RU2577939C2 - Method for specifying surgical correction of spinal canal - Google Patents

Abstract

FIELD: medicine.

SUBSTANCE: method involves pre- and post-surgical spiral computed and magnetic resonance tomography of an involved spine. A height of superjacent spine H_a and subjacent spine H_b are measured. A cross-sectional dimension of the spinal canal of the superjacent spine is measured as a distance from a posterior surface of the vertebral body to an inner surface of the related vertebral arch in a median sagittal plane d_a. A cross-sectional dimension of the spinal canal of the superjacent spine is measured as a distance from a posterior surface of the vertebral body to an inner surface of the related vertebral arch in a median sagittal plane d_a. A cross-sectional dimension of the spinal canal within a maximum narrowing is measured as a pre- d and post-surgical d^* distance from the posterior surface of the vertebral body to the inner surface of the related vertebral arch in the median sagittal plane. A pre- h and post-surgical h^* distance from the posterior surface of the vertebral body to a stenosis factor point farthest from the posterior surface of the vertebral body in the median sagittal plane is measured. A pre- s and post-surgical s^* horizontal half-distance between extreme stenosis factor points on the inner surface of the vertebral arch is measured. A spinal canal surgical correction coefficient K_k, pre- V_d and post-surgical V_d ^* spinal canal volume deficiency coefficients, a pre- V_s and post-surgical V_s ^* volume of a stenosis factor portion penetrating into the spinal canal, non-dimensional variables x and y, x^* and y^* are calculated by formulas. If K_k is more than 0.4, the surgical correction of the spinal canal is considered satisfactory.

EFFECT: method enables the accurate quantitative assessment of the spinal canal stenosis at any level thereof and the accurate qualitative assessment of the surgical correction of the spinal canal by performing spiral computed and magnetic resonance tomography and measuring the most important dimensions that makes it possible to calculate the volume of the stenosis factor portion penetrated into the spinal canal.

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Description

Description of the invention

Technical field

The invention relates to methods for diagnosing diseases in medicine, namely in neurosurgery, traumatology, orthopedics and radiation diagnostics, and can be used to quantify the effectiveness of surgical operations to eliminate spinal stenosis.

State of the art

The closest technical solution (prototype) is a method for determining surgical correction of the spinal canal (RF patent No. 2429782, publication date 09/27/2011). The method is as follows. The patient undergoes a spiral computed or magnetic resonance imaging of the affected spine before and after surgery. The pre-operative tomogram measures the diameter of the spinal canal (i.e., the distance from the back surface of the vertebral body to the inner surface of the vertebral arch) at the point of maximum narrowing d ₂ , the diameter of the vertebral canal of the overlying vertebra d ₁ and the diameter of the underlying vertebra d ₃ . The spinal stenosis coefficient before surgery (K _st1 ) is _calculated by the formula:

K _st1 = 1-2d ₂ ² : (d ₁ ² + d ₃ ² ).

The terms “overlying” and “underlying” denote the vertebrae located above and below the affected part of the spine, respectively, in relation to the vertical position of the person. Definition and understanding of the signs “overlying”, “upper”, “underlying”, “lower”, etc. given, for example, in the source http://osteo911.ru/otdely-pozvonochnika-cheloveka.html.

The tomogram made after the operation measures the diameter of the spinal canal at the site of maximum narrowing d ₂ ^* , the diameter of the spinal canal of the overlying vertebra d ₁ ^* and the diameter of the underlying vertebra d ₃ ^* . The spinal stenosis coefficient after surgery (K _st2 ) is _calculated by the formula:

K _st2 = 1-2d ₂ ^{* 2} : (d ₁ ^{* 2} + d ₃ ^{* 2} ),

The coefficient of surgical correction of the spinal canal (K _k ) is determined by the formula:

K _k = 1-K _st2 : K _st1 .

When the value of K _k above 0.4, surgical correction of the spinal canal is considered satisfactory.

The disadvantage of the prototype is the lack of accuracy in evaluating the effectiveness of surgical correction of the spinal canal. This is due to the fact that the diameters of the cross section of the spinal canal are used as initial data for calculating the coefficient of spinal stenosis, which reduces objectivity, because allows you to calculate the degree of stenosis strictly in a certain plane. Meanwhile, the factors causing spinal canal stenosis (fragments of the vertebral body, ligaments, hematomas, disk sequesters) are volume bodies.

The technical result of the invention is to increase the accuracy of evaluating the effectiveness of surgical correction of the spinal canal.

The technical result is achieved due to the fact that in the method for determining surgical correction of the spinal canal, spiral computed or magnetic resonance imaging of the affected spine is performed before and after surgery, the size of the cross section of the spinal canal of the overlying vertebra, the size of the cross section of the spinal canal at the site of maximum narrowing , the size of the cross section of the spinal canal of the underlying vertebra, after which the coefficient of surgical correlation is calculated ktsii spinal canal K _k, and a value of higher than 0.4 K _k surgical correction of spinal canal is considered satisfactory, measure the height H of the overlying vertebra _and, underlying vertebra height H _b, as the cross-sectional size of the spinal canal overlying vertebra measure the distance from the rear surface of the body vertebra to the inner surface of the arc of this vertebra in the median sagittal plane d _a , as the size of the cross section of the spinal canal of the underlying vertebra, measure the distance from the back the surface of the vertebral body to the inner surface of the arc of this vertebra in the median sagittal plane d _b , as the size of the cross section of the vertebral canal at the point of maximum narrowing, measure the distance from the back surface of the vertebral body to the inner surface of the arc of this vertebra in the median sagittal plane before surgery d and after surgery d ^*, measure the distance from the rear surface of the vertebral body to the point of stenosis factor, most distant from the rear surface of the vertebral body, in the median sagittal plane plane h prior to surgery and after surgery h ^*, half the distance in a horizontal plane between the extreme points stenosis factor on the inner surface of the arc s vertebra prior to surgery and after surgery s ^*, surgical correction coefficient calculation spinal canal K _k is performed according to the formula K _k = 1- V _d / V _d ^* , while the coefficient of deficiency of the volume of the spinal canal before surgery V _{d is} calculated by the formula V _d = 1 - ((πd _a ² H _a + πd _b ² H _b -8V _s ) / (πd _a ² H _a ² + πd _b H _b)), where the volume factor stenosis portion, penetrating into the vertebral canal before surgery V _s, is calculated by the pho mule V _s = ((2.437x-0.1755x ²⁾ (y-x-1) ² + (0.9586x-0.3906x ²⁾ (y-x-1), ³⁾ d ^3/8, and the dimensionless variables x and y calculated by the formulas x = (h ² + s ² ) / dh, y = 1 + (s ² -h ² ) / dh, while the coefficient of deficiency of the spinal canal volume after surgery V _d ^{* is} calculated by the formula: V _d ^* = 1 - ((πd _a ² H _a + πd _b ² H _b -8V _s ^* ) / (πd _a ² H _a + πd _b ² H _b )), where the volume of the part of stenosis factor penetrating the spinal canal after surgery, V _s ^* calculated by the formula: V _s ^* = ((2.437х ^* -0.1755 (х ^* ) ² ) (у ^* -х ^* -1) ² + (0.9586х ^* -0.3906 (х ^* ) ² ) (у ^* -х ^* 1) ³⁾ (d ^{*) 3/8,} dimensionless variables x ^* and y ^* is calculated according to the formulas: x ^* = ((h ^{*) 2} + (s ^{*) 2) / d * h *, y} * = 1 + ((s ^* ) ² - (h ^* ) ² ) / d ^* h ^* .

Brief Description of the Drawings

The invention is illustrated by the drawing (FIGS. 1-3), where in FIG. 1 shows a thoracic vertebra; FIG. 2 - thoracic vertebra with spinal stenosis, in FIG. 3 is an illustration for calculation; FIG. 4 - an additional illustration to the calculation.

Disclosure of invention

The drawings indicate: vertebra 1, vertebral body 2, spinal canal 3, transverse process 4, superior articular process 5, lower articular process 6, spinous process 7, vertebral arch 8, stenosis factor 9.

The implementation of a method for quantifying surgical operations to eliminate spinal stenosis is illustrated in FIG. 1, 2 and 3. In FIG. 1 shows the vertebra 1 formed by the vertebral body 2 and the vertebral arc 8. Seven processes extend from the vertebral arch 8: paired transverse processes 4, paired superior articular processes 5, paired lower articular processes 6 and unpaired spinous process 7. Between the vertebral body 2 and the arch vertebra 8 is the vertebral foramen. Together, the vertebral openings of all the vertebrae form the spinal canal 3. Figure 2 shows the vertebra 1 with spinal stenosis. The figure 3 shows an illustration for the calculation, namely: two intersecting circles with letter designations necessary for calculating the dimensions.

Figure 2 shows that stenosis factor 9, penetrating the spinal canal 3, reduces its volume, compresses the spinal cord and nerve roots. To eliminate pressure on the spinal cord or nerve roots, it is necessary to perform an operation to eliminate stenosis of the spinal canal 3, for example, decompressive laminectomy. To determine the effectiveness of the operation, a method for quantifying surgical operations to eliminate spinal stenosis 3 was used.

The implementation of the invention

A method for diagnosing a disease and a patient’s condition during treatment is as follows. Before the operation to eliminate stenosis of the spinal canal 3, the patient undergoes a spiral computed or magnetic resonance imaging of the affected spine.

The patient undergoes surgery to eliminate stenosis of the spinal canal 3. During the operation, the patient is on the operating table in a position on his stomach or side. A small skin incision is performed along the midline above the compression region of the nerve root or spinal cord. Subcutaneous fatty tissue and paravertebral muscles are pushed back. In this case, the posterior surface of the spinal column and the yellow ligament connecting the plates of neighboring vertebrae are exposed. In many cases, during the operation, fluoroscopy is performed to identify the desired vertebra. Next, perform the removal of part of the arc of the vertebra 8. In this case, the spinal canal 3 becomes available for examination and manipulation. Decompression of nerve structures is performed. Decompression of nerve structures is the removal of formations (disc herniation, tumor, scar tissue) that compress the spinal cord or nerve root. At the end of the operation, layer-by-layer suturing of tissues (muscles and skin) is performed. With the development of spinal instability, in many cases, a laminectomy is supplemented with stabilizing operations. During such operations, stabilizing systems securely secure the vertebrae 1 in the desired position. After a few months, the vertebrae 1 fuses into a single bone formation.

After the operation, a spiral computed or magnetic resonance imaging of the affected spine is repeated. The tomogram made before the operation for the vertebra 1 at the level of stenosis in the median sagittal plane measures the distance from the back surface of the vertebral body 2 (under the back surface of the vertebral body we understand the surface along which the posterior longitudinal ligament is located URL: anatomy_atlas.academic.ru/1680/ Vertebral connections, accessed July 30, 2014) to the inner surface of the vertebral arch 8d, in the median sagittal plane, measure the distance from the back surface of the vertebral body 2 to the point of stenosis factor 9 as far as possible from the back on top vertebral body 2, h, half the distance in the horizontal plane (the horizontal plane of the human body is the plane perpendicular to the sagittal and frontal planes of the human body, dividing the body of a vertically standing person into upper and lower parts, URL: http://anfiz.ru/ekzamen /item/f00/s00/z0000000/st001.shtml, accessed July 30, 2014) between the extreme points of stenosis factor 9 on the inner surface of the vertebral arch 8s. Also, for two adjacent vertebrae 1 in the median sagittal plane, the distances from the back surface of the vertebral body 2 to the inner surface of the vertebral arch 8d _a and d _b and the height of the spinal canal 3H _a and H _b are measured. From the tomogram made after the operation, the distance from the back surface of the vertebral body 2 to the inner surface of the vertebral arch 8d ^{* is} measured in the median sagittal plane; the distance from the back surface of the vertebral body 2 to the point of stenosis factor 9 maximally distant from the back surface is measured in the median sagittal plane vertebral body 2, h ^* , half the distance in the horizontal plane between the extreme points of stenosis factor 9 on the inner surface of the vertebral arch 8s ^* .

Next, calculate the volume of the part of stenosis factor 9 that has penetrated the spinal canal 3, before and after surgery. When calculating the volume of the spinal canal 3, take the volume of the cylinder, the height of which is equal to the height of the spinal canal 3, and the diameter is equal to the distance from the back surface of the vertebral body 2 to the inner surface of the vertebral arch 8. It is believed that the border of stenosis factor 9 on the side of the spinal canal 3 parts of the surface of the ball. Thus, for the volume of the part of the stenosis factor 9 that penetrated the spinal canal 3, take the volume of the segment of the ball, actually pressed into the cylinder.

The problem of calculating the volume of the depressed segment is solved in a cylindrical coordinate system. The origin is located on the axis of the cylinder in a plane passing through the center of the ball perpendicular to the axis of the cylinder. The polar axis is directed from the axis of the cylinder to the center of the ball.

The equation of the cylindrical surface:

ρ = R,

where ρ is the polar radius,

R is the radius of the cylinder.

Spherical surface equation:

(ρcosφ-l) ² + ρ ² sin ² φ + z ² = r ² => ρ ² -2ρcosφ + l ² + z ² = r ²

where ρ is the polar radius,

φ is the polar angle,

l is the distance from the center of the ball to the axis of the cylinder,

r is the radius of the ball,

the z axis is directed along the axis of the cylinder.

From the equation of the sphere, z is expressed:

z = ± (z ² -ρ ² + 2ρlcosφ-l ² ) ^1/2

- the equation of the lower and upper hemispheres.

Putting z = 0, we obtain the equation of the circle of the big circle of the ball:

ρ ² -2ρcosφ + l ² = r ²

Putting ρ = R, find the value of the polar angle φ _s at which the circle of the big circle of the ball and the circle with the radius of the cylinder R intersect:

cosφ _s = (R ² -r ² + l ²⁾ / 2Rl

Find the value of the polar angle φ _τ , at which the ray drawn from the origin in the plane of the big circle of the ball touches the circumference of the big circle of the ball:

sinφ _τ = r / l

Solve the equation of the circle of a large circle of the ball with respect to the polar radius ρ

ρ = lcosφ ± (r ² -l ² sin ² φ) ^1/2

where the “-” sign in front of the root corresponds to the arc closest to the cylinder axis, the “+” sign - to the farthest.

If the point of contact of the beam drawn at an angle φ _τ lies outside the cylinder, taking into account symmetry, the expression for the desired volume has the form:

If the point of contact is inside the cylinder, then an additional term is added to the written integral:

Due to the complexity of the obtained integral, it is analytically possible to calculate only the internal integral with respect to the variable ρ. Therefore, the integral was calculated using specialized software. For convenience of calculations, a transition was made to dimensionless variables:

x = r / R, y = l / R

Where

r = (s ² -h ² ) / 2h,

l = R + (s ² + h ²⁾ / 2h,

0 <x <1; 1 <l <1 + r.

Approximation formulas were derived for calculating the volume of the depressed segment before and after the operation:

V _s = ((0.1755h ^2.437h-2) (y-x-1) ² + (0.9586h ^0.3906h-2) (y-x-1), ³⁾ d ^3/8

where V _s is the volume of the part of stenosis factor 9 penetrating the spinal canal 3, before surgery,

d is the distance from the back surface of the vertebral body 2 to the inner surface of the arc of the vertebra 8 in the median sagittal plane before surgery,

x and y are dimensionless variables introduced for ease of calculation. The transition from the values measured on the tomograms to the dimensionless variables x and y is carried out according to the formulas:

x = (h ² + s ² ) / dh,

y = 1 + (s ² -h ²⁾ / dh.

V _s ^* = ((2.437x ^* -0.1755 (x ^* ) ² ) (y ^* -x ^* -1) ² + (0.9586x ^* -0.3906 (x ^* ) ² ) (y ^* -x ^* -1) ³ ) (d ^{*) 3/8,}

where V _s ^* is the volume of the part of stenosis factor 9 penetrating the spinal canal 3, after surgery,

d ^* is the distance from the back surface of the vertebral body 2 to the inner surface of the arc of the vertebra 8 in the median sagittal plane after surgery,

x ^* and y ^* are dimensionless variables introduced for ease of calculation. The transition from the values measured on the tomograms to the dimensionless variables x ^* and y ^{* is} carried out according to the formulas:

x ^* = ((h ^* ) ² + (s ^* ) ² ) / d ^* h ^* ,

y ^* = 1 + ((s ^* ) ² - (h ^* ) ² ) / d ^* h ^* .

The volumes of the spinal canals of 3 of two adjacent vertebrae are determined:

V _a = πd _a ² H _a / 4,

V _b = πd _b ² H _b / 4.

The average volume of the spinal canal 3 is determined as the arithmetic average of the volumes of the spinal canal 3 of two adjacent vertebrae under consideration:

V _{1 = (V a + V b)} / 2

The volume of the spinal canal 3 is determined at the level of stenosis before surgery, as the difference between the average volume of the spinal canal 3 and the volume of the depressed segment before surgery:

V = V ₁ -V _s

The volume of the spinal canal 3 is determined at the level of stenosis after surgery, as the difference between the average volume of the spinal canal 3 and the volume of the depressed segment after surgery:

V ^* = V ₁ -V _s ^*

Determine the coefficient of deficiency of the volume of the spinal canal 3 before surgery:

V _d = 1-V / V ₁ .

and after surgery:

V _d ^* = 1-V ^* / V ₁ .

The coefficient of surgical correction of the spinal canal 3 is used as a criterion for the quantitative assessment of stenosis of the spinal canal 3 and the effectiveness of surgical intervention to eliminate stenosis of the spinal canal 3 (it can also be called the coefficient of volumetric surgical correction of the spinal canal). The coefficient of surgical correction of the spinal canal 3 is calculated by the formula:

K _k = 1-V _d / V _d ^* .

Surgical correction of the spinal canal 3 is considered satisfactory with a coefficient of surgical correction (which can also be defined as the coefficient of volumetric surgical correction of the spinal canal 3), equal to 0.4 and higher. If the result is unsatisfactory, the operation to eliminate stenosis is repeated.

Thus, this method of determining surgical correction of the spinal canal 3 provides a more accurate quantitative assessment of stenosis of the spinal canal 3 in case of injury and diseases of the spine at any level, as well as a more accurate quantitative assessment of the effectiveness of surgical correction of the spinal canal 3. To calculate the coefficient of volume correction of the spinal canal 3 measure not just the distance from the back surface of the vertebral body 2 to the inner surface of the vertebral arch 8 for the vertebra at the level of stenosis and two adjacent vertebrae (as in the prototype), but also the penetration depth of stenosis factor 9, half the distance in the horizontal plane between the extreme points of stenosis factor 9 on the inner surface of the vertebral arch 8 and the height of the spinal canal 3 for two adjacent vertebrae. The measurement data allows us to calculate the volume of the part of stenosis factor 9 that has penetrated the spinal canal 3, which increases the accuracy of evaluating the effectiveness of surgical correction of the spinal canal 3, since the factors causing spinal stenosis (bone fragments of the vertebra, spinal tumors, hematomas, disk sequestration, etc. e.) are volumetric bodies and the calculation of the degree of stenosis strictly in a certain plane gives a significant error.

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Claims (1)

A method for determining the effectiveness of surgical correction of the spinal canal, consisting in the fact that they conduct a spiral computed or magnetic resonance imaging of the affected spine before and after surgery, measure the size of the cross section of the spinal canal of the overlying vertebra, the size of the cross section of the spinal canal at the site of maximum narrowing, the size of the cross sections of the spinal canal of the underlying vertebra, after which the coefficient of surgical correction of the spinal canal K _k , and and K _k value above 0.4 surgical correction of spinal canal is considered satisfactory, characterized in that the measured height H _and the overlying vertebra, the height of the underlying vertebra H _b, as the cross-sectional size of the spinal canal overlying vertebra measure the distance from the rear surface of the vertebral body to an internal the surface of the arc of this vertebra in the median sagittal plane d _a , as the size of the cross section of the vertebral canal of the underlying vertebra, measure the distance from the back surface and the vertebral body to the inner surface of the arc of this vertebra in the median sagittal plane d _b , as the size of the cross section of the vertebral canal at the point of maximum narrowing, measure the distance from the back surface of the vertebral body to the inner surface of the arc of this vertebra in the median sagittal plane before surgery d and after surgery d ^* , measure the distance from the back surface of the vertebral body to the point of stenosis factor, the most remote from the back surface of the vertebral body, in the median sagittal plane before surgery h and after surgery h ^* , half the distance in the horizontal plane between the extreme points of the stenosis factor on the inner surface of the vertebral arch before surgery s and after surgery s ^* , the calculation of the coefficient of surgical correction of the spinal canal K _{k is} carried out according to the formula K _k = 1-V _d / V _d ^* , while the coefficient of deficiency of the volume of the spinal canal before surgery V _{d is} calculated by the formula V _d = 1 - ((πd _a ² H _a + πd _b ² H _b -8V _s ) / (πd _a ² H _a + πd _b ² H _b )), where the volume of the part of the stenosis factor penetrating the spinal canal before surgery V _s is calculated by the formula V _s = ((2.43 7x ^0.1755h-2) (y-x-1) ² + (0.9586h ^0.3906h-2) (y-x-1), ³⁾ d ^3/8, and the dimensionless variables x and y is calculated according to the formulas X = (h ² + s ² ) / dh, y = 1 + (s ² -h ² ) / dh, while the coefficient of deficiency of the volume of the spinal canal after surgery V _d ^{* is} calculated by the formula: V _d ^* = 1 - ((πd _a ² H _a + πd _b ² H _b -8V _s ^* ) / (πd _a ² H _a + πd _b ² H _b )), where the volume of the part of the stenosis factor penetrating the spinal canal after surgery, V _s ^{* is} calculated by the formula: V _s ^* = ((2.437x ^* -0.1755 (x ^* ) ² ) (y ^* -x ^* -1) ² + (0.9586x ^* -0.3906 (x ^* ) ² ) (y ^* -x ^* -1) ³ ) ( d ^{*) 3/8,} dimensionless variables x ^* and y ^* is calculated according to the formulas: x ^* = ((h ^{*) 2} + (s ^{*) 2)} / d ^* h ^*, y ^* = 1 + ((s ^{*) 2} - (h ^* ) ² ) / d ^* h ^* .

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