Predicting nonunion – a hybrid machine-learning model combining patient factors and mechanobiological simulation features exceeds clinician accuracy

Abstract

Aims

To compare the accuracy of a mechanobiological simulation against that of clinicians in forecasting long bone nonunions, and to determine whether the simulation’s results can be effectively used as input for a machine-learning algorithm.

Methods

This was a retrospective diagnostic accuracy study using a cohort of 98 patients who underwent surgery for tibial shaft fractures at four tertiary care trauma institutions in Germany between January 2018 and December 2023, 20 of whom developed nonunion. Biplanar pre- and postoperative radiographs and detailed demographic and clinical information (sex, age, BMI, comorbidities, fracture characteristics, surgical protocol, and implants used) were provided to clinicians to predict the likelihood of nonunion. All data were also analyzed with the Leeds-Genoa Non-Union-Index (LEG NUI) and entered into a mechanobiological simulation model, a machine-learning model, and a hybrid model. Performance metrics were then compared across all five assessment methods.

Results

Comparing the overall predictive performance of the clinicians’ heuristic, the LEG NUI score, and the three computational models, the hybrid model outperforms all contenders concerning sensitivity (80%), positive predictive value (59%), negative predictive value (94%), and Matthews correlation coefficient (59%). Specificity was high (86%), solely outperformed by the specificity of the LEG NUI score (95%) and the mechanobiological simulation (90%).

Conclusion

The AI-based hybrid model outperforms human experts in predicting nonunions in long bone fractures, enabling the early detection of patients at risk and the modification of treatment strategies to improve patient outcomes.

Cite this article: Bone Joint Res 2026;15(10):1196–1205.

Article focus

• Comparison of the predictive accuracy of experienced clinicians versus a mechanobiological simulation for forecasting tibial shaft nonunions.

• Development and validation of a hybrid machine-learning model that integrates patient-specific simulation features with clinical risk factors.

• Assessment of whether computational models can serve as objective decision-support tools to surpass human heuristics in orthopaedic trauma surgery.

Key messages

• A hybrid model combining mechanobiological simulation and machine learning significantly outperforms clinician heuristics and the Leeds-Genoa Non-Union-Index (LEG NUI) score in predicting nonunion.

• The hybrid model demonstrates a high negative predictive value (94%), enabling reliable early identification of low-risk patients to avoid unnecessary interventions.

• While mechanobiological simulation alone underperformed compared to clinicians, its integration with clinical data creates a superior tool for early decision-making.

Strengths and limitations

• This is the first study to directly benchmark a mechanobiological patient-specific simulation and a hybrid AI model against the predictive performance of a large group of experienced clinicians (n = 24).

• The study utilizes a multicentre dataset from four tertiary care trauma institutions, ensuring a broad clinical basis for model training.

• Limitations include the retrospective study design, the relatively small sample size (n = 98), and necessary biomechanical assumptions (e.g., weightbearing conditions) within the simulation.

Introduction

Fracture nonunion, defined as incomplete or failed healing after six to nine months, is a challenging complication in orthopaedic trauma. It predominantly affects long bones, particularly the tibia.^1-3 Primary fracture care, whether via open reduction and internal fixation, intramedullary nailing, or a combination thereof, must integrate fracture-related variables (e.g., morphology, complexity, soft-tissue status) with patient-specific risk factors such as diabetes mellitus, smoking, and drug use to achieve a stable construct and adequate soft-tissue coverage aimed at preventing nonunion.^4,5 Currently, heuristic reasoning by orthopaedic surgeons and radiologists, relying on plain radiographs, CT, and MRI, remains the mainstay for predicting healing outcomes and guiding treatment decisions.⁶ Although prediction rules like the Leeds-Genoa nonunion Index (LEG NUI) were developed to improve accuracy,⁷ subsequent studies indicate that such indices often lack sensitivity and overlook crucial risk factors.^8,9

Recent advancements in computational modelling offer two promising approaches for early prediction of nonunion development: mechanobiological simulations and AI. Mechanobiological simulations model tissue differentiation in response to biomechanical stimuli in order to forecast bone healing, and have shown acceptable accuracy in predicting femoral nonunion.¹⁰ In contrast, machine learning (ML) is a data-driven subset of AI, in which an algorithm is not explicitly programmed with biological rules but is trained on large datasets to identify complex patterns and make predictions on new data.^11-14 ML has already been successfully implemented in radiology to enhance diagnostic decision-making,^11,15,16 and has been used to predict nonunions across various anatomical regions.^17-20 However, neither approach has yet been benchmarked against clinicians’ predictions. Furthermore, a hybrid model combining mechanobiological simulation and ML has not been investigated.

This study aims to compare the predictive accuracy of a mechanobiological simulation to that of human experts for forecasting long bone nonunions, and determine if this simulation’s predictive power can be enhanced by integrating a ML algorithm.

Methods

Study design and case collection

The patient dataset used in this multicentre, retrospective diagnostic accuracy study was previously described and analyzed by Armbruster et al.⁶ In brief, anonymized data from four German tertiary care trauma institutions of patients who were surgically treated for tibial fractures between January 2018 and December 2023 were collected. A pragmatic sample size was established through a targeted enrichment protocol, consisting of 20 randomly selected unions and five randomly selected nonunions contributed by each centre. After excluding two patients for insufficient data, the final cohort comprised 98 cases. Additionally, anonymized clinical and surgical patient data, fracture characteristics, and implant specifications were collected. A comprehensive description of patient demographics, the inclusion/exclusion protocol, and the selection process can be found in the publication by Armbruster et al.⁶

Prediction by clinicians

A total of 24 raters, six from each of the four centres, independently assessed anonymized cases. Each centre’s group included five raters with orthopaedic/trauma surgery backgrounds (head of department, consultant, specialist, resident, intern) and one radiologist. After an initial prediction based on preoperative data, a final prediction was made using postoperative information. These evaluations were previously reported by Armbruster et al.⁶ Only the final prediction was used for this study’s comparison.

LEG NUI classification scheme

The Leeds-Genoa Non-Union-Index (LEG NUI) score (Figure 1) was calculated by two blinded raters (JA, NM).

Fig. 1.

Binary features (“risk factors”) considered by the Leeds-Genoa Non-Union-Index (LEG NUI) scoring scheme as proposed by Santolini et al.⁷

Mechanobiological simulation

Patient-specific numerical models were created by OSORA (OSORA medical, Germany) using Autodesk Fusion (v. 15.8.0.1827; Autodesk, USA) by first scaling a tibia template’s height to match that of the patient’s tibia before fitting 152 contour points (76 per view) to the patient’s tibia surface geometry as visible on the biplanar radiographs. Fracture lines were reconstructed, implants integrated, and a spherical haematoma added (callus index 1.5 to 2.0).¹⁰ Finite element models were created in Altair Simlab 2024.1 (Altair Engineering, USA) using quadratic tetrahedral elements with an average size of 2.5 mm. Boundary conditions were set to mimic full weightbearing during walking by fixing the distal end and applying an axial force of three times the body weight to the tibial plateau.^21-23 Screw-bone interactions were modelled as bonded contacts, while nail-bone contact permitted tangential sliding.

The Ulm bone healing model was employed, wherein each (non-implant) finite element represents a mixture of tissue concentrations.^24,25 The model works by iteratively applying a quasi-static finite element analysis (Calculix v. 2.18, Guido Dhondt, Germany) to compute mechanical stimuli, followed by a fuzzy logic controller to drive tissue differentiation and update tissue concentrations in each non-implant element. Aside from the spatial evolution of tissue distribution over time, outputs included interfragmentary movement, bridging day for each quadrant, and maximum and average implant stress. All implants were modelled using the material properties of a titanium alloy (elastic modulus: E = 90 GPa; Poisson’s ratio: ν = 0.3). The initial tissue state for the simulation was defined with the cortical shell as 100% lamellar bone, the epi-/metaphysis as 60% lamellar bone (homogenized cancellous bone), the medullary canal as 100% vascularized connective tissue, and the haematoma as 100% avascular connective tissue. Simulations modelled up to 250 days of healing time (computational runtime approximately 24 hours/case) or until consolidation (≥ 3 quadrants bridged with ≥ 50% lamellar bone). Consolidations within 120 simulated days (~17 weeks) were classified as “union”; all others as “nonunion” (Figure 2).

Fig. 2.

Schematic of the simulation-based risk assessment: based on the clinical data, a digital twin of the patient’s anatomy is reconstructed and used to predict the tissue evolution over time using an established bone healing model (Niemeyer et al,²⁴ Engelhardt et al²⁵). Quantitative outputs from the simulation, such as consolidation time or interfragmentary movement, are then used to classify the fracture outcome. This classification is done by either an empirical rule or a machine learning (ML) classifier (hybrid model), which may also consider additional data from the patient record that did not directly enter the simulation model. FEM, finite element model.

Machine learning and hybrid model

After blinded nonunion predictions were generated by the mechanobiological simulation, ground truths were disclosed, and ML models were trained using multiple logistic regression.

The ML model was trained on patient-specific features and variables derived from imaging, i.e. postoperative fracture gap size. Feature selection was performed using Orange’s (v. 3.36.2) “Feature Importance” tool, targeting Matthews correlation coefficient (MCC), resulting in “Fracture type” (AO classification), “comorbidities” (yes/no), “fibula fractured” (yes/no) and “age” (years) as the most influential predictors.²⁶

Additionally, a hybrid model was developed to integrate patient data with simulation-derived features. This final model incorporated the key patient predictors alongside selected simulation outputs: “Interfragmentary movement at simulation day 90,” “predicted consolidation time,” and “maximum implant stress at the final simulated day.”

Performance evaluation

The ML and hybrid model’s performances were evaluated using 20-fold stratified cross-validation. False positives (FP) referred to cases incorrectly classified as nonunion, whereas false negatives (FN) represented misclassified unions. Predictive performance was assessed using confusion matrices and classification metrics including sensitivity, specificity, positive and negative predictive values (PPV, NPV), MCC, and area under the receiver operating characteristic curve (AUROC).

Results

Patient and rater characteristics

The study included 98 patient cases, of which 78 showed osseus consolidation while 20 cases developed a nonunion. Table I summarizes their main characteristics. The blinded 24 clinician raters had a mean experience of 11.7 years (0 to 36, SD 10.5) in their respective field.

Table I.

Patient characteristics.

Characteristic	Value, n (%)	Mean (SD)
Treatment outcome
Union	78 (80)
Nonunion	20 (20)
Age, yrs	98 (100)	39.9 (16.5)
Male	68 (69)	39.8 (16.7)
Female	30 (31)	40.1 (16.0)
Treatment
Nail	70 (71)
Plate	27 (28)
TEN	1 (1)
Open fracture
Yes	29 (30)
No	69 (70)
Obesity
Yes	7 (7)
No	91 (93)
Nicotine use
Yes	9 (9)
No	89 (91)
Compartment syndrome
Yes	9 (9)
No	89 (91)
Polytrauma
Yes	6 (6)
No	92 (94)
Plastic soft-tissue coverage
Yes	3 (3)
No	95 (97)
Fibula fractured
Yes	76 (78)
No	22 (22)
Soft-tissue damage, °
0 or N/A	69 (70)
1	18 (18)
2	7 (7)
3	4 (4)

Percentage rounded to whole numbers. This table is adapted from Armbruster et al.⁶

N/A, not assessable; TEN, titanium elastic nail.

Hybrid model outperforms clinicians in nonunion prediction metrics

When comparing the overall predictive performance of the clinicians’ heuristic, the LEG NUI scheme, and the three computational models, the hybrid model outperformed all other approaches across all evaluated classification metrics, with the exception of specificity (Figure 3 and Table II). Nevertheless, specificity of the hybrid model remained high at 86%, and was only exceeded by the LEG NUI score (95%) and the simulation model (90%). These higher specificity values were achieved at the expense of markedly lower sensitivity, resulting in reduced overall performance as reflected by the MCC.

Fig. 3.

Comparison of classification metrics across all prediction methods. Bars for clinicians represent the mean value, and error bars visualize the 95% bootstrapped CI. The clinicians, Leeds-Genoa No-Union-Index (LEG NUI), and mechanobiological simulation model (simulation) made blinded predictions without knowledge of the true outcome. In contrast, the machine learning (ML) and hybrid models required access to outcome information (= ground truth) for training and were therefore evaluated using 20-fold cross validation.

Table II.

Classification metric values for all prediction methods.

Prognosis method	Sensitivity	Specificity	PPV	NPV	MCC	AUROC
Clinicians, rounded average (95% CI)	0.60 (0.54 to 0.66)	0.71 (0.67 to 0.75)	0.36 (0.34 to 0.38)	0.88 (0.87 to 0.89)	0.27 (0.24 to 0.29)	N/A
LEG NUI	0.05	0.95*	0.20	0.80	0.00	N/A
Simulation	0.25	0.90	0.38	0.82	0.18	N/A
ML model†	0.75	0.71	0.39	0.92	0.38	0.74
Hybrid model†	0.80*	0.86	0.59*	0.94*	0.59*	0.84*

^*Best performing method for each metric.

^†Mean values from 20-fold stratified cross validation.

AUROC, area under the receiver operating characteristic curve; LEG NUI, Leeds-Genoa Non-Union-Index; MCC, Matthews correlation coefficient; N/A, not applicable; NPV, negative predictive value; PPV, positive predictive value; Simulation, mechanobiological simulation.

Consistent with the superior sensitivity and specificity of the hybrid model compared to the ML model, the area under the curve was also greater for the hybrid model (0.84).

In case of the hybrid model, 59% of the cases predicted to become nonunions actually developed a nonunion outcome, surpassing the PPV of any other prognosis method.

Analysis of the confusion matrices revealed distinct error tendencies among the prediction models. The simulation model showed a bias towards false negatives, while the ML model tended to produce false positives (Table III). By combining both approaches, the hybrid model substantially reduced these errors, resulting in a total of only 15 misclassifications, while increasing the number of true positives and only marginally reducing the number of true negatives.

Table III.

Confusion matrix entries for all prediction methods.

Prognosis method	TN	TP	FN	FP
Clinicians, rounded average (95% CI)	55 (52.0 to 58.3)	12 (10.8 to 13.1)	8 (6.91 to 9.21)	23 (19.6 to 26.0)
LEG NUI	74*	1	19	4*
Simulation	70	5	15	8
ML model	55	15	5	23
Hybrid model	67	16*	4*	11

^*Best performing method.

FN, false negative; FP, false positive; LEG NUI, Leeds-Genoa Non-Union-Index; ML, machine learning; Simulation, mechanobiological simulation; TN, true negative; TP, true positive.

Subgroup analyses

When stratifying cases into subgroups by the presence of comorbidities in general, the different models showed distinct error patterns. The simulation model was prone to false negatives (Figure 4), while the ML model remained overly conservative, resulting in an increased number of false positives. By mitigating these opposing biases, the hybrid model minimized the overall number of misclassifications in both subgroups. However, the hybrid model’s performance was weaker in patients with comorbidities, where it produced significantly more misclassifications than in patients without. Despite this, the hybrid model still made fewer prediction errors in both the comorbidity and non-comorbidity groups compared to the assessments by clinicians and the LEG NUI score.

Fig. 4.

Comparative confusion matrices for all prediction methods, stratified by the presence or absence of patient comorbidities. Values for clinicians represent the rounded average with bootstrapped 95% CIs in brackets. Simulation = mechanobiological simulation. FN, false negative; FP, false positive; TN, true negative; TP, true positive. LEG NUI, Leeds-Genoa Non-Union-Index.

Further subgroup analysis revealed distinct error patterns related to specific patient factors such as nicotine abuse (Figure 5a). The LEG NUI score fails to correctly identify any of the nonunion cases in this group. In contrast, the hybrid model correctly classified all cases within the nicotine abuse subgroup.

Fig. 5.

Comparative confusion matrices for all prediction methods, stratified by a) patient nicotine abuse and b) fracture type. Values for clinicians represent the rounded average with bootstrapped 95% CIs in brackets. Simulation = mechanobiological simulation; FN, false negative; FP, false positive; TN, true negative; TP, true positive.

In the analysis of fracture types (Figure 5b), the hybrid model’s performance in open fractures was notable for shifting the error distribution toward false positives rather than reducing overall misclassifications compared to the simulation. Nevertheless, the hybrid model still outperformed both clinicians and the LEG NUI score in open and closed fracture subgroups.

Summary of classification metrics

The hybrid model consistently outperformed all other prediction approaches, including clinicians’ assessments, across nearly all metrics and in almost every subgroup analyzed (Figure 6; see Supplementary Figure 1 for individual data distribution).

Fig. 6.

Comparison of classification metrics across all prediction methods stratified by patient subgroups. Values for clinicians represent the mean value, and error bars visualize the 95% bootstrapped CI. Individual data points for this analysis are provided in Supplementary Figure 1. The clinicians, Leeds-Genoa Non-Union-Index (LEG NUI), and mechanobiological simulation model (simulation) made blinded predictions without knowledge of the true outcome. In contrast, the machine learning (ML) and hybrid models required access to outcome information (= ground truth) for training and were therefore evaluated using 20-fold cross validation. The positive predictive value (PPV) of LEG NUI in the “Nicotine = yes” subgroup cannot be calculated due to both true positives and false positives being 0. NPV = negative predictive value.

Discussion

The present study analyzed and compared the predictive performance of clinicians’ heuristics, the LEG NUI, and three computational models for forecasting fracture nonunion. Consistent with existing literature, the LEG NUI demonstrated high specificity but low sensitivity, likely due to excluding key clinical factors such as comorbidities.⁹ This limitation became particularly evident in patients with nicotine abuse, where the LEG NUI severely underestimated the nonunion risk because it completely omits smoking as a predictive parameter.

In the first direct comparison of its kind, the mechanobiological simulation model underperformed relative to clinicians’ predictions, a result likely attributable to missing key biological data. Notably, the ML model, which was trained solely on patient data without imaging information, also outperformed the simulation. This finding suggests that, within this dataset, biological factors rather than mechanical ones may be the primary drivers of nonunion.

The hybrid model achieved the most promising results by integrating temporal simulation outputs with patient-specific risk factors, thereby combining the predictive strengths of both approaches. It exhibited a high NPV of 94%, indicating that patients who were predicted to be at low risk for nonunion would infrequently require alterations in therapeutic management. Although the PPV remained moderate, it exceeded that of clinicians and other computational models evaluated in this study.

The hybrid model’s performance diminishes slightly in the presence of comorbidities, highlighting room for improvement. The dataset contained only nine patients with nicotine abuse, three of whom developed a nonunion. Consequently, no generalized conclusions can be drawn from this subgroup; however, as a ML-based tool, the hybrid model is continuously trainable and expected to improve with larger datasets.

Compared to clinicians, the hybrid model demonstrated superior overall performance across all subgroup analyses. Accurate long bone fracture nonunion prediction post-surgery – or ideally intraoperatively, based on imaging methods – could enable immediate therapeutic interventions to prevent nonunion.

To our knowledge, the largest clinical study applying ML to predict nonunion healing across various anatomical regions was conducted by Donié et al.¹⁸ Using data from 797 patients, their model achieved 70% sensitivity and 66% specificity. While the ML model in the present study achieved comparable metrics, our hybrid model noticeably surpassed both the Donié et al¹⁸ model and our own standalone ML model. Similarly, Leister et al¹⁹ trained a ML model on 415 patients with odontoid fractures, reporting an area under the curve of 0.71, which is comparable to our ML model (0.74) but surpassed by the hybrid model (0.84).

While Donié et al¹⁸ and Leister et al¹⁹ did not compare their results to clinicians’ predictions, Takahashi et al¹⁷ did. They trained a ML algorithm to predict nonunions in osteoporotic vertebral fractures using MRI data, achieving an AUROC of 0.86 and surpassing the clinicians’ predictive metrics. Both the high AUROC value and the fact that the ML algorithm outperformed clinicians match the results of this study. However, the fundamental differences in biomechanics and treatment strategies between spinal and long bone fractures limit a direct comparison.

Interestingly, Yu et al²⁰ trained a ML algorithm in a preclinical setting with micro-CT data in rats, achieving a very high area under the curve of 0.995. This highlights the theoretical potential of ML-based predictions; however, clinical translation remains difficult due to the radiation exposure associated with repeated micro-CT scans.

While the exact implementation costs of the hybrid model (e.g., software, user training) require future health-economic evaluation, they are likely offset by substantial socioeconomic savings. With nonunion costs estimated at approximately €85,000 per case,²⁷ improved early risk identification can prevent expensive revision surgeries and productivity loss, bridging the gap between computational innovation and clinical implementation.²⁸

This study has several limitations. First, the performance of the ML and hybrid model was estimated on a dataset only consisting of 98 cases. The models’ performance was evaluated using 20-fold cross-validation to mitigate bias, however the risk of limited generalizability due to feature selection bias remains. The limited dataset constrained model complexity, necessitating a basic logistic regression approach. Future studies will validate the hybrid model on larger datasets. Furthermore, the mechanobiological simulations relied on several assumptions. In the absence of specific loading information, full weightbearing was assumed. Additionally, bone geometry reconstruction from plain radiographs was approximate, and material properties generalized.

In summary, this study presents the first application of mechanobiological simulation for predicting long bone nonunion benchmarked against clinician heuristics. While the simulation alone lacked sufficient accuracy, its integration into a hybrid ML model yielded superior results, outperforming both human experts and the LEG NUI score. These findings underscore the value of integrating simulation-derived features into prognostic models. Future iterations trained on larger datasets are expected to further enhance accuracy. Used alongside clinical judgment, this hybrid tool could enable earlier, more precise interventions to improve patient outcomes.

Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.