Changes in varus and valgus slope caused by tibial cutting block rotation in total knee arthroplasty

William Oetojo; Hector Castillo; Brian Seguin; Nicholas Brown

doi:10.1016/j.jorep.2025.100643

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Research Article

2025

:4;

100643

doi:

10.1016/j.jorep.2025.100643

Changes in varus and valgus slope caused by tibial cutting block rotation in total knee arthroplasty

William Oetojo^a, Hector Castillo^b, Brian Seguin^c, Nicholas Brown^b,

a Stritch School of Medicine, Loyola University, Maywood, IL, 60153, USA

b Loyola University Health System, Department of Orthopaedic Surgery and Rehabilitation, Maywood, IL, 60153, USA

c Loyola University Chicago, Department of Mathematics and Statistics, Chicago, IL, 60660, USA

⁎Corresponding author: Nicholas Brown. nicholas.brown002@lumc.edu

Received: 2025-2-4, Accepted: 2025-3-14, Published: 2025-3-16

The Authors

Disclaimer:
This article was originally published by Reed Elsevier India Pvt. Ltd. and was migrated to Scientific Scholar after the change of Publisher.

Abstract

Most surgeons attempt to cut their tibial slope to align with their intended tibial component rotation; however, there is variability in guide placement and rotational landmarks. Tibial slope varies between 5 and 15 °, while tibial cutting guide rotation can vary up to 40 ° in either direction. Just as acetabular cup positioning can be altered based on pelvic tilt, this study sought to quantify the analogous change in varus and valgus slope for every degree of tibial cutting guide rotation.

Post-rotational varus and valgus tilt was quantified by the expression 90°−cos−1(−cos⁡(θ)sin⁡(σ)+sin⁡(θ)sin⁡(ϕ)), and post-rotational posterior tibial slope (PTS) was quantified by 90°−cos−1(−sin⁡(θ)sin⁡(σ)−cos⁡(θ)sin⁡(ϕ)), where θ represents the tibial cutting block rotation, σ represents any preexisting varus/valgus slope, and ϕ represents the PTS before rotation. Rotation was calculated using a standard 5° slope for CR components, mean anatomic slope of 7°, and larger degree of anatomic slope, 10°.

There was a non-linear relationship between tibial varus and valgus change and rotation. Mean change for neutral varus/valgus knees every 10° over a 40° range yielded 0.80° for 5° PTS, 1.12° for 7° PTS, and 1.60° for 10° PTS. Additionally, there was a non-linear decrease in mean PTS per 10° rotation of 0.29° for 5° PTS, 0.41° for 7° PTS, and 0.59° for 10° PTS.

Newer kinematic methods of total knee arthroplasty aim to restore pre-arthritic native anatomy. Surgeons should be aware of the potential impact of changing the rotation of tibial slope on both sagittal and coronal plane balance.

Keywords

Total knee arthroplasty

Tibial cutting guide rotation

Posterior tibial slope

Tibial alignment

Kinematic alignment

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1 Introduction

Mechanical alignment (MA) has been long utilized as the standard of TKA, given its proposed success on clinical outcomes and survivorship.¹^,² However, there have been studies demonstrating the use of kinematic alignment (KA), which aims recreate native joint lines while preserving rotational axes around the knee.^3–7 According to Hirschmann et al., functional knee phenotypes can vary on average 3° in either varus or valgus along the hip-knee-angle, femoral mechanical angle, and/or tibial mechanical angle.³ Thus, surgeons who perform unrestricted KA attempt to match pre-arthritic anatomy as closely as possible.

Unfortunately, there is a paucity of data investigating the variability in tibial component positing, with studies noting between 5 and 15 ° of variation in posterior tibial slope,^8–11 and a possible range of 38 ° of internal rotation and 31 ° of external rotation variation in tibial component positioning.¹² For proper tibial rotation, most surgeons attempt to cut their tibial slope to align with their intended rotation; however, there is variability in guide placement and rotational landmarks. Many methods have since been described for intraoperative tibial component rotation, common examples include anatomical placement of an asymmetrical tibial tray on the cut tibial surface, usage of the tibial tubercle as a landmark for tibial tray rotation, and rotation of the tibial tray that follows femoral component into extension.^13–15

From literature investigating spinopelvic relationships, it has been noted that every degree of change in pelvic tilt can alter 0.7° of anteversion and 0.3° of inclination.¹⁶ Given the possibly similar mechanistic change of the tibial rotation in space, it can be hypothesized that there might be quantifiable varus and valgus changes based on tibial rotation. D'Lima et al. utilized a computer module and identified that coronal alignment of the tibial cut changed by 0.07° per degree of axial rotation and 0.22° per degree of posterior slope.⁸ However, that study looked at a maximum of 15° of external rotation and 25° of internal rotation, with a maximum 7° PTS. Using formulaic derivation, this study sought to validate D'Lima et al. and quantify the change in varus and valgus slope for every degree of tibial cutting guide malrotation using a formula that can capture larger ranges of tibial rotation and PTS.

2 Methods

Present study was IRB exempt. The coordinate system is set up such that the axial cut of the knee is represented by the xy-plane, the sagittal cut of the knee in the yz-plane, and the frontal cut in the xz-plane (Figure A.1). For the following equations, σ represents any preexisting varus/valgus tilt (Figure A.2), ϕ represents the angle of the original posterior tibial slope (PTS) before rotation, and θ represents tibial cutting block rotation in degrees counterclockwise about the z-axis – thus, a positive θ would represent internal rotation for a right knee, versus external rotation in a left knee (Figure A.3).

Using linear algebra and vector calculations, post-rotational varus and valgus tilt was quantified by Eq. (A.9),(9)90°−cos−1(−cos⁡(θ)sin⁡(σ)+sin⁡(θ)sin⁡(ϕ)),

and post-rotational posterior tibial slope (PTS) was quantified by Eq. (A.11),(11)90°−cos−1(−sin⁡(θ)sin⁡(σ)−cos⁡(θ)sin⁡(ϕ)).

Full proof of the derivation of these results can be found in the appendix; this was all verified by a professor of mathematics with a PhD in mathematical sciences.

Rotation was calculated using a standard 5° slope for CR components, the mean anatomic slope of 7°, and larger degree of anatomic slope, 10°. Preexisting varus/valgus tilt (σ) was used to quantify any coronal changes in tibial rotation for different knee phenotypes of neutral varus/valgus deviation as well as 3, 6, and 9° of tibial varus/valgus deviation.³ Changes in both tibial varus/valgus tilt as well as post-rotational PTS was quantified every 10°, up to 40° of deviation in either internal or external rotation; however, the equations allow for a large range if needed.

3 Results

3.1

3.1 Neutral tibial phenotypes (σ = 0)

There was a non-linear relationship between varus and valgus change and degrees of rotation. Mean change in varus and valgus tilt for neutral varus/valgus knees every 10° over a 40° range yielded 0.80° for 5° PTS, 1.12° for 7° PTS, and 1.60° for 10° PTS. At 20° of internal rotation, 5° of PTS yielded 1.71° of additional tibial valgus, 7° of PTS an additional 2.39° of tibial valgus, and 10° PTS an additional tibial 3.40° of valgus; 20° of external rotation for a neutral knee would demonstrate equivalent change but in varus. At a maximum of 40° internal rotation, 5° of PTS yielded 3.21° of additional tibial valgus, 7° of PTS an additional 4.49° of tibial valgus, and 10° PTS an additional 6.41° of tibial valgus (Table A.1) Additionally, there was a non-linear decrease in mean PTS per 10° degree rotation of 0.29° for 5° PTS, 0.41° for 7° PTS, and 0.59° for 10° PTS (Table A.2).

3.2

3.2 Non-neutral tibial phenotypes

At 5° PTS, mean change in varus and valgus tilt every 10° of internal rotation over a 40° range yielded an additional 0.98° of valgus in knees with preexisting 3° of tibial varus, 1.16° in knees with 6° of tibial varus, 0.63° in knees with 3° tibial valgus, and 0.46° in knees with 6° of tibial valgus. For knees with preexisting 3° tibial varus, 40° of internal rotation was enough to erase the preexisting varus slope and yield a post-rotational valgus tilt of 0.91° (Table A.3). Additionally, there was a non-linear decrease in mean PTS per 10° internal rotation of 0.78° for 3° tibial varus, and 1.26° for 6° tibial varus. For knees with preexisting tibial valgus, there was a non-linear increase in mean PTS per 10° internal rotation, yielding an additional 0.19° for 3° tibial valgus, and 0.68° for 6° tibial valgus (Table A.4).

At 7° PTS, mean change in varus and valgus tilt every 10° of internal rotation over a 40° range yielded an additional 1.30° of valgus in knees with preexisting 3° of tibial varus, 1.48° in knees with 6° of tibial varus, 0.95° in knees with 3° tibial valgus, and 0.78° in knees with 6° of tibial valgus. For knees with preexisting 3° tibial varus, 30° of internal rotation was enough to erase the preexisting varus slope and yield a post-rotational valgus tilt of 0.89°, while internal rotation >40° will erase the preexisting varus slope in knees with preexisting 6° tibial varus (Table A.5). Additionally, there was a non-linear decrease in mean PTS per 10° internal rotation of 0.90° for 3° tibial varus, and 1.38° for 6° tibial varus. For knees with preexisting tibial valgus, there was a non-linear increase in mean PTS per 10° internal rotation, yielding an additional 0.08° for 3° tibial valgus, and 0.56° for 6° tibial valgus (Table A.6).

At 10° PTS, mean change in varus and valgus tilt every 10° of internal rotation over a 40° range yielded an additional 1.78° of valgus in knees with preexisting 3° of tibial varus, 1.95° in knees with 6° of tibial varus, 1.43° in knees with 3° tibial valgus, and 1.26° in knees with 6° of tibial valgus. For knees with preexisting 3° tibial varus, 20° of internal rotation was enough to erase the preexisting varus slope and yield a post-rotational valgus tilt of 0.59°, while internal rotation of 40° was enough for knees with preexisting 6° tibial varus to yield a new 1.81° valgus tilt (Table A.7). Additionally, there was a non-linear decrease in mean PTS per 10° internal rotation of 1.08° for 3° tibial varus, 1.56° for 6° tibial varus, and 0.10° for 3° tibial valgus. For knees with preexisting 6° tibial valgus, there was a non-linear increase in mean PTS per 10° internal rotation, yielding an additional 0.39° of valgus (Table A.8).

4 Discussion

This study found an equation to quantify the non-linear change in coronal alignment after tibial rotation. For neutral knees without preexisting tibial varus or valgus, 10° of internal rotation yielded approximately 1.12° of post-rotational valgus in an average PTS of 7°. This change was minimized in smaller PTS (5°) and magnified in larger PTS (10°).

Newer kinematic methods aim to match native varus/valgus tilt and PTS. Methods of alignment, whether using manual instruments or robotics have demonstrated variability.¹⁷ A study by Matziolis et al. utilized 3D CT for rotational alignment and noted variation of 2.9° valgus to 3.1° varus, with rotation ranging from 11° external rotation to 21° of internal rotation.¹⁸ Another study demonstrated coronal deviation of 3.8° valgus to 3.9° varus when rotational variations ranged from 15° of external rotation to 26° of internal rotation.¹⁹ Lastly, D'Lima et al. utilized computerized findings to malignment of 1.8° for 15° of tibial rotation at 7° PTS,⁸ which is exactly the amount of varus/valgus tilt if 15° of axial rotation and 7° PTS is inputted into the derived formula (assuming no preexisting varus/valgus tilt). Overall, the findings of this paper validate previous literature, which noted 1.21° malalignment for 10° tibial rotation and 2.39° for 20° tibial rotation at 7° PTS for neutral knees without any preexisting varus or valgus tilt. There currently aren't any clear methods of alignment that are superior to the other. Aligning with anatomical placement of an asymmetrical tibial tray on the cut tibial surface, usage of the tibial tubercle as a landmark for tibial tray rotation, and rotation of the tibial tray that follows femoral component into extension methods can still lead to wide variability.^13–15 Additionally, the tibial cut is made prior to rotating the tibial tray, so the tibial cut plane is essentially an educated guess as to how the tibial component will be rotated.

Further, the equations derived in this study include the possibility of preexisting tibial varus and valgus, mimicking the variability of anatomic knee phenotypes.³ Simply put, anatomically tibial varus knees lost approximately 1° of varus for every 10 degrees of internal rotation at an average PTS of 7°. This change was lessened with smaller PTS and magnified with larger PTS. With excessive internal rotation (>30°), it's possible to entirely lose the preexisting tibial varus and demonstrate a new post-rotational tibial valgus.

Limitations of this study reside in its theoretical nature. This has not been utilized in practice nor trialed on living or cadaveric knees. Given the wide variability in human anatomy, the equations proposed in this study would benefit from usage in large cohorts. Nevertheless, the roles of the proof and equations of this study are still applicable given that it includes possible anatomic variations of the knee (e.g. preexisting tibial varus and valgus slope). It is also important to note that although results shown in this study were largely described in internal rotation, it can be assumed that the values will be reciprocated such that external rotation would lead to increased tibial varus change. Furthermore, the equations themselves can be used to find any combination of PTS, preexisting varus/valgus tilt, and axial rotation; thus, the results reported by the study merely state the possible results of an infinite range of values. For the ideal knee, this study was able to highlight the need for further understanding of optimal placement of tibial cutting guide, which inevitably promotes the accuracy of kinematic alignment and balance in TKA.

5 Conclusions

Newer kinematic methods of total knee arthroplasty aim to restore pre-arthritic native anatomy. Both manual and robotic methods of placing the tibial component have variability, which is exacerbated by the wide variability of human knee anatomy and methods of rotating the tibial component. Surgeons should be aware of the potential impact of changing the rotation of tibial slope on both sagittal and coronal plane balance.

CRediT authorship contribution statement

William Oetojo: Methodology, Formal analysis, Data curation, Investigation, Writing – original draft, Writing – review & editing, Visualization. Hector Castillo: Conceptualization, Methodology, Validation, Investigation, Writing – review & editing, Visualization, Supervision. Brian Seguin: Conceptualization, Methodology, Validation, Investigation, Writing – original draft, Writing – review & editing, Visualization, Supervision, Project administration. Nicholas Brown: Conceptualization, Methodology, Validation, Investigation, Writing – original draft, Writing – review & editing, Visualization, Supervision, Project administration.

Ethical approval and patient consent

IRB exempt.

Ethical and patient's consent

This retrospective study was IRB exempt.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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