Gravity lines

In static imbalance, the only force involved is weight. For example, assume that a rotor is perfectly balanced and, therefore, will not vibrate regardless of the speed of rotation. Also, assume that this rotor is placed on frictionless rollers or knife edges. If a weight is applied on the rim at the center of gravity line between two ends, the weighted portion immediately rolls to the 6 o clock position due to the gravitational force. 

To use Figure 58 start at the right side of the chart and proceed vertically along the 1930 psia pressure line to a temperature of 200° F. From this point proceed horizontally to the left to the 30° API oil gravity line. Then continue vertically to the 0.75 gas gravity line. Finally, proceed horizontally to the left and the required gas solubility is found to be 350 S.C.F./stock tank barrel. 

Enter the chart in Figure 70 from the left at 350 cubic feet per barrel and proceed horizontally to the 0.75 gas gravity line. Drop vertically to the 30° API on gravity line and then proceed horizontally to the 200° F reservoir temperature line. By dropping vertically again the required oil formation volume factor is, found to be 1.22. 

A practice often used for column testing is to operate the coliunn on a steam-water mixture. The main purpose of this operation is to check heat exchanger and column performance, observe that gravity lines operate properly, and check for leaks and malfunctions prior to the introduction of chemicals. This operation also acquaints operators with a new column. 

The characteristic of dysplastic high grade slips is not the anterior translation of L5, but really rotation of L5 around the sacral dome, with the lum-bo-sacral kyphosis, and associated perturbation of sagittal alignment. The gravity line still falls through the lumbo-sacral junction and close to the posterior centre of the femoral heads. Little adaptation has to be done to keep the sagittal balance, and the problem is purely localised at the lumbosacral junction. 

On the other hand, in dysplastic forms, progressive slippage of L5 around the dome creates an acute lumbo-sacral kyphosis. To preserve balance of the trunk and to try to maintain the gravity line between the two feet, secondary phenomena appeared hyperlordosis of the lumbar spine above... 

We can see again that the all trunk imbalance contributes to permanent shear stress and imbalance non-economic status, where the apex of kyphosis is not only far from the gravity line, but also oblique even vertical compared to usual kyphosis where the apex is horizontal. 

However beside those angle modifications, the most interesting part is the decreasing distance between the lumbo-sacral junction and the gravity line. 

Without distraction, the L5 vertebral body just rolls over the sacral dome. The instrumented postero-lateral fusion moved close to the vertical gravity line, with subsequently less stress. It is strong enough to maintain the correction without anterior fusion. 

In dysplastic spondylolisthesis, the incidence has been found to be higher than in normal population (up to 80-90°, compared to 50° normal). Incidence is not corrected by the reduction of spondylolisthesis, and despite correction of the lumbo-sacral kyphosis and the retroversion of the pelvis, the gravity line stays still more anterior to the lumbo-sacral junction than in normal population. The only way to modify this factor would be to do a pelvis osteotomy. 

Fig. 2. Behavior of the positional parameters in ankylosing spondylitis (Morbus Bechterew) a behavior of the positional parameters and the gravity-line in ankylosing spondylitis (Morbus Bechterew). Clear retroversion of the sacrum is expressed in the sacro-femoral tilting and in the overhang, b Normalization of the positional parameters and the gravity-line after pedicle substraction osteotomy in the lumbar spine...

I mentioned above that the body will always try to transmit its mass center of gravity over the hip joints into the lower extremities. This is of vital significance for the upright position of the human in space. This means that the gravity line of the body - which has unfortunately not yet been defined - must lie in close relationship to the hip joint. The anterior shift of the fifth lumbar vertebral body towards the sacrum results, independent from this exact definition, in an inevitable anterior shift of the gravity line. 

Through formation of lumbar hyperlordosis and flattening of thoracic kyphosis, the slipping process can be compensated up to a certain point, i.e., the position of the gravity line will, as described above, move around the center of the femoral heads. However, if a critical value is exceeded during the slipping process, there are two basic possibilities as to how the spine behaves towards the center of the femoral head ... 

Forward tilting of the entire trunk towards the center of the femoral head. This occurs rarely however, it can be observed from time to time (Fig. 3). Retroversion of the sacrum - verticalization of the sacrum - permits the mass gravity line of the trunk to be closely related to the femoral head center, i.e., the trunk remains well centered over the femoral heads (Fig. 4). This coincides best with most of our observations in cases of spondyloptosis. 

Fig. 4. Behavior of the positional and spinal parameters in a 25-year of female patient with spondyloptosis despite retroversion of the sacrum and changs of the positional parameters, there Is no forward tilting of the trunk. Hyperlordosis of the lumbar spine with further remaining kyphosis develops. Through sacrum reclination, the gravity line Is centered through the center of the femoral head...

The definition of mass gravity line anterior to the T9 vertebral body is defined by the term T9 projection (Fig. 7 a). In this correlation, the term of the T9 (Fig. 7b) tilting = gite (Fig. 7b) is of particular significance. This... 

Fig. 9. Definition of the gravity center and the gravity line according to Duval-Beaupere. One can clearly see that under physiological conditions the gravity center is presumed to lie anterior to TH9. The gravity line falls posterior to the center of the femoral head into the lower extremities...

The sagittal tilting, now angled more anteriorly, has an effect that goes from anterior to posterior the gravity line runs posterior to the center of the femoral heads. 

The pelvic position-dependent parameters show a sacro-femoral tilting of 45°, the overhang is 68 mm. Spinal parameters the lumbar lordosis measured between T12 and L5 is 62°, the thoracic kyphosis measured between T2 and T12 is 12°. The sagittal tilting shows an anteriorly directed element. The gravity line (measured from C7) lies anterior to the center of the femoral heads. 

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