0030-598710.15674/0030-5987202325-12Study of the inuflence of the position of the tendon graft hamstring muscle on the stability of the knee joint under the conditions of plasticity of the structures of the posterolateral angleM. L. Golovakha1S. P. Panchenko0S. A. Bondarenko1A. A. Bezverkhyi1Dnipro University of Technology.UkraineZaporizhzhia State Medical University.Ukraine2023Knee jointtransplanttendon
Study of the influence of the position of the tendon graft hamstring muscleon the stability of the knee joint under the conditions of plasticityof the structures of the posterolateral angle
M. L. Golovakha 1, S. P. Panchenko 2, S. A. Bondarenko 1, A. A. Bezverkhyi 1
1 Zaporizhzhia State Medical University. Ukraine2 Dnipro University of Technology. Ukraine
* Maxim Golovakha, MD, Prof. in Traumatology and Orthopaedics: golovahaml@gmail.com
* Serhii Panchenko: panchenko.s.p@nmu.one
* Stanislav Bondarenko, MD: trauma.bon.s@gmail.com
Damage to the posterolateral angle of the knee joint is an injurythat occurs occasionally and can be isolated or combined withtears of the posterior or anterior cruciate ligaments. The keylink of damage to the posterior lateral corner is the ruptureof the tendon of the hamstring muscle, mained stabilizer of excess external rotation lower legs. Objective. Determine the optimal fixation position tendon graft on the posterior surfaceof the tibia subject to recovery of the hamstring muscle whichensuring the greatest stability of the lower leg during externalrotation. Methods. Models of the knee joint were built with different attachment points of the popliteal graft muscle in the ANSYS software environment. The criteria for evaluating the effectiveness of selecting the fixation point of the transplant werechosen as the degree of movement of the finite parts elementsof the model. Results. The smallest movements in all directionsreceived in the case when the transplant fixed as far as possibleoutwards and upwards, near the joint surface. Maximum — in the direction of the coordinate axes, as well as full movementwere recorded for the control model, in the absence of the hamstring tendon The nature of the distribution of displacementifelds in all models p graft and control were identical. Biggest there were additional displacements in the direction of the x axis (outward). on the front border of the platform, and thelargest negative (so far redins) on the back. The largest additionalshifts to the sides the y (front) axes are fixed at the leftmost limitand the largest negative (back) — to the right. Conclusions. Inview of the stability of the lower leg during rotational loading,the most efective is fixation of the hamstring graft on the backsurface of the fibula is as late as possible and closer to its cardiac surface, finished in this case, the dimensions are found tobe the smallest in all directions. The greatest displacement in alldirections obtained in the control model for less tendonhamstring muscle.
Key words. Knee joint, transplant, tendon
Ушкодження задньолатерального кута колінного суглоба — травма, яка трапляється зрідка, може бути ізольованою чи поєднаною з розривами задньої або передньої схрещених зв’язок. Ключовою ланкою ушкодження задньолатерального кута є розрив сухожилка підколінного м’яза, основного стабілізатора надлишкової зовнішньої ротації гомілки. Мета. Визначити оптимальне положення фіксації сухожилкового трансплантата на задній поверхні великогомілкової кістки за умов відновлення підколінного м’яза, що забезпечує найбільшу стабільність гомілки під часзовнішньої ротації. Методи. Побудовано моделі колінного суглоба з різними точками кріплення трансплантата підколінного м’яза в програмному середовищі ANSYS. Критеріями оцінювання ефективності вибору точки фіксації трансплантата обрано ступень переміщення частин скінченних елементів моделі. Результати. Найменші переміщення у всіх напрямках отримані у випадку, коли трансплантат фіксували максимально назовні та догори, біля суглобової поверхні. Максимальні — у напрямку координатних осей, а також повного переміщення зафіксовані для контрольної моделі, за відсутності сухожилка підколінного м’яза. Характер розподілу полів переміщень у всіх моделей із трансплантатом і контрольній був ідентичним. Найбільші додатні переміщення у напрямку осі x (назовні) виникали на передніймежі платформи, а найбільші від’ємні (досередини) — назадній. Найбільші додатні переміщення у бік осі y (вперед) зафіксовані на крайній лівій межі, а найбільші від’ємні (назад) — на правій. Висновки. З огляду на стабільність гомілкипід час ротаційного навантаження найефективнішою єфіксація трансплантата підколінного м’яза на задній поверхні великогомілкової кістки максимально латерально та ближчедо її суглобової поверхні, оскільки вцьому випадку величинипереміщень виявились найменшими у всіх напрямках. Найбільші переміщення у всіх напрямках отримані в контрольній моделіза відсутності сухожилка підколінного м’яза.
An injury to the posterolateral angle of the kneejoint occurs occasionally and may be isolated orcombined with tears of the posterior or anteriorcruciate ligaments [1, 2]. The key link of damage tothe posterolateral corner is the rupture of the tendonof the popliteal muscle — the main stabilizer ofexcess external rotation of the shin (Fig. 1). Suchinjuries can be isolated or occur in complex traumas, incombination with ruptures of the posterior and anteriorcruciate ligaments, dislocations of the lower leg, etc.
Reconstruction of the posterolateral angle according to LaPrade. Lateral and posterior view. FCL — bundle that restores the peroneal bypass ligament, PLT — tendon of the popliteal muscle, PFL —popliteal fibular ligament [3]
Popliteal tendon repair is often referred to asthe «key» to successful treatment of posterior kneeinstability. At the same time, the problem is thatthe restoration of the function of the popliteal muscleis performed not quite anatomically, accuratelyreproducing only its attachment to the femoral condyle. Surgical intervention for plastic surgery of thepopliteal tendon involves drilling a channel in the externalcondyle of the tibia from front to back, the exit pointof which on the back surface of the tibia is the geometric place of attachment of the graft — in theprojection of the popliteal tendon (Fig. 2, tendon graftis shown in green color). In addition, repair involvesreplacement of the muscle that contracts and pullsthe tibia in relation to the thigh with a tendon graftof constant length. Such restoration will never beeither anatomical or physiological. However, there isno other option to restore the function of the poplitealmuscle, and choosing the lesser of two evils, westabilize the external rotation of the tibia with a tendongraft of constant length. Graft attachment point onthe back surface of the tibia is the subject of ourinterest in the present study. Exact recommendations forits selection are not given in the literature.
Three-dimensional model of the knee joint: view from the back (a), from the outside (b), from the front (c), and from the inside (d)
Purpose: to determine the optimal position of fixation of the tendon graft on the back surface of thetibia under conditions of recovery of the poplitealmuscle, which provides the greatest stability of the tibiaduring its external rotation.
Material and methods
The research was carried out using thesoftware package, based on the finite element methodin the ANSYS software environment. The objectof the study was the knee joint and its ligaments. Inorder to simplify calculations, the geometric modelcomprised only the articular ends of the tibia, bfiula,and femur, which form the knee joint (Fig. 3).
Diagram of the location of the ligaments of the knee joint: view from the back (a), from the outside (b), from the front (c) and from the inside (d)
Considering the complex geometry of the bonesurface, the articular ends were constructed fromcomputed tomography (CT) data of an adult kneejoint using specialized CT-images processingsoftware (3D Slicer).
The received model in stl format was used forfurther calculations. Therefore, the shape anddimensions of the model corresponded to the real humanknee joint. At the same time, the overall (maximum)dimensions of the model in the horizontal plane were 100 × 70 mm. To reduce the total number of finiteelements, the model was limited in height to 15 cm. The calculated model of the knee joint correspondedto the position of extension in its vertical orientation.
It stands to mention that when modeling thestability of the knee joint, it is quite dicfiult to fullyreeflct its structure and the behavior of individual ligaments, both in terms of the geometry and physicsof this anatomical structure. Each ligament consistsof bfiers that form bundles; the latter are attached tothe articular ends of the bones at several points,occupying a certain area on the surface of the bone. Atthe same time, the ligament can vary in thickness,expanding to the places of attachment, and also, dueto the diefrent direction of the bfiers, it can havea rotation of the cross section around its longitudinalaxis. In addition, ligaments possess not only elasticphysico-mechanical properties, but also such ascontractility and relaxation, which are a time-consumingtask to define and take into account.
It is obvious that the reproduction of thepeculiarities of the structure and properties of connectionswould signicfiantly increase the time for buildingthe model (geometrical side of the problem) andperforming the calculation (physical side of theproblem). In addition, sometimes it is impossible to takeinto account some features of ligaments.
With this in mind, we have considered theligament as a tension-only element, that is, we haveassumed that only longitudinal forces can occur inthe ligament that stretch it. Therefore, we consideredit possible to replace the actual forms of connectionswith cylindrical elements with low bending stifness (by reducing the dimensions of the cylinderdiameter). The bases of the cylinders were fixed at the starting points of the ligaments, which were defined asthe center of the ligament contact zone with the bonesurface. The diameters of all cylinders were equal to 2 mm, and the lengths were determined by the placesof attachment of ligaments (Fig. 4).
Model of the knee joint: a) used coordinate system; b, c) connection of the tibia and fibula bones in the proximal epiphysis; d) direction of the rotational load action
Table 1 shows the actual cross-sectionaldimensions and ligament lengths of the knee joint.
Dimensions of the ligaments of the knee joint [3‒8]
Ligament
Length,mm
Cross-sectional plane,mm2
Anterior cruciate
32.00
37.40
Posterior cruciate
35.00
64.05
Lateral collateral
48.15
8.76
Medial collateral
68.99
24.54
Popliteal tendon
34.30
21.90
The material of the elements (bone and ligamentof the knee joint) was considered elastic,homogeneous and isotropic. Since the subject of research is,ifrst of all, the stressed-deformed state of the ligamentous apparatus of the knee joint, and also takinginto account the signicfiant diefrence in the elasticproperties of bone tissue and ligaments, the articularends of the bones were given the properties ofcompact bone tissue (spongy bone was not selected):module Young's ratio is 2 × 104 MPa, Poisson'sratio is 0.25 [10]. Mechanical values of the ligamentapparatus used in the calculations corresponded tothe average values of the properties of the ligamentsof the knee joint of an adult (Table 2).
It should be noted that replacing the anatomicalshape of the ligaments with their simpliefid models in the form of cylinders results in a change insome characteristics of the models, namely: stifnessof the cross section of the rod (ligaments) duringstretching (EA), Young's modulus (E), cross-sectionalplane (A). Therefore, it was necessary to determinesuch modulus of elasticity, the value of which wouldgive the models of connections stifness indicatorssimilar to the real ones. For this purpose, thegiven elastic modulus of the ligaments was calculatedbased on the equality of the tensile stifness valuesof the ligament and the cylinder simulating it:
ElAl = EcAc,
where ElAl is the tensile stifness of the ligament, EcАc is the tensile stifness of the cylinder.
Hence, the modulus of elasticity of the ligament is:
Ec = ElAl / Ac (2).
The results of the calculations are given in Table 2.
Mechanical properties of ligaments of the knee joint [7‒9]
Ligament
Young'smodulus, MPa
Poisson'sratio
Reduced Young'smodulus, MPa
Anterior cruciate
123
0.4
1464
Posterior cruciate
168
0.4
3425
Lateral collateral
280
0.4
781
Medial collateral
224
0.4
1750
Popliteal tendon
130.9
0.4
913
The calculation model was loaded as follows. From the side of the shin, the knee joint is known tobe formed by the articular ends of two bones: tibiaand bfiula, which are shown in the calculation model. These bones can be movable relative to each other,and in the case of applying a load to the lower leg, the impact on both bones must be transmitted simultaneously. In order to exclude mutual displacementof the bfiula and tibia bones, the joint ends in the lower part of the model were rigidly connected to eachother by a cylindrical element (platform) with a heightof 10 mm and a diameter of 120 mm (Fig. 5, a, b, d). Mechanical properties of the platform correspondedto the properties of compact bone.
Diagram of the location of fixation points of the graft for the reconstruction of popliteal tendon
The basis of this study is the evaluation of oneof the functions of the popliteal muscle — ensuring the stability of the lower leg during externalrotation. There fore, the load of the model was carriedout by a torque, which was applied to the lower baseof the cylindrical platform in the outward direction (Fig. 5, d). That is, external rotation of the tibia wasperformed. The magnitude of the moment waschosen arbitrarily, and after preliminary calculations itwas determined at the level of 15 N × m.
The following boundary conditions were appliedto the model: movement of the femur fragment in alldirections was prohibited, vertical movements wereallowed for the lower leg model, and free movementswere allowed in other directions.
For ease of orientation, a rectangularcoordinate system was introduced (Fig. 5, a). In relation tothe model, x-axis was directed from the inside-out; y — perpendicular to x-axis, back to front; z wasperpendicular to the x0y plane, from bottom to top. Thatis, z-axis coincided with the vertical axis of the lower (1) limb model, and the x0y plane was perpendicular tothis axis.
In order to carry out a study on determiningthe most optimal fixation position of the poplitealmuscle graft on the back surface of the tibia, 9 calculation schemes were built, which diefred in the placeof its attachment. A control 10th model was also built,where there was no popliteal tendon. The transplantwas modeled in the form of a cylinder with adiamer of 2 mm; its elastic properties are shown in Table 2. The upper edge of the graft was attached tothe anatomical starting point of the popliteal tendonon the external condyle of the femur, and theposition of its fixation on the back surface of the tibiawas changed vertically and horizontally in the frontalplane. For the convenience of attaching the lower partof the graft to the tibia, it was carried out throughcylindrical elements created on the back surface of itsexternal condyle (Fig. 6, a, b).
Distribution of displacement fields in the calculation models (top view): along the x-axis (a), y-axis (b) and full displacement d (c). Arrows show the points of origin and directions of the specified maximum displacements
Results and their discussion
Based on the results of the calculations, thepatterns of the distribution of stresses, deformationsand movements in the elements of the knee joint model (articular ends of bones and ligaments) wereobtained. It should be reminded that the study wasconducted to determine the optimal position of the graftfor restoration of the popliteal muscle on the backsurface of the external condyle of the tibia. Since the main goal of the operation is to ensure the stability of the lower leg during rotational loading, wechose the degree of movement of parts of the finite elements of the model as criteria for evaluatingthe eefctiveness of selecting the graft fixation point.
The main values were the maximum displacements of the points of the cylindrical platform in the directions of the x, y coordinate axes, as well as the total displacement of the platform.
Table 3 shows the largest and smallest, takinginto account the sign, displacement of the pointsof the model along the coordinate axes, as well asthe magnitude of total displacement. We can see thatthe outward displacement of the tibia in the frontalplane (positive direction along the x-axis) was greaterthan in the sagittal (along the y-axis) for all variantsof graft fixation. At the same time, the values ofoutward movements were greater than inwardmovements, and forward movements were greater thanbackward movements. This indicates that underconditions of rotational load on the knee joint, thepredominant displacement of the lower leg model occursoutward and forward.
Evaluation of movements along the x-axis (inthe frontal plane) showed the following: regardlessof the height of the graft fixation (levels 1, 2, 3), if the attachment point is shifted from the outsideto the inside (from points C to points A, Fig. 6, b),the values of xmax increase. At the same time, xmindisplacements during fixation of the graft belowthe articular surface (points 2ABS and 3ABS) decrease when moving from the lateral fixation point(point C) to the middle (point B), and then increase again when moving from the middle pointB to the medial point A. However, at the upper level (1АВС), under the conditions of displacementof the fixation point from the outside to the inside(from C to A), the displacement of the xmin (in thedirection of the x-axis to the inside) and xmax platformpoints gradually increases.
The nature of the distribution of ymax and ymindisplacements in the direction of the y coordinateaxis was similar to those along the x-axis (Table 3).
Displacement of platform points
xmax, xmin — displacement along x-axis in positive and negative directions (xmax — outward, xmin — inward), ymax, ymin — displacement along y-axis (ymax — forward, ymin — backward), d — maximum total displacement.
Point location
Displacement, mm
along x-axis
along y-axis
maximum
total displacement (d)
xmax
xmix
ymax
ymix
1A
9.999
-4.324
8.369
-5.955
10.245
1B
9.703
-4.125
8.136
-5.691
9.959
1C
9.147
-4.015
7.710
-5.452
9.385
2A
9.954
-4.422
8.335
-6.042
10.183
2B
9.487
-4.149
7.963
-5.673
9.722
2C
9.431
-4.292
7.949
-5.773
9.651
3A
9.947
-4.471
8.336
-6.082
10.170
3B
9.672
-4.365
8.127
-5.909
9.894
3C
9.644
-4.529
8.127
-6.047
9.848
Without tendon
10.696
-5.491
8.994
-7.192
10.848
The change in the values of total movements (d) depending on the position of the fixation pointof the hamstring muscle graft on the tibia was fullycorrelated with the change in movements in thefrontal plane xmax, xmin (along the x-axis).
Thus, it was established that under the conditionsof displacement of the place of fixation of the graftfrom points C to points A (from the peripheryof the tibial plateau to the center), the displacementsincrease in all directions, that is, the resistanceof the knee joint to external rotation deteriorates. Atthe same time, there is either a gradual increase ora decrease in values under the conditions of thetransition from point C to point B and then an increaseagain due to displacement of the fixation from point B to point A. However, in all calculated cases, themagnitudes of displacements in the case of graft fixationat point A were higher than such at point C. The onlyexception was the movement of xmin (to the inside,in the frontal plane) for models of graft fixation atthe 3ABS level. In this case, the xmin movementsat point A turned out to be slightly smaller than atpoint C.
The specified increase in displacements inthe event of displacement of the fixation pointof the graft from the outside to the inside is explainedby the increase in the length of the graft in this caseand its state of axial stretching. And according tothe formula for determining the absolute elongationobtained according to Hooke's law [11]:
Δl = Nl / EA (3)
it follows that, all other conditions being equal,the elongation will be greater in the element whoselength is greater.
The described nature of changes in the movementof model points indicates that the lower and morecentral we fix the graft on the tibia during poplitealplastic surgery, the less rotationally stable the kneejoint will be.
Discussion
Among all the calculation schemes, where thepresence of the restored popliteal muscle wasmodeled, the smallest movements in all directions wereobtained in the case when the graft was fixed atpoint 1C — maximally outward and upward, near thearticular surface. And the largest xmax and ymax areobtained in the model with fixation of the graft at theupper level in the center of the tibia (point 1A). The maximum movement of xmin was recorded when thegraft was attached at the lower level from the outside (point 3C), and ymin was also fixed at the lower level,but in the center of the tibia (point 3A).
It should be noted that among all calculated values,as expected, the maximum values of displacements in the direction of the coordinate axes, as well as thetotal displacement, were obtained for the control model, where the inuflence of the popliteal tendon was nottaken into account, i. e. it was absent. The consideredvalues of displacements (xmax, xmin, ymax, ymin, d) obtained in the control model exceeded similar values inthe model with minimum displacements by 17, 37, 17,32, 16 %, respectively. At the same time, the largestmovements among the models with the installationof a popliteal muscle graft exceeded the similarminimum values by 9, 13, 8, 11, 9 %. In addition, thedisplacement values of the platform points of the controlmodel exceeded the largest similar values obtained incalculations with the installation of a popliteal musclegraft by 7, 21, 7, 18, 6 %.
The values of xmin were smaller than xmax depending on the point of attachment of the graft by 53‒57 %, and ymin compared to ymax — by 26‒30 %.The displacements of ymax were smaller than xmax by 15‒16 %, but ymin were higher than xmin by 33‒38 %.
In the model in which the popliteal muscle wasabsent, the diefrence between the values of these movements was lower and they amounted to 48 % (xmin —xmax), 20 % (ymin — ymax), 31% (ymin — xmin), however,for the ymax pair — xmax the speciefid diefrenceremained at the level of 16 %. For all fixation models,the displacement of the platform points mainlyoccurred in the outward and forward directions.
Maximum positive and negative displacementsoccurred at the points of the platform furthest fromits center (Fig. 7). It was determined that the natureof the distribution of displacement efilds in all modelswith a transplant and control was identical. Thelargest positive displacements in the direction of thex-axis (outward, red arrow) occurred at the front boundaryof the platform, and the largest negativedisplacements (inward, blue arrow) occurred at the rearboundary (Fig. 7, a). At the same time, the largestpositive movements in the direction of the y-axis(forward, red arrow) are recorded on the extreme leftborder, and the largest negative (back, blue arrow) on the right (Fig. 7, b). The maximum totaldisplacements (d) were obtained at the points of the platform,which are located between the points where thelargest displacements xmax and ymax occurred (Fig. 7, c). The direction of the full displacement d can bedetermined by the parallelogram rule, which is used to addvectors (the direction of the red arrow).
Anatomical structures of the posterolateral corner of the knee joint: 1 — external head of the gastrocnemius muscle; 2 — lateral bypass ligament; 3 — popliteal tendon [3]
Assessment of the obtained data by the valuesof the maximum displacements, as well as the location of the points of their occurrence and thedirection of displacements show that the optimal fixationpoint of the popliteal muscle graft on the back surfaceof the femur is point 1C.
Conclusions
In view of the stability of the lower leg duringrotational loading, the most eefctive is the attachment of the graft under the conditions of plastic surgeryof the popliteal muscle on the back surface of the tibia as laterally as possible and closer to its articular surface. This is confirmed by the displacements, which in this case turned out to be the smallest in all directions.
The largest displacements in all directions wereobtained in the control model, where the popliteal tendon was absent.
Under the conditions of displacement of the fixation point of the popliteal muscle graft on the backsurface of the tibia, displacements increase fromthe outside to the inside, indicating a decrease in the stability of the tibia during external rotation.
Conflict of interest. The authors declare no conflictof interest.
STUDY OF THE INFLUENCE OF THE POSITION OF THE TENDON GRAFTHAMSTRING MUSCLE ON THE STABILITY OF THE KNEE JOINT UNDERTHE CONDITIONS OF PLASTICITY OF THE STRUCTURESOF THE POSTEROLATERAL ANGLE
1 Zaporizhzhia State Medical University. Ukraine
2 Dnipro University of Technology. Ukraine
* Maxim Golovakha, MD, Prof. in Traumatology and Orthopaedics: golovahaml@gmail.com
* Serhii Panchenko: panchenko.s.p@nmu.one
* Stanislav Bondarenko, MD: trauma.bon.s@gmail.com
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