# Multi-Stage Platform for (Semi-)Automatic Planning in Reconstructive Orthopedic Surgery

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## Abstract

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## 1. Introduction

- Most planning methods rely on the combination of salient proxy structures. This indirect description implies a greater number of error sources, which translates to higher observer-variability if the planning is done manually;
- Certain surgical planning can have a high level of geometric complexity. Sufficiently precise manual execution is only possible with tailored software tools or otherwise requires great amounts of time and labor;
- The ability to register pre-operative planning and intra-operative live data is highly complex due to the variable configuration of the joint and arbitrary relation between patient, table, and imaging system;
- Ad-hoc modifications of the surgical plan are essential to compensate for motion during the intervention;
- Manual interaction with a computer-assisted planning system is undesirable due to the surgery’s sterile setting. At the same time, the planning system should offer granular controls to correct each construction step with real-time visualization.

## 2. Related Work and Contribution

#### 2.1. Image-Based Surgical Planning in Orthopedics and Traumatology

#### 2.2. Multi-Task Learning and Task Weighting

#### 2.3. Contribution

- This work establishes a multi-stage workflow that covers all necessary steps for image-based surgical planning on 2D X-ray images. The workflow is designed to mimic the clinically-established manual planning process, enabling granular control over each anatomical feature contributing to the planning geometry;
- We evaluate the model for three trauma-surgical planning applications on both diagnostic as well as intra-operative X-ray images of the knee joint. The numeric results match clinical requirements and encourage further clinical evaluation;
- We empirically show that the detection of anatomical landmarks benefits from a MTL setting. We confirm that explicit task weighting significantly reduces the landmark localization error, and illustrate that a multi-head network topology achieves similar performance to task-specific decoders, which are computationally much more expensive.
- Our study demonstrates that sharing tasks across anatomically related applications does not significantly improve performance compared to the single-application variant.

#### 2.4. Article Structure

## 3. Materials and Methods

#### 3.1. (Semi-)Automatic Workflow for 2D Surgical Planning

#### 3.1.1. Multi-Stage Planning Algorithm

- Semantically coherent regions. Segmentation of connected regions that share certain characteristics, mostly bones and tools;
- Anatomical keypoints. Point-like landmarks that pinpoint features of interest on the bone surface;
- Elongated structures. Straight and curved lines that describe edges, ridges, or that refer to indirect features, such as anatomical axes.

#### 3.1.2. Stage A) MTL for Joint Extraction of Anatomical Features

- Uniform (constant). All tasks are weighted uniformly: ${w}^{t}=1$.
- Balanced relative learning rates (dynamic). Gradient normalization by Chen et al. [68] to ensure balanced training rates of all tasks, i.e., approximately equally-sized update steps for each task: ${w}^{t}=\mathrm{GradNorm}\left(t\right)$.

- Single-task baseline. For comparison, a STL baseline of independent encoder-decoder structures is optimized. Here, no parameters are shared;
- Multi-head topology. Both the encoder and decoder parameters are shared between the tasks in this variant. The output of the decoder is fed into task-specific prediction heads, which involve significantly less dedicated parameters and, thus, require a multi-purpose feature decoding. We argue that such a constrained decoder might benefit learning for highly similar tasks;
- Multi-decoder topology. After feature extraction in a shared feature encoder, the latent representation is used as input for the task-specific decoders and prediction heads. In other words, an abstract representation has to be found that serves the reconstruction for different kinds of tasks.

#### 3.1.3. Stage B) Extraction of Geometric Objects and Post-Processing

#### 3.1.4. Stage C) Geometric Construction of Individual Planning Steps

#### 3.2. Multi-Task Network Architecture

#### 3.3. Dataset, Ground Truth, and Augmentation Protocol

#### 3.3.1. Cohort 1: Diagnostic X-ray Images

#### 3.3.2. Cohort 2: Intra-Operative X-ray Images

#### 3.3.3. Augmentation and Ground Truth

#### 3.4. Training Policy and Implementation Details

#### 3.5. Evaluation Protocol

## 4. Results

#### 4.1. Research Questions

- Rq (1).
- How does the MTL network topology and task weighting strategy affect anatomical feature extraction?
- Rq (2).
- Does sharing tasks across anatomically related applications improve the feature extraction and target positioning compared to the single-application variant?
- Rq (3).
- How does the number of training data affect the planning accuracy?
- Rq (4).
- Can the performance on highly-standardized diagnostics images be applied to more complex imaging data in the intra-operative environment?

#### 4.2. Rq (1) Network Topology and Task Weighting

#### 4.3. Rq (2) Combining Tasks across Multiple Surgical Applications

#### 4.4. Rq (3) Effect of the Number of Training Data

#### 4.5. Rq (4) Application to Intra-Operative Data

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MPFL | Medial Patellofemoral Ligament |

ACL | Anterior Cruciate Ligament |

PCL | Posterior Cruciate Ligament |

AM | Anteromedial |

PL | Posterolateral |

OR | Operating room |

MTL | Multi-task learning |

STL | Single-task learning |

GradNorm | Gradient normalization |

ASSD | Average symmetric surface distance |

ED | Euclidean distance |

## Appendix A. Pre-Operative Planning Examples

**Figure A1.**Planning predictions on pre-operative test data with multi-head topology and GradNorm task weighting. (

**a**), MPFL. (

**b**), ACL. (

**c**), PCL.

## Appendix B. Planning Geometry

#### Appendix B.1. MPFL Reconstruction

**Figure A2.**Geometric relations of the considered surgery planning types. (

**a**), MPFL. (

**b**,

**c**), femoral and tibial ACL. (

**d**), PCL.

#### Appendix B.2. ACL Reconstruction

#### Appendix B.2.1. Femoral Bundle Attachments

#### Appendix B.2.2. Tibial Bundle Attachments

#### Appendix B.3. PCL Reconstruction

## Appendix C. Neural Network Topology

**Table A1.**Detailed topology of the used multi-task network in the multi-head configuration. The architecture is adapted from the Stacked Hourglass Network by Newell et al. [76]. The bottleneck and head topology are illustrated in Figure A3. (s: stride, p: padding, ⊕: feature fusion by element-wise addition, NN: nearest-neighbor).

Block | Input | Operation | C_{in} | C_{out} | Input Size | Output Size | |
---|---|---|---|---|---|---|---|

Pre | P1 | – | 3 × 3 conv, p = 1 | 1 | 64 | $256\times 256$ | $256\times 256$ |

P2 | P1 | Bottleneck | 64 | 128 | $256\times 256$ | $256\times 256$ | |

P3 | P2 | Bottleneck | 128 | 128 | $256\times 256$ | $256\times 256$ | |

Encoder | E1 | P3 | Bottleneck | 128 | 128 | $256\times 256$ | $256\times 256$ |

$2\times 2$ max pool, s = 2 | 128 | 128 | $256\times 256$ | $128\times 128$ | |||

E2 | E1 | Bottleneck | 128 | 128 | $128\times 128$ | $128\times 128$ | |

$2\times 2$ max pool, s = 2 | 128 | 128 | $128\times 128$ | $64\times 64$ | |||

E3 | E2 | Bottleneck | 128 | 128 | $64\times 64$ | $64\times 64$ | |

$2\times 2$ max pool, s = 2 | 128 | 128 | $64\times 64$ | $32\times 32$ | |||

E4 | E3 | Bottleneck | 128 | 128 | $32\times 32$ | $32\times 32$ | |

$2\times 2$ max pool, s = 2 | 128 | 128 | $32\times 32$ | $16\times 16$ | |||

Skip Con. | S1 | P3 | Bottleneck | 128 | 128 | $256\times 256$ | $256\times 256$ |

S2 | E1 | Bottleneck | 128 | 128 | $128\times 128$ | $128\times 128$ | |

S3 | E2 | Bottleneck | 128 | 128 | $64\times 64$ | $64\times 64$ | |

S4 | E3 | Bottleneck | 128 | 128 | $32\times 32$ | $32\times 32$ | |

Decoder | D1 | E4 | Bottleneck | 128 | 128 | $16\times 16$ | $16\times 16$ |

×2 NN up-sampling | 128 | 128 | $16\times 16$ | $32\times 32$ | |||

D2 | D1⊕S1 | Bottleneck | 128 | 128 | $32\times 32$ | $32\times 32$ | |

×2 NN up-sampling | 128 | 128 | $32\times 32$ | $64\times 64$ | |||

D3 | D2⊕S2 | Bottleneck | 128 | 128 | $64\times 64$ | $64\times 64$ | |

×2 NN up-sampling | 128 | 128 | $64\times 64$ | $128\times 128$ | |||

D4 | D3⊕S3 | Bottleneck | 128 | 128 | $128\times 128$ | $128\times 128$ | |

×2 NN up-sampling | 128 | 128 | $128\times 128$ | $256\times 256$ | |||

Heads | H1 (t = 1) | D4⊕S4 | Head | 128 | C_{1} | $256\times 256$ | $256\times 256$ |

H2 (t = 2) | D4⊕S4 | Head | 128 | C_{2} | $256\times 256$ | $256\times 256$ | |

H3 (t = 3) | D4⊕S4 | Head | 128 | C_{3} | $256\times 256$ | $256\times 256$ |

**Figure A3.**Topology of utilized neural network building blocks based on the work from Newell et al. [76] and He et al. [77]. (

**a**), layout of 3-layer pre-activation bottleneck with identity mapping [77]. If the number of input and output channels is different, the identity function is replaced by a 1 × 1 convolution. (

**b**), task heads which output ${C}_{t}$ predictions. (p: padding, ⊕: feature fusion by element-wise addition).

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**Figure 1.**Illustration of the three considered surgical planning guidelines for ligament reconstruction on the knee joint. (

**a**) Description and localization of relevant anatomical structures for all plannings. (

**b**) Localization of the anatomic femoral insertion site for Medial Patellofemoral Ligament (MPFL) reconstruction surgery. The construction builds upon the clinical study by Schoettle et al. [21]. (

**c**) Identification of the surface attachment points for the anteromedial (AM; orange) and posterolateral (PL; teal) bundles for Anterior Cruciate Ligament (ACL) reconstruction surgery. The planning follows the quadrant method by Bernard et al. [32] and Stäubli/Rauschning [34] for the femur and tibia, respectively. (

**d**) Detection of the optimal drill path angulation and position for transtibial reconstruction of the Posterior Cruciate Ligament (PCL) according to Johannsen et al. [23].

**Figure 2.**Overview of the automatic planning workflow. After selecting a planning blueprint and a corresponding configuration, the target X-ray image is processed in three consecutive stages. After extraction the 2D anatomical features with a multi-task network, they are transformed to their corresponding geometric descriptors. The individual construction steps defined in the planning blueprint are automatically calculated by interrelating the extracted geometry (here, steps 1–3 in Stage C)). If needed, the user can manually modify the planning by adjusting individual control points upon real-time updates of the complete plan.

**Figure 3.**Architecture of the proposed multi-task network. After calculating a shared representation of the input image ${x}_{i}$ with the meta learner, an individual learner for each task computes an corresponding prediction ${y}_{i}^{T}$ in the task solution space ${\mathcal{Y}}^{t}$. Two strategies for the individual learners with different levels of parameter sharing are displayed: (i) Multi-decoder topology with independent decoders and prediction heads, (ii) Multi-head topology with shared decoder but independent prediction heads. Details of the architecture are provided in Figure A3, Table A1.

**Figure 4.**Radar charts of prediction errors per application and anatomical feature according to Stage A) (Section 3.1.2) and different model topologies and optimization policies. For all metrics but the mean Dice coefficient (mDice ↑) for segmentation tasks, lower is better. (

**a**), MPFL. (

**b**), ACL. (

**c**), PCL. (

**d**), combined (MPFL, ACL, PCL).

**Figure 5.**Visualization of heatmap prediction quality for different model topologies and task weighting strategies for a random sample from the test set.

**Figure 6.**Boxplots of the planning metrics for each surgical application and different model topologies and optimization policies (without fliers/outliers). (

**a**), MPFL. (

**b**), ACL. (

**c**), PCL. (

**d**), combined (MPFL, ACL, and PCL). For each boxplot and topology pairing, we tested statistical significance with a two-sided Mann–Whitney U rank test ((n) not significant: $p\ge 0.05$, (*) significant: $p<0.05$, (**) highly significant: $p<0.001$).

**Figure 7.**Comparison between single- and multi-application model performance on the test set. (

**a**), MPFL. (

**b**), ACL. (

**c**), PCL. For each boxplot and pairing, we tested statistical significance with a two-sided Mann–Whitney U rank test ((n) not significant: $p\ge 0.05$, (*) significant: $p<0.05$.

**Figure 8.**Effect of different amounts of training data on the planning metrics (logarithmic scale for y-axis for better visibility). (

**a**), MPFL. (

**b**), ACL. (

**c**), PCL. (

**d**), combined (MPFL, ACL, PCL). We report correlation coefficients $\rho $ with rejection probability $p<0.05$ based on two-sided Spearman’s rank correlation measure.

**Figure 9.**Planning predictions on intra-operative test data with multi-head topology and GradNorm task weighting. (

**a**), MPFL. (

**b**), ACL.

**Table 1.**Mathematical representation of the relevant anatomical structures that allow subsequent optimization and geometric analysis.

Anatomical Structure | Spatial Representation |
---|---|

Semantically coherent regions | Pixel-wise and multi-label segmentation. The multi-label aspect allows for overlap-aware segmentation, e.g., in areas between bones or metal implants. |

Anatomical keypoints | Individual heatmaps/activation maps. For that purpose, a multivariate Gaussian distribution with its mean at the keypoint coordinate and a predefined standard deviation is sampled. |

Elongated structures | Line-symmetric heatmap/activation map. The distance to the line segment or the axis of interest is evaluated and transformed using a Gaussian function. |

**Table 2.**Analysis of the maximum intensity of keypoint heatmaps for different model topologies and task weighting strategies. Each variant’s values for mean and standard deviation $(\mathrm{mean}\pm \mathrm{std})$ are calculated across all application-specific keypoints on every test set image. The results of the best network variant for each planning methodology is marked in bold.

Multi-Head | Multi-Decoder | Single-Task | |||
---|---|---|---|---|---|

Planning | Uniform | GradNorm | Uniform | GradNorm | Uniform |

MPFL (n = 2) | $0.64\pm 0.11$ | $\mathbf{0}.\mathbf{83}\pm \mathbf{0}.\mathbf{09}$ | $0.76\pm 0.09$ | $0.76\pm 0.11$ | $0.80\pm 0.12$ |

ACL (n = 5) | $0.42\pm 0.08$ | $0.71\pm 0.12$ | $0.43\pm 0.07$ | $\mathbf{0}.\mathbf{73}\pm \mathbf{0}.\mathbf{12}$ | $0.57\pm 0.16$ |

PCL (n = 1) | $\mathbf{0}.\mathbf{90}\pm \mathbf{0}.\mathbf{11}$ | $0.84\pm 0.11$ | $0.83\pm 0.09$ | $0.79\pm 0.10$ | $0.84\pm 0.08$ |

Comb. (n = 7) | $0.41\pm 0.12$ | $0.66\pm 0.12$ | $0.38\pm 0.10$ | $\mathbf{0}.\mathbf{71}\pm \mathbf{0}.\mathbf{12}$ | $0.23\pm 0.11$ |

**Table 3.**Numerical planning results on intra-operative test data. Each metric value is reported w.r.t. the original resolution of $[\mathrm{H}:976\times \mathrm{W}:976]\phantom{\rule{0.166667em}{0ex}}\mathrm{px}$. The results of the best network variant for each planning methodology is marked in bold. In three ACL cases, planning was not possible due to poor segmentation quality.

Multi-Head | Multi-Decoder | ||||
---|---|---|---|---|---|

Planning | Metric [px] | Median, ${\mathbf{CI}}_{95\%}$ | Cnt. | Median, ${\mathbf{CI}}_{95\%}$ | Cnt. |

MPFL | Schoettle Pt. | $\mathbf{9}.\mathbf{08},\phantom{\rule{0.166667em}{0ex}}[6.35,\phantom{\rule{0.166667em}{0ex}}128.21]$ | 15 | $14.02,\phantom{\rule{0.166667em}{0ex}}[9.72,\phantom{\rule{0.166667em}{0ex}}22.46]$ | 15 |

ACL | AM Femur | $8.17,\phantom{\rule{0.166667em}{0ex}}[5.34,\phantom{\rule{0.166667em}{0ex}}15.65]$ | 12 | $\mathbf{4}.\mathbf{80},\phantom{\rule{0.166667em}{0ex}}[3.79,\phantom{\rule{0.166667em}{0ex}}14.04]$ | 12 |

PL Femur | $5.66,\phantom{\rule{0.166667em}{0ex}}[4.17,\phantom{\rule{0.166667em}{0ex}}12.84]$ | 12 | $\mathbf{5}.\mathbf{04},\phantom{\rule{0.166667em}{0ex}}[2.85,\phantom{\rule{0.166667em}{0ex}}12.48]$ | 12 | |

AM Tibia | $22.13,\phantom{\rule{0.166667em}{0ex}}[9.52,\phantom{\rule{0.166667em}{0ex}}82.04]$ | 12 | $\mathbf{14}.\mathbf{18},\phantom{\rule{0.166667em}{0ex}}[10.27,\phantom{\rule{0.166667em}{0ex}}42.87]$ | 12 | |

PL Tibia | $\mathbf{13}.\mathbf{17},\phantom{\rule{0.166667em}{0ex}}[10.09,\phantom{\rule{0.166667em}{0ex}}38.74]$ | 12 | $16.55,\phantom{\rule{0.166667em}{0ex}}[12.85,\phantom{\rule{0.166667em}{0ex}}41.71]$ | 12 |

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## Share and Cite

**MDPI and ACS Style**

Kordon, F.; Maier, A.; Swartman, B.; Privalov, M.; El Barbari, J.S.; Kunze, H. Multi-Stage Platform for (Semi-)Automatic Planning in Reconstructive Orthopedic Surgery. *J. Imaging* **2022**, *8*, 108.
https://doi.org/10.3390/jimaging8040108

**AMA Style**

Kordon F, Maier A, Swartman B, Privalov M, El Barbari JS, Kunze H. Multi-Stage Platform for (Semi-)Automatic Planning in Reconstructive Orthopedic Surgery. *Journal of Imaging*. 2022; 8(4):108.
https://doi.org/10.3390/jimaging8040108

**Chicago/Turabian Style**

Kordon, Florian, Andreas Maier, Benedict Swartman, Maxim Privalov, Jan Siad El Barbari, and Holger Kunze. 2022. "Multi-Stage Platform for (Semi-)Automatic Planning in Reconstructive Orthopedic Surgery" *Journal of Imaging* 8, no. 4: 108.
https://doi.org/10.3390/jimaging8040108