company Amtek (Brno, Czech Republic). The fixation frame can be dismantled by means of couplings and in its longest part it is 1.1 m in length, which enables easy transport in the boot of a car in the event of field examination.
Positioning the subject in the fixation frame is carried out as follows: the subject steps into the fixation frame and assumes the free standing posture. A ruler for determining the beginning of the ideal vertical is placed so that it touches the calcanei and the zero mark of the ruler is placed in the centre of a connecting line between the calcanei. The height and width of the shoulder rests are then adjusted by sliding out the rests so that there is 30 mm between the rests and the front part of the shoulders in the anterioposterior direction. The subject is asked to bend forward and lean his/her shoulders against the rests and not to change the posture any more. The head rest is brought into play so that it gently touches the root of the nose without changing the head position. The front rest of the pelvis gets pushed towards the front part of the pelvis in the area of the anterior superior iliac spines and, finally, the rear pelvis rest is pushed towards the rear part of the pelvis just below the posterior superior iliac spines.
The instrument
The DTP3 system (Palacky University, Olomouc, Czech Republic) (Figure 2) was developed primarily for noninvasive contacttype assessment of spinal deformity in the sagittal and frontal planes. The measurement is based on determining the threedimensional (3D) coordinates of points on the skin surface by means of an electromechanical position sensor. Data is transmitted to a computer for subsequent processing. The position sensor consists of a mechanical pantograph with three incremental encoders. The measuring stylus of the position sensor ends in a hemisphere of radius of 1 mm. The position sensor allows measurement of the points with standard error of 0.5 mm in the sphere of 2,200 mm diameter [18].
The socalled ideal vertical (IV), i.e. mathematical simulation of a plumb line erected from the centre of the connecting line between the calcanei, is used to evaluate the spinal balance. The orientation of the 3D Cartesian coordinate system is as follows: axis z is on the ideal vertical and oriented in the caudal–cranial direction, axis x is parallel to the intercalcaneal line and in the leftright direction, and axis y is in the posterior–anterior direction. As a result, the frontal plane is defined by axes xz and the sagittal plane by axes yz.
Before using the DTP3 system for examining spinal shape, the skin projections of the following anatomic points are palpated and marked: the lateral parts of the acromions, the posterior superior iliac spines (PSIS), and the spinous processes of the vertebrae C3–C7, T1–T12, and L1–L5. After positioning the subject, the marked points are scanned by touching them with the position sensor stylus.
The software for spinal shape evaluation
Direct assessment of 3D coordinates x
_{
i
}
y
_{
i
}
z
_{
i
} of all spinous processes, i = 1, 2, …, 22, for each subject is timeconsuming. Therefore, special DTP3 software was used to evaluate the spinal shape. The heart of the algorithm is fitting the six degrees polynomial to the measured points. A new normalized coordinate Z which is the coordinate z scaled to the interval [−1, 1] is introduced. The lowest spinous process L5 has the height of −1 and the highest spinous process C3 has the height of 1. The formula of the sixdegree polynomial in the sagittal plane is
y=b0+b1Z+b2\text{P}2\left(Z\right)+b3\text{P}3\left(Z\right)+b4\text{P}4\left(Z\right)+b5\text{P}5\left(Z\right)+b6\text{P}6\left(Z\right)\text{,}
(1)
where \text{P}2\left(Z\right)=\frac{3}{2}{Z}^{2}\frac{1}{2}
\text{P}3\left(Z\right)=\frac{5}{2}{Z}^{3}\frac{3}{2}{Z}^{}
\text{P}4\left(Z\right)=\frac{35}{8}{Z}^{4}\frac{15}{4}{Z}^{2}+\frac{3}{8}\text{,}
\text{P}5\left(Z\right)=\frac{63}{8}{Z}^{5}\frac{35}{4}{Z}^{3}+\frac{15}{8}Z and \text{P}6\left(Z\right)=\frac{231}{16}{Z}^{6}\frac{315}{16}{Z}^{4}+\frac{105}{16}{Z}^{2}\frac{5}{16}\text{,} are the Legendre polynomials [19]. This scaling and orthogonal procedure increases the numerical stability and reduces the influence of the roundingoff error. The clinical interpretation of polynomial coefficients in the sagittal plane is as follows:

b
_{0} – anterioposterior shift of the spine from IV

b
_{1} – anterioposterior tilt of the spine to IV

b
_{2} – overall spinal curvature (i.e. primarily the curvature of thoracic kyphosis)

b
_{3} and b
_{4} – curvature of the upper and lower parts of the spine (i.e. the curvature of cervical and lumbar lordosis)

b
_{5} and b
_{6} – residual spinal curvature of just units of millimetres
A sixdegree polynomial was chosen to describe spinal shape in the sagittal plane since it represented the best approximation to the physiological curvature of the spine with two inflexion points [18]. The positions of the two inflexion points might be interpreted as a cervicothoracic junction (CT) and a thoracolumbar junction (TL). These junctions split the spine into three sections: the cervical, the thoracic and the lumbar spines. The curvature of the respective spinal section could be described with angle parameter (Figure 3) defined as follows:

aC – the cervical lordosis curvature is the angle between the normal lines (perpendicular line to the tangent of the polynomial curve) projected from the spinous processes at C3 and the CT junction.

aT – the thoracic kyphosis curvature is the angle between the normal lines projected from the CT junction and the TL junction.

aL  the lumbar lordosis curvature is the angle between the normal lines projected from the TL junction and the spinous processes L5.
Calculation of the sagittal shift and sagittal tilt is also available and the procedure is as follows: The centre point between the left and right PSIS is calculated. The sagittal shift is the anteroposterior displacement of the centre point from IV. The sagittal tilt is the angle between IV and the connecting line between the centre point and spinous processes C7 [20]. Such calculation produces more straightforward output than the polynomial coefficients b
_{0} and b
_{1}.
The DTP3 software that utilizes the abovementioned algorithm was validated by means of xray examination. When using a rigid model of the human spine, good concordance between noninvasive DTP3 and traditional xray Cobb angles was demonstrated [21].
Study group
The experimental part of the study included 70 subjects, 33 men and 37 women, aged 23.4 ± 3.0 years (mean ± SD), weight 70.5 ± 10.4 kg, height 174.2 ± 8.6 cm. The height of the spine given by the vertical distance between the spinous processes of C3 and L5 was 49.4 ± 3.1 cm. The group included healthy students from the Faculty of Physical Culture of Palacky University without any spinal disorders. The study was approved by the Ethical Committee of the Faculty of Physical Culture of Palacky University. All of the subjects participating in this study were volunteers and had given their informed consent.
Measurement protocol and statistics
Measurement of the marked points was repeated five times for each of the two postures (A – free standing posture, G – standing posture in fixation frame) and individual measurements followed immediately in succession. The duration of one measurement was less than 30 s.
The postural sway of each spinous process was evaluated for each examined subject by way of standard deviations SD
_{
x
}
SD
_{
y
}
SD
_{
z
} according to the formulas
SDx=\sqrt{\frac{1}{51}\sum _{i=1}^{5}{(\overline{x}xi)}^{2}}\text{,}\phantom{\rule{1em}{0ex}}SDy=\sqrt{\frac{1}{51}\sum _{i=1}^{5}{(\overline{y}yi)}^{2}}\text{,}\phantom{\rule{1em}{0ex}}SDz=\sqrt{\frac{1}{51}\sum _{i=1}^{5}{(\overline{z}zi)}^{2}}
(2)
in which x
_{
i
}
y
_{
i
}
z
_{
i
} are the coordinates of the spinous process in ith repetition of the measurement (measurement was repeated five times in the selected posture), \overline{x}\text{,}\phantom{\rule{0.5em}{0ex}}\overline{y}\text{,}\phantom{\rule{0.5em}{0ex}}\overline{z} are the mean coordinates of the spinous process. For evaluating postural sway of each spinous process within the group of 70 subjects, examined in a selected posture, means of standard deviations MSD
_{
x
}
MSD
_{
y
}
MSD
_{
z
} were calculated as average values of standard deviations SD
_{
x
}
SD
_{
y
}
SD
_{
z
} in the entire group [15, 17].
Calculations for evaluating postural sway and spinal shape were performed using MATLAB 7.6 (MathWorks, Natick, MA) and STATISTICA Cz 8.0 (StatSoft, Prague, Czech Republic).