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 Table of Contents  
ORIGINAL ARTICLE
Year : 2020  |  Volume : 6  |  Issue : 2  |  Page : 116-120

Reference values of the femur and tibia mechanical axes and angles in the sagittal plane, determined on the basis of three-dimensional modeling


1 Research Department of Trauma, Vreden Russian Research Institute of Traumatology and Orthopedics, Ministry of Health of Russia, St. Petersburg, Orthopedic Surgeon; Department of General Surgery, St. Petersburg State University, St. Petersburg, Russia
2 “Ortho-SUV” Ltd., Technical Consultant, Russia
3 Department of Orthopedics, Saint Petersburg State University Hospital, Orthopedic Surgeon; Research Department for Bone Pathology, H. Turner National Research Center for Children's Orthopedics and Trauma Surgery, Russia

Date of Submission10-Oct-2020
Date of Decision07-Dec-2020
Date of Acceptance10-Dec-2020
Date of Web Publication31-Dec-2020

Correspondence Address:
Dr. Victor A Vilenskiy
Department of orthopedics #3, Saint-Petersburg State University Hospital, Saint-Petersburg
Russia
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/2455-3719.305861

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  Abstract 


Background: The reference values of the anatomical, mechanical lines and angles of the femur and tibia in the frontal plane have been sufficiently studied. At the same time, the data concerning the mechanical axis and angles in the sagittal plane are rather contradictory. Aims and objectives. The aim of this study was to determine the 3D reference values of the mechanical axes and angles of the femur and tibia in the sagittal plane. Materials and Methods: The study included data of 23 adult volunteers for whom computer tomography (CT) was done. The inclusion criteria were: absence of the deformity confirmed by long-leg films (using known reference lines and angles (RLA) assessment), absence of torsional deformity confirmed by CT and extended position of the limb. Results: It was found that the mechanical axis of the lower limb in the sagittal plane divides the distal joint line of the femur into two segments: anteriorly - 43.8+7.9%, posteriorly - 56.2+7.9%. The proximal joint line of the tibia, correspondingly, is divided into 23.3+8.8% anteriorly and 76.7+8.8% posteriorly. The found values of mechanical angles were the following: mechanical Posterior Proximal Femoral Angle (mPPFA) - 84.7 + 8.8 °, mechanical Posterior Distal Femoral Angle (mPDFA) - 81.1 + 3.95 °, mechanical Posterior Proximal Tibial Angle (mPPTA) - 81.6 + 2.8 °, mechanical Anterior Distal Tibial Angle (mADTA) - 79.9 + 2.98°. Conclusion: The obtained data on the mechanical axis of the lower limb for the sagittal plane can be used both for deformity assessing, planning and estimating the accuracy of deformity correction.

Keywords: Deformity correction, deformity correction planning, MAD, mechanical axis deviation, 3D planning


How to cite this article:
Solomin LN, Utekhin AI, Vilenskiy VA. Reference values of the femur and tibia mechanical axes and angles in the sagittal plane, determined on the basis of three-dimensional modeling. J Limb Lengthen Reconstr 2020;6:116-20

How to cite this URL:
Solomin LN, Utekhin AI, Vilenskiy VA. Reference values of the femur and tibia mechanical axes and angles in the sagittal plane, determined on the basis of three-dimensional modeling. J Limb Lengthen Reconstr [serial online] 2020 [cited 2021 Sep 22];6:116-20. Available from: https://www.jlimblengthrecon.org/text.asp?2020/6/2/116/305861




  Introduction Top


When analyzing and planning the correction of long bone deformities, reference lines and angles (RLA) are used.[1],[2] The reference values of the anatomical, mechanical lines and angles of the femur and tibia in the frontal plane have been sufficiently studied.[3],[4],[5],[6],[7],[8],[9],[10],[11] At the same time, the data concerning the mechanical axis and angles in the sagittal plane are rather contradictory.

According to Paley,[2] at 5° of flexion in the knee joint, the mechanical axis in the sagittal plane intersects the distal joint line of the femur at the point of rotation in the knee joint (the point of intersection of the line that is a continuation of the posterior cortex of the femur and the Blumensaat line). When fully extended, the mechanical axis runs anterior to the point of rotation in the knee joint (the author does not indicate the exact location or segment).

Standard et al.[9] suppose that the mechanical axis intersects the distal joint line of the femur “slightly anterior to the point of rotation in the knee joint.” These authors have proposed the so-called. “Modified mechanical axis of the femur for the sagittal plane,” which is the line connecting the center of the femoral head and the point on the border of the anterior 1/3 and middle 1/3 of the distal joint line of the femur. It is assumed that the angle formed by the intersection of the modified mechanical axis and the distal joint line of the femur is equal to the anatomical posterior distal femoral angle (anatomical posterior distal femoral angle [aPDFA]). Thus, it is argued that the anatomical and mechanical axis of the femur intersect the distal joint line of the femur at one point with the same range of normal values for the posterior distal femoral angle. The contradiction of the given data is that the mechanical axis of the limb and the mechanical axis of the femur do not coincide, because “the border of the anterior 1/3 and middle 1/3 of the distal joint surface of the femur” and “slightly anterior to the point of rotation in the knee joint” are completely different points.

It should be also noted that the standard two-plane (based on long-leg films) analysis and planning of deformity correction has a significant drawback. It is known that even the minimum rotation when performing radiographs distorts the RLA values.[12] Therefore, in the presence of a torsion component, it is impossible to determine the apex of the deformity accurately. This leads to the wrong choice of the level of the osteotomy and subsequently, to the translation of the bone fragments, or to inaccurate correction.

The solution of the problem could be the use of three dimensional (3D) technologies, which have already proved their effectiveness in high-tibia,[13],[14] low-femur,[15],[16] and derotation osteotomies of the femur and tibia in the treatment of the patella chronic instability.[17] Therefore, it is possible to accept that for the most accurate determination of RLA one should use volumetric, three-plane objects. Thus, the aim of our study was to determine the 3D reference values of the mechanical axes and angles of the femur and tibia in the sagittal plane.


  Materials and Methods Top


The study included the data of 23 volunteers (23 limbs) aged from 18 to 65 years (36.4 ± 15.5), for whom the computer tomography was done simultaneously for two lower extremities to estimate the deformity of one of them. Fourteen out of 23 volunteers (61%) were female. The inclusion criteria for the study were:

  1. Age over 18 years
  2. Absence of the deformity of both femur and tibia of one of the legs in the frontal and sagittal planes, confirmed by long-leg films with RLA assessment
  3. Absence of a torsional component of deformity according to computer tomography data
  4. The extended position of the knee joint (no flexion or hyperextension) when performing computer tomography.


The absence of deformity was confirmed by long-leg film radiographs according to the standard Paley's method.[2] The following RLA were measured: Mechanical axis deviation, mechanical lateral proximal femoral angle, mechanical lateral distal femoral angle, mechanical medial proximal tibial angle, mechanical lateral distal tibial angle, anatomical medial proximal femoral angle, anatomical lateral distal femoral angle, anatomical medial neck-shaft angle, aPDFA, anatomical posterior proximal tibial angle, anatomical anterior distal tibial angle, and anatomical anterior neck-shaft angle.

Tomograms in these patients were obtained using a Toshiba Aquilon 64 computed tomograph (Toshiba Medical Systems, Japan). The thickness of the slices was 1 mm. The absence of flexion or hyperextension in the knee joint was assessed by 3D reconstructions of tomography data by drawing lines along the anterior cortex of the femur in the lower third and the tibia in the upper third.[9] To confirm the absence of torsion, the technique proposed by Strecker et al. was used.[17] According to this technique, imaging sections are obtained through the proximal femur to show the axis of the femoral neck, through the distal femoral condyles to show the axis of the knee (line between the most posterior points of both condyles). Composite overlay of hip and knee allow to measure torsion of femur that is the angle between femoral neck axis and knee axis. To measure tibial torsion, the imaging sections are obtained through proximal tibia to show the axis of the knee (line between the most posterior points of both condyles), through the distal tibia to show the axis of the ankle. Composite overlay of knee and ankle allows to calculate tibial torsion that is angle between knee axis and ankle axis.

The correspondence of all the listed parameters to the range of known normal values indicated the absence of deformity in the frontal and sagittal planes.

To analyze the computer tomography data, the Radiant Dicom Viewer 2020.1 software (Poznan, Poland) was used. A three-dimensional reconstruction of the lower limb was viewed on the monitor screen from its internal surface [Figure 1]a. The reference points were determined as follows, measured on a lateral projection:
Figure 1: Mechanical axis and joint lines for the sagittal plane: (a) Three-dimensional reconstruction of computed tomography of the patient, medial view; (b-f) construction of joint lines; (h) points of intersection of the mechanical axis with the joint lines; (i) reference angles (explanations are in the text)

Click here to view


  1. Center of the femoral head [Figure 1]b. Using the ellipse tool, a circle with a diameter equal to that of the femoral head was created, and its center was determined
  2. Apex of the greater trochanter [Figure 1]c
  3. Anterior point of the distal joint line of the femur. It corresponds to the place where the joint cartilage ends along the anterior surface of the femur [Figure 1]d
  4. Posterior point of the distal joint line of the femur. It corresponds to the place where the joint cartilage ends along the back of the femur [Figure 1]d
  5. Anterior point of the proximal joint line of the tibia. It corresponds to the place where the proximal joint line of the tibia begins anteriorly [Figure 1]e;
  6. Posterior point of the proximal joint line of the tibia. It corresponds to the place where the proximal joint platform of the tibia ends posteriorly [Figure 1]e
  7. Anterior point of the distal joint line of the tibia. It corresponds to the place where the distal joint platform of the tibia begins anteriorly [Figure 1]f
  8. Posterior point of the proximal joint line of the tibia. It corresponds to the place where the distal joint platform of the tibia ends posteriorly [Figure 1]f
  9. The middle of the distal joint line of the tibia. It corresponds to the middle of the distance (gi) [Figure 1]f.


Thus, the following lines were formed:

  • Line /ab/ – the proximal joint line of the femur [Figure 1]g
  • Line | cd/ – distal joint line of the femur [Figure 1]g
  • Line / ef/ – the proximal joint line of the tibia [Figure 1]g
  • Line / gi/ – distal joint line of the tibia [Figure 1]g
  • Line / ah/ – mechanical axis of the lower limb [Figure 1]h.


Intersection of the mechanical axis | ah | with the distal joint line of the femur | cd | forms point (j) [Figure 1]h.

Intersection of the mechanical axis | ah | with the proximal joint line of the tibia | ef | forms point (k) [Figure 1]h.

The following lengths were measured:

  • Segment | cj|
  • Segment | jd|
  • Lines | cd|
  • The segment | ek|
  • Segment | kf|
  • Lines | ef|.


Length of the distal joint line of the femur | bd | was taken as 100%. The following ratios were measured:

  • |cj|/|cd| × 100%
  • |jd|/|cd| × 100%.


The length of the proximal joint line of the tibia | eg | was taken as 100%. The following ratios were measured:

  • |ek|/|ef| × 100%
  • |kf|/|ef| × 100%.


Then, the following angles, formed by the intersection of the mechanical axis and joint lines, were measured [Figure 1]i:

  • -∝baj-mechanical posterior proximal femoral angle (mPPFA)
  • -∝ajd-mechanical posterior distal femoral angle (mPDFA)
  • -∝fkh-mechanical posterior proximal tibial angle (mPPTA)
  • -∝khg-mechanical anterior distal tibial angle (mADTA).


The results of investigation were processed using parametric analysis methods. To determine compliance with the normal distribution, the Shapiro–Wilk test was used. In the obtained variation series, the arithmetic mean values (M) and standard deviations were calculated.


  Results Top


The main results of the study to determine the RLA in the sagittal plane are given in [Table 1].
Table 1: Sagittal plane mechanical reference lines and angles

Click here to view


It was found that the mechanical axis of the lower limb in the sagittal plane | ah| [Figure 2]a crossing the joint line of the femur |cd | divides it into two segments in such a way that the anterior segment | cj | is 43.8% ± 7.9%, and the posterior | jd|-56.2% ± 7.9%. Simplifying somewhat, we can assert that | cj | takes 2/5, and | jd|-3/5 of the segment | cd| [Figure 2]b.
Figure 2: Mechanical reference lines and angle in the sagittal plane: (a and b) Mechanical axis of the limb in the sagittal plane and its relationship with the distal joint line of the femur and the proximal joint line of the tibia (explanations in the text), (c) reference angles formed by the intersection of the mechanical axis and joint lines in the sagittal plane

Click here to view


Mechanical axis of the lower limb in the sagittal plane | ah| [Figure 2]a crossing the proximal joint line of the tibia | ef | divides it into two segments in such a way that the anterior segment | ek | is 23.3% ± 8.8%, and the posterior | kf|-76.7% ± 8.8% [Figure 2]a. Simplifying somewhat, we can assert that | ek | takes 1/4 and | kf|-3/4 of the segment | ef|[Figure 2]b.

In this case, the value of ∝ baj (mPPFA) was 84.7° ± 8.8°; ∝ajd (mPDFA)-81.1° ± 3.95°; ∝fkh (mPPTA)-81.6° ± 2.8°; ∝khg (mADTA)-79.9° ± 2.98° [Figure 2]c.


  Discussion Top


Numerous publications devoted to the RLA of the sagittal plane[3],[4],[5],[6],[7],[8],[9],[10],[11] describe in detail the anatomical axis of the femur and tibia and accordingly, the anatomical angles formed by their intersection with the joint lines. Furthermore, a large number of publications are devoted to the anatomical curvature of the femur in the sagittal plane and its influence on arthroplasty of the knee joint,[18],[19] osteosynthesis with intramedullary nails.[20],[21] Hence, it was found that in the population of Japanese citizens, the curvature of the femur in the sagittal plane is greater than in other nations, i.e., standard “European” intramedullary locking nails and stems of oncological endoprostheses do not correspond to this curvature.[22]

At the same time, the mechanical axis, described in such detail for the frontal plane,[5],[8],[9] for the sagittal one, has not been studied until now. For example, one of the publications[23] describes an experiment in which a three-dimensional mechanical axis of the lower limb was constructed on a three-dimensional reconstruction of computed tomography data of the lower extremities by connecting the center of the femoral head and the center of the ankle joint. The influence of the level of detorsion osteotomy and the plane of the femoral osteotomy on the deviation of the mechanical axis in the sagittal plane was compared. One group consisted of models on which subtrochanteric osteotomy was simulated, in the second-supracondylar osteotomy. It was revealed that the level of detorsion osteotomy as well as its plane do not affect the deviation of the mechanical axis in the sagittal plane. At the same time, the researchers did not specify how the mechanical axis of the lower limb passes for the sagittal plane in normal conditions and what angles it forms with the joint surfaces of the femur and tibia.

Our research does not confirm the statement of Standard et al.[9] that the mechanical axis of the limb for the sagittal plane, like the anatomical, intersects the distal joint line of the femur at the border of the anterior 1/3 and posterior 2/3 of the joint line of the femur. Our results indicate that the mechanical axis divides the distal joint line of the femur into two segments of unequal length. The anterior one occupies 2/5 of the total joint line, the posterior one-3/5 of it.

Furthermore, our results do not correspond to another statement by Standard et al.[9] that the mechanical axis crosses the proximal joint line of the tibia at the border of its anterior 1/5. According to the data obtained on the basis of 3D modeling, the mechanical axis divides the joint line into segments, the anterior of which is ¼ of its total length.

When determining the mechanical angles in the sagittal plane, the data obtained in our study (mPDFA-81.1° ± 3.95°; mPPTA-81.6° ± 2.8°; and mADTA-79.9° ± 2.98°), in general, confirm and elaborate on data from Standard et al.,[9] for which, mPDFA was 83° (79°–87°); mPPTA-81° (77°–84°); mADTA-80° (78°–82°).

At the same time, attention is paid to the fact that the determination of the posterior proximal angle of the femur in the sagittal plane (mPPFA) from the joint line is not devoid of disadvantages inherent to its determination in the frontal plane. Namely, a significant dependence on the accuracy of determining the apex of the greater trochanter. This factor can play a negative role in the routine determination of the mechanical axis of the proximal femur fragment in the sagittal plane. Obviously, it is necessary to develop, by analogy with the frontal plane,[11] methods for determining this axis on the basis of the femoral neck and the anatomical axis of the proximal third of the femoral shaft.


  Conclusion Top


The obtained data on the mechanical axis of the lower limb for the sagittal plane and the reference angles formed by it with the joints can be used both in assessing deformity, planning its correction, and also to assess the accuracy of deformity correction. There is an objective need to determine all known RLA based on 3D modeling.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.



 
  References Top

1.
Paley D, Herzenberg JE, Tetsworth K, McKie J, Bhave A. Deformity planning for frontal and sagittal plane corrective osteotomies. Orthop Clin North Am 1994;25:425-65.  Back to cited text no. 1
    
2.
Paley D. Principles of Deformity Correction. 1st ed. New York: Spinger-Verlag; 2002.  Back to cited text no. 2
    
3.
Chao EY, Neluheni EV, Hsu RW, Paley D. Biomechanics of Malalignment. Orthop Clin North Am 1994;25:379-86.  Back to cited text no. 3
    
4.
Chiu KY, Zhang SO, Zhang GH. Posterior slope of tibial plateau in Chinese. J Arthroplasty 2000;15:224-7.  Back to cited text no. 4
    
5.
Hsu RW, Himeno S, Coventry MB, Chao EY. Normal axial alignment of the lower extremity and load-bearing distribution at the knee. Clin Orthop 1990;255:215-27.  Back to cited text no. 5
    
6.
Matsuda S, Miura H, Nagamine R, Urabe K, Ikenoue T, Okazaki K, et al. Posterior tibial slope in the normal and varus knee. Am J Knee Surg 1999;12:165-8.  Back to cited text no. 6
    
7.
Moreland JR, Bassett LW, Hanker GJ. Radiographic analysis of the axial alignment of the lower extremity. J Bone Joint Surg Am 1987;69:745-9.  Back to cited text no. 7
    
8.
Paley D, Tetsworth K. Mechanical axis deviation of the lower limbs: Preoperative planning of uniapical angular deformities of the tibia or femur. Clin Orthop 1992;280:48-64.  Back to cited text no. 8
    
9.
Standard SC, Herzenberg JE, Conway JD, Siddiqui NA, McClure PK. The Art of Limb Alignment. 8th ed. Baltimore: Rubin Institute for Advanced Orthopedics, Sinai Hospital of Baltimore; 2019.  Back to cited text no. 9
    
10.
Yoshioka Y, Siu D, Cooke TD. The anatomy and functional axes of the femur. J Bone Joint Surg Am 1987;69:873-80.  Back to cited text no. 10
    
11.
Solomin LN. The Basic Principles of External Skeletal Fixation Using the Ilizarov and Other Devices. 2nd ed./Milan: Springer-Verlag Italia; 2012. p. 1593.  Back to cited text no. 11
    
12.
Jamali AA, Meehan JP, Moroski NM, Anderson MJ, Lamba R, Parise C, et al. Do small changes in rotation affect measurements of lower extremity limb alignment? J Orthop Surg Res 2017;12:77.  Back to cited text no. 12
    
13.
Fucentese SF, Meier P, Jud L, Köchli GL, Aichmair A, Vlachopoulos L, et al. Accuracy of 3D-planned patient specific instrumentation in high tibial open wedge valgisation osteotomy. J Exp Orthop 2020;7:7.  Back to cited text no. 13
    
14.
Munier M, Donnez M, Ollivier M, Flecher X, Chabrand P, Argenson JN, et al. Can three-dimensional patient-specific cutting guides be used to achieve optimal correction for high tibial osteotomy? Pilot study. Orthop Traumatol Surg Res 2017;103:245-50.  Back to cited text no. 14
    
15.
Jacquet C, Chan-Yu-Kin J, Sharma A, Argenson JN, Parratte S, Ollivier M, et al. “More accurate correction using “patient-specific” cutting guides in opening wedge distal femur varization osteotomies. Int Orthop 2019;43:2285-91.  Back to cited text no. 15
    
16.
Shi J, Lv W, Wang Y, Ma B, Cui W, Liu Z, et al. Three dimensional patient-specific printed cutting guides for closing-wedge distal femoral osteotomy. Int Orthop 2019;43:619-24.  Back to cited text no. 16
    
17.
Strecker W, Leppler P, Gebhard F, Kinzl L. Length and torsion of the lower limb. J Bone Joint Surg 1997:79-B:1019-23.  Back to cited text no. 17
    
18.
Kazemi SM, Shafaghi T, Minaei R, Osanloo R, Abrishamkarzadeh H, Safdari F, et al. The effect of sagittal femoral bowing on the femoral component position in total knee arthroplasty. Arch Bone Jt Surg 2017;5:250-4.  Back to cited text no. 18
    
19.
Ko JH, Han CD, Shin KH, Nguku L, Yang IH, Lee WS, et al. Femur bowing could be a risk factor for implant flexion in conventional total knee arthroplasty and notching in navigated total knee arthroplasty. Knee Surg Sports Traumatol Arthrosc 2016;24:2476-82.  Back to cited text no. 19
    
20.
Buford WL Jr., Turnbow BJ, Gugala Z, Lindsey RW. Three-dimensional computed tomography-based modeling of sagittal cadaveric femoral bowing and implications for intramedullary nailing. J Orthop Trauma 2014;28:10-6.  Back to cited text no. 20
    
21.
Egol KA, Chang EY, Cvitkovic J, Kummer FJ, Koval KJ. Mismatch of current intramedullary nails with the anterior bow of the femur. J Orthop Trauma 2004;18:410-5.  Back to cited text no. 21
    
22.
Abdelaal AH, Yamamoto N, Hayashi K, Takeuchi A, Morsy AF, Miwa S, et al. Radiological assessment of the femoral bowing in japanese population. SICOT J 2016;2:2.  Back to cited text no. 22
    
23.
Jud L, Andronic O, Vlachopoulos L, Fucentese SF, Zingg PO. Mal-angulation of femoral rotational osteotomies causes more postoperative sagittal mechanical leg axis deviation in supracondylar than in subtrochanteric procedures. J Exp Orthop 2020;7:46.  Back to cited text no. 23
    


    Figures

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    Tables

  [Table 1]



 

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