Prediction of biomechanical properties of ex vivo human femoral cortical bone using Raman spectroscopy and machine learning algorithms

Abstract

This study applied Raman spectroscopy (RS) to ex vivo human cadaveric femoral mid-diaphysis cortical bone specimens (n = 118 donors; age range 21–101 years) to predict fracture toughness properties via machine learning (ML) models. Spectral features, together with demographic variables (age, sex) and structural parameters (cortical porosity, volumetric bone mineral density), were fed into support vector regression (SVR), extreme tree regression (ETR), extreme gradient boosting (XGB), and ensemble models to predict fracture-toughness metrics such as crack-initiation toughness (K_init) and energy-to-fracture (J-integral). Feature selection was based on Raman-derived mineral and organic matrix parameters, such as ν₁Phosphate (PO₄)/CH₂-wag, ν₁PO₄/Amide I, and others, to capture the complex composition of bone. Our results indicate that ensemble models consistently outperformed individual models, with the best performance for crack initiation toughness (K_init) prediction being achieved using the ensemble approach. This yielded a coefficient of determination (R²) of 0.623, root-mean squared error (RMSE) of 1.320, mean absolute error (MAE) of 1.015, and mean percentage absolute error (MAPE) of 0.134. For prediction of the overall energy to propagate a crack (J-integral), the XGB model achieved an R² of 0.737, RMSE of 2.634, MAE of 2.283, and MAPE of 0.240. This study highlights the importance of incorporating mineral quality properties (MP) and organic matrix properties (OMP) for enhanced prediction accuracy. This work represents the first-ever study combining Raman spectroscopy with other clinical and structural features to predict fracture toughness of human cortical bone, demonstrating the potential of artificial intelligence (AI) and ML in advancing bone research. Future studies could focus on larger datasets and more advanced modeling techniques to further improve predictive capabilities.

Highlights

• •Applied machine learning to predict fracture toughness of human cortical bone.
• •Combined Raman spectroscopy properties with clinical and structural bone data.
• •Ensemble models outperformed individual ML methods (SVR, XGB and ETR) for crack initiation toughness.
• •XGB model achieved high accuracy for predicting energy to propagate a crack.
• •Demonstrated the potential of AI/ML in advancing bone mechanical property research.

1. Introduction

Bone fragility is a significant global public health issue affecting a large proportion of the population (Cooper et al., 1992) with one in three women and one in five men having osteoporosis worldwide (Salari et al., 2021). The condition is characterized by an increased risk of bone fractures due to the deterioration of bone tissue quality, microarchitecture, and bone mass (Unal et al., 2018a). Fractures can have severe consequences, including high mortality rates, significant economic costs, and a diminished quality of life (Lewiecki et al., 2019). Consequently, accurate prediction of fracture risk is essential for the identification of individuals who require an intervention. To achieve comprehensive assessment of fracture risk, various factors affecting the mechanical competence of bone must be considered. Among mechanical properties of bone, fracture toughness testing characterizes the capacity of a material to resist crack growth (Zimmermann et al., 2015). All fractures result from both crack initiation and the progressive accumulation and coalescence of microcracks to a critical size. Therefore, fracture toughness plays a pivotal role in understanding bone diseases and fracture risk assessment (Zimmermann et al., 2015; Launey et al., 2010). Human cortical bone exhibits considerable variability in fracture toughness properties across individuals due to factors such as age, sex, overall bone quality, and diseases (Unal et al., 2019; Makowski et al., 2017; Granke et al., 2016). Traditional methods for assessing fracture toughness properties involve destructive, ex vivo testing of bone samples and so are not suitable for clinical use. Like bone strength, which assesses resistance to permanent deformation (i.e., yield stress), fracture toughness can be predicted using non-destructive surrogates (Granke et al., 2015).

Raman spectroscopy (RS) is a label-free, non-destructive vibrational spectroscopy technique that interrogates molecular bonds by measuring the inelastic scattering of monochromatic light, thus it provides detailed biochemical fingerprints of tissues without requiring chemical labels or extensive sample preparation (Unal et al., 2021). Other vibrational spectroscopy techniques include Fourier-transform infrared spectroscopy (FTIR) and near-infrared (NIR) spectroscopy. While FTIR often requires sample dehydration or thin-sectioning due to strong water absorption (Klaushofer et al., 2017; Taylor and Donnelly, 2020), NIR spectroscopy offers greater penetration depth but yields broader overtone bands with reduced molecular specificity (Ailavajhala et al., 2020; Rajapakse et al., 2017). However, RS measurements deliver sharp, well-defined peaks that enable direct quantification of bone matrix-quality markers in bulk or hydrated specimens with improved molecular specificity, all without compromising sample integrity (Unal et al., 2021). Especially, emerging spatially offset Raman spectroscopy (SORS) techniques and novel fiber-optic probe designs now also permit non-destructive interrogation of bone signals through overlying soft tissues (Gautam et al., 2023; Ahmed et al., 2023). SORS acquires spectra at multiple source–detector separations, enabling the isolation of subsurface bone signals from overlying skin and adipose tissue. This approach has been successfully demonstrated in animal models (Maher et al., 2017) and human phantoms (Buckley et al., 2015; Buckley et al., 2014) for transcutaneous assessment of bone composition. These advances further underscore RS's strong potential for clinical translation in predicting bone biomechanical properties.

The conventional methods of predicting bone biomechanical properties rely on either computational model such as Finite Element Analysis (FEA) (Parashar and Sharma, 2016; Engelke et al., 2016) or empirical regression models (Granke et al., 2015; Helgason et al., 2008). Empirical regression models derive statistical relationships between observed variables such as bone density, geometry, and other measurable factors and bone biomechanical properties by fitting predictive equations to experimental datasets (Granke et al., 2015; Helgason et al., 2008). In contrast, FEA constructs a detailed computational mesh of the bone's geometry, assigns spatially varying material properties, and numerically solves the governing equations of continuum mechanics to predict local stress distributions and fracture initiation under defined loading conditions (Parashar and Sharma, 2016; Engelke et al., 2016).

Although artificial intelligence (AI), machine learning (ML), and deep learning (DL) algorithms have been utilized in medicine for the past decade (Hamet and Tremblay, 2017), their application in bone research (Liu et al., 2024) and biomechanics (Phellan et al., 2020) has recently increased due to the availability of vast amounts of data, significant improvements in computer power, and advancements in algorithms (Unal et al., 2025). As a consequence, there has been growing interest in utilizing these techniques to predict bone biomechanical properties based on more in-depth information about bone structure, composition and other parameters (Mouloodi et al., 2022; Mouloodi et al., 2021). These AI-based techniques have been increasingly employed in various aspects of bone research to enhance diagnosis, treatment, and predictive modeling (Gitto et al., 2024; Kong and Shin, 2021). For example, ML algorithms have been employed to accelerate FEA-based biomechanical simulations, enabling real-time biomechanical responses such as deformation, reaction forces and Von Mises stress in analyzing anatomical structures (Phellan et al., 2020). Furthermore, ML algorithms have been employed to assess hip fracture risk in elderly and diabetic patients by combining autonomous FEA and ML algorithm to accurately classify subjects with a hip fracture within 2 years and subjects without any fracture (Yosibash et al., 2020). Moreover, Artificial Neural Networks (ANNs) have been increasingly used for tasks such as the prediction of loading history-dependent lumbar spine biomechanics under cyclic loading, showcasing their potential in biomechanical analyses (Wilmanns et al., 2023). Additionally, a multiscale method combining FEA and neural networks has been developed to model trabecular bone adaptation in the femur. Neural networks replaced mesoscale computations, using data from simulations to predict bone properties such as elastic modulus, fatigue damage, and damage accumulation (Hambli, 2011a; Hambli, 2011b). Several ML algorithms have been also utilized in the prediction of tissue adaptation loads from trabecular bone density distributions, demonstrating the versatility of AI in bone research (Zadpoor et al., 2013). Overall, ML algorithms are considered to accelerate finite element modeling (FEM)-based biomechanical simulations of bone (Phellan et al., 2020). The researchers also developed image analysis models that utilized ML feature to estimate trabecular bone stiffness from micro-CT images, demonstrating the potential of ML in assessing bone properties (Ran et al., 2023). Similarly, a recent study presented an automated tool that utilized ML to predict bone mineral density and assess fracture risk using plain radiographs, highlighting the application of ML in bone fracture risk assessment (Hsieh et al., 2021). Moreover, the work by Yasaka et al. (2020) demonstrated the feasibility of ML in bone density estimation by predicting bone mineral density from CT using a convolutional neural network (CNN) (Yasaka et al., 2020). Overall, these AI-based techniques have the potential to increase the accuracy of fracture risk prediction and facilitate the diagnosis and treatment of bone disorders like osteoporosis.

Recent advances in ML techniques have opened promising avenues for the non-invasive prediction of bone fracture resistance properties, including fracture toughness. Such predictions can be achieved by integrating alternative modalities, such as RS and clinical data. RS allows for insights to be gained into the molecular compositional properties of bone tissue (Unal et al., 2021; Morris and Mandair, 2011), while clinical data encompasses a vast range of patient-specific variables, including sex, age, areal or volumetric bone mineral density (vBMD) and porosity. Integrating AI/ML frameworks with Raman spectral data can help to fully harness compositional information for robust fracture-risk prediction. Therefore, AI/ML techniques with multi-modal dataset like RS and clinical information may enhance prediction of bone fracture resistance and may facilitate improvements in clinical decision-making for bone health.

In our prior work (Unal et al., 2019), a general linear model incorporating donor age and vBMD from 58 cadaveric femoral mid-diaphysis specimens without any ML methods, explained 40.7 % of the variance in crack-initiation toughness (K_init) and 12.7 % of the variance in the final J-integral (J-int). By adding RS–derived compositional properties, the explained variance increased to 50.2 % for K_iₙᵢₜ and 53.9 % for the J-int, yielding a more than fourfold improvement in J-int prediction. These results underscore RS's ability to capture matrix quality features beyond bone mineral quantity alone and highlight its potential to enhance fracture-toughness prediction. In the present study, we build on this foundation by applying advanced ML algorithms to an expanded cohort, with the aim of enhancing the prediction of cortical bone fracture toughness properties through ensemble regression models that integrate cortical porosity, age, sex, vBMD, and RS-derived features.

Towards that end, we examine the application of various ML algorithms to predict the fracture toughness of femoral mid-diaphysis cortical bone from donors aged 21–101 years by utilizing both RS and other measurable variables. Our objective is to develop ML-based predictive models that can assess bone fracture resistance.

2. Method

2.1. Data obtaining

In this study, the dataset includes Raman spectra from single-edge notched beams (SENB) of cortical bone that were extracted from the femurs of 118 human cadavers (58 males and 60 females, aged between 21 and 101 years). With a total number of 118 cadaveric femurs, this donor number is notable for being one of the largest cadaveric human cortical bone dataset available in literature in terms of RS and fracture toughness properties. Detailed information regarding sample preparation and data collection methodology can be found in our previous publications that include different donors (Unal et al., 2019; Granke et al., 2015). Briefly, SENB with lengths (L) of 25–49 mm, widths (B) of approximately 2.5–4 mm, and depths (W) of approximately 4–5 mm were prepared from the femoral mid-diaphysis of each cadaveric specimen. Fracture toughness properties, including K_init and final J-int, were measured using a non-linear fracture mechanics approach known as R-curve testing on hydrated bone (Granke et al., 2015). In brief, fracture-toughness properties were obtained from all 118 cadaveric femoral specimens using SENB in three-point bending at 0.5 mm/min under continuous PBS spray at 22 °C, as described in details (Unal et al., 2019; Granke et al., 2015), and served as the ground-truth targets for our ML models.

For 58 donors (30 female and 28 male donors), 16 Raman spectra were collected from 2 longitudinal surfaces of cortical bone adjacent to each SENB using an Xplora Raman microscope (Horiba Jobin Yvon, Edison, NJ, USA) and the following conditions a 785 nm diode laser at ∼35 mW, 20× objective (NA = 0.40), 12 accumulations with a 5-s acquisition, wavenumber range of 785–1800 cm⁻¹ at a spectral resolution ∼1.25 cm⁻¹ (Unal et al., 2019). For the new 60 donors (30 female and 30 male donors), 20 Raman spectra were acquired from the crack propagation region (4 × 5 grid) prior to R-curve testing using an inVia Raman microscope (Renishaw, New Mills, Gloucestershire, UK) and the following conditions: 830 nm diode laser at ∼35 mW, 20× objective (NA = 0.4), 5 accumulations with a 10-s acquisition, wavenumber range of 785–1800 cm⁻¹ at a spectral resolution of ∼1 cm⁻¹. Our recent study (Unal et al., 2025) demonstrated that as few as 7–8 spectra reliably capture cortical bone compositional heterogeneity. For each specimen, individual spectra were averaged into a single composite spectrum for downstream ML analysis. Therefore, acquiring either 16 or 20 spectra per specimen is not expected to affect the calculated spectral properties/features or model performance. Regarding RS-based measurements of bone matrix quality, we calculated several RS-derived features based on peak intensities after processing the raw spectra as described in our prior publications (Unal et al., 2019; Unal et al., 2023). Briefly, background fluorescence was removed using a fifth-order polynomial fitting algorithm, and spectra were then processed with the Horiba LabSpec D-n digital smoothing algorithm to minimize spectral noise. The calculated RS-derived features encompass the mineral-to-matrix ratio (MMR, ν₁PO₄/Amide I, ν₁PO₄/Amide III, ν₁PO₄/CH₂-wag and ν₁PO₄/Proline) (Unal et al., 2021; Timlin et al., 1999; Mabilleau et al., 2024), Type-B carbonate substitution (CO₃/ ν₁PO₄) (Timlin et al., 1999; Awonusi et al., 2007), crystallinity (the inverse of the line-width of the ν₁PO₄ peak at half the height from baseline or half-maximum; 1/FWHM) (Querido et al., 2018), collagen enzymatic crosslinks/matrix maturity ratio (calculated as ∼I₁₆₇₀/I₁₆₉₀ cm⁻¹) (Oest et al., 2016; Zhang et al., 2016), and novel collagen helical status ratio (∼I₁₆₇₀/I₁₆₄₀ cm⁻¹) (Table1) (Unal et al., 2023; Unal et al., 2018b; Unal et al., 2016).

2.2. Overall approach

In this study, various regression and ensemble models were employed to predict fracture toughness properties of human femoral cortical bone. The dataset used in these models was divided into four primary categories as shown in Table 1 and Fig. 1:

Table 1.

Categories of the features used in ML regression models.

Categories	Features
RS Mineral to Matrix Ratio (MMR)	ν1PO4/Amide I
	ν1PO4/Amide III
	ν1PO4/CH2-wag ν1PO4/Proline
RS Mineral Properties (MP)	CO3/ ν1PO4
	1/FWHM (ν1PO4)
RS Organic Matrix Properties (OMP)	∼I1670/I1690
	∼I1670/I1640
Clinical & Structural Properties (CSP)	Age
	Sex
	Porosity
	vBMD

Fig. 1.

Flowchart illustrates the application of ML algorithms in predicting the fracture toughness properties of human cortical bone.

As illustrated in Fig. 1, regression models were first applied using the CSP model including clinical and structural features along with one feature from the MMR group. The goal was to identify the best MMR property/feature, defined as the one that, when added to the CSP features, provided the best prediction outcome among the four MMR features. To select this best MMR feature, the RMSE, MAE and MAPE scores of the best models were considered.

In the second step, regression models were applied again by adding MP feature to the CSP model and the selected MMR feature. The results were then compared in terms of error metrics and R² scores. Finally, the performance of the models was evaluated using the CSP model, the best MMR, MP, and OMP features. This methodology aimed to determine the impact of various combinations of bone quality features on the models in conjunction with the CSP features. Additionally, this approach was applied to predict two target values: K_init and J-int. Consequently, the following sections present the results separately for both K_init and J-int.

2.3. Dataset

We had 118 samples with 12 features and two dependent variables as shown in Table 2, reporting the basic descriptive statistics of both the dependent and independent variables. Cadaveric femurs were obtained from the Musculoskeletal Tissue Foundation, the National Disease Research Interchange (NDRI), and the Vanderbilt Donor Program, representing a geographically diverse U.S. population. All tissues were de-identified prior to receipt, and no personally identifiable information was available. Donor ages spanned from 21 to 101 years (mean ± SD: 68.3 ± 18.9 years; median: 70.5 years; interquartile range: 57.0–82.8 years), as detailed in Table 2. This wide age distribution confirms that our ML models were developed and tested across the full adult lifespan. Since the four properties in MMR are considered the same RS-derived mineral property, providing information about local mineralization at measured volume (Unal et al., 2021; Mabilleau et al., 2024; Mandair and Morris, 2015), we initially selected the most relevant MMR feature (we called this as the best MMR) by creating a dataset comprising the CSP model along with one of the MMR features. We refer to this model as Model-1, which consists of four distinct datasets used in the first stage (Fig. 1). The Model-2, used in the second step, consists of the CSP features along with the best MMR and OMP features. Lastly, Model-3, used in the final stage, consists of the CSP features as well as the best combination of MMR, OMP, and MP features. We classified these features into four categorized as MMR, MB, OMP and CSP features (Unal et al., 2019; Unal, 2021) as shown in Table 1 for corresponding features.

Table 2.

Descriptive statistics for the dependent and independent variables.

		Mean	Std	Min	25 %	50 %	75 %	Max
Age (years)	Independent Variables	68.28	18.87	21.00	57.00	70.50	82.75	101.00
vBMD (mgHA/cm3)		927.16	67.57	589.91	912.91	939.82	963.85	1009.26
Porosity (%)		6.86	6.89	0.86	3.40	4.66	7.08	42.89
v1PO4/Amide I		20.92	2.62	15.99	18.77	20.67	22.49	28.20
v1PO4/Proline		7.10	0.66	5.46	6.68	7.16	7.62	8.40
v1PO4/Amide III		17.92	1.35	14.73	16.93	17.92	18.97	21.15
v1PO4/CH2-wag		17.33	1.38	13.79	16.51	17.41	18.18	20.91
CO3/ v1PO4		0.18	0.01	0.17	0.18	0.18	0.19	0.21
1/FWHM (ν1PO4)		0.0512	0.0010	0.0483	0.0506	0.0512	0.0518	0.0547
∼I1670/I1640		1.39	0.08	1.29	1.34	1.37	1.41	1.67
∼I1670/I1690		1.85	0.14	1.46	1.74	1.85	1.95	2.22
Kinit	Dependent Variables	8.26	2.26	3.18	7.005	7.855	9.57	15.7
J-int		10.87	4.98	3.92	7.31	9.24	12.76	29.05

2.4. Selected machine learning algorithms

We applied four machine learning algorithms: Support Vector Regression (SVR), Extreme Gradient Boosting (XGB), Extra Trees Regression (ETR), and an ensemble of these three algorithms (see details in Supplemental Materials). Initially, we also tested other ML algorithms such as k-nearest neighbors (KNN) and Gradient Boosting (GB) as part of a pilot study (Unal et al., 2022) but we found that SVR, XGB, and ETR generally showed superior potential for predicting fracture toughness properties of human cortical bone. These algorithms were selected for their ability to capture complex, non-linear relationships and handle high-dimensional datasets as well as for their distinct advantages, with the goal of offering a thorough comparison of various ML methods (Supplemental Materials). SVR is known for its robustness in regression tasks with limited data (Vapnik, 1999), XGB excels in handling large datasets while preventing overfitting (Chen and Guestrin, 2016), and ETR is effective in capturing feature interactions without requiring extensive tuning (Geurts et al., 2006). The ensemble approach combines the strengths of all three models, enhancing prediction accuracy and robustness. By averaging the predictions of these individual methods, the ensemble strategy ensures that the results are not worse than the worst-performing model, while potentially improving overall prediction reliability. This approach provides more robust predictions and is less sensitive to abnormal values. The details of these models can be found in the Supplemental Material. Studies often find that splits like 70:30 or 80:20 provide a good balance between training the model sufficiently and having enough data to reliably test its performance (Uçar et al., 2020; Padmapriya et al., 2024). Therefore, we split the data into 80 % training (n = 94) and 20 % test (n = 24) sets, following best practices in ML to balance model training and evaluation (Ly et al., 2021). Hyperparameters were selected via grid search combined with a 5-fold cross-validation within the training set to avoid test-set leakage. Model hyperparameters were selected by performing an inner 5-fold cross-validation on the training set (80 % of the data). In each fold, four partitions were used to train candidate models across a predefined grid of hyperparameters, and the remaining partition served for validation. The hyperparameter combination yielding the lowest mean validation error was then used to retrain the model on the entire training set. Finally, performance was assessed on the independent 20 % test set, which was not accessed during any tuning step.

2.5. ML evaluation metrics and statistical analysis

We evaluated model performance using four widely adopted regression metrics (Phellan et al., 2020): root mean squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and the coefficient of determination (R²). Their mathematical definitions are provided in Table 3.

Table 3.

Evaluation metrics used in this study and their formulations. While ${\widehat{\mathit{y}}}_{\mathit{i}}$ represent the predicted value, ${\mathit{y}}_{\mathit{i}}$ represents the true/actual values and ${\overline{\mathit{y}}}_{\mathit{i}}$ represents the mean of all values.

Metrics	Formulations
RMSE	$\sqrt{\frac{\sum _{i=1}^n{\left({\widehat{y}}_i-y_i\right)}^2}{n}}$
${\text{R}}^2$	$1-\frac{\sum _{i=1}^n{\left({\widehat{y}}_i-y_i\right)}^2}{\sum _{i=1}^n{\left(y_i-{\overline{y}}_i\right)}^2}$
MAE	$\left(\frac{1}{n}\right)\sum \left|y_i-{ŷ}_i\right|$
MAPE	$\left(\frac{100}{n}\right)\sum \left|\frac{\left(y_i-{ŷ}_i\right)}{y_i}\right|$

All statistical analyses were performed using Minitab 18 statistical software (Minitab, LLC State College, Pennsylvania, USA). Linear correlations between the RS properties, age, porosity or vBMD and fracture toughness properties were determined at a significance level of 0.05.

3. Results

3.1. Correlations between Raman features and fracture toughness properties

Age and porosity were negatively correlated with both fracture toughness properties. While vBMD was only correlated with K_init, ν₁PO₄/CH₂-wag showed a negative correlation with J-int (Table 4). Crystallinity did not correlate with any of fracture toughness properties, while other traditional Raman features (e.g., ν₁PO₄/Amide I, ν₁PO₄/Amide III, ν₁PO₄/Proline and CO₃/ν₁PO₄) negatively correlated with all two fracture toughness properties, explaining 6.8 % to 32.5 % of the variance (Table 4). The Amide I sub-peak ratio of ∼I₁₆₇₀/I₁₆₉₀ correlated with both fracture toughness properties. Especially, the Amide I sub-peak ratio of ∼I₁₆₇₀/I₁₆₄₀ alone explained 32.5 % of the variance in J-int (Table 4), 28.9 % of the variance in K_init (Table 4). Both RS-derived features and other clinically relevant parameters showed weak to moderate correlations and were able to explain up to 32.5 % of the variance in fracture toughness properties when assessed individually.

Table 4.

Correlations between Raman spectroscopy properties or CSP and fracture toughness properties. R² in bold and corresponding p-values below 0.05 in italics refers to statistically significant. Otherwise, the correlation was not statistically significant (NS).

Characteristic Property		Fracture Toughness
		Kinit (N = 118)	J-int (N = 118)
Age	(years)	(−) 0.205 (0.0001)	(−) 0.145 (0.0001)
Porosity	(%)	(−) 0.147 (0.0001)	(−) 0.056 (0.010)
Bone mineral density	vBMD (mgHA/cm3)	(+) 0.062 (0.006)	NS
Mineral-to-matrix ratio	ν1PO4/Amide I	(−) 0.278 (0.0001)	(−) 0.289 (<0.001)
	ν1PO4/Amide III	(−) 0.068 (0.004)	(−) 0.073 (0.003)
	ν1PO4/Proline	(−) 0.106 (0.0001)	(−) 0.061 (0.007)
	ν1PO4/CH2-wag	NS	(−) 0.257 (<0.001)
Carbonate substitution	CO3/ν1PO4	(−) 0.079 (0.002)	(−) 0.046 (0.020)
Crystallinity	1/FWHM(ν1PO4) (cm−1)	NS	NS
Collagen Cross Links	∼I1670/I1690	(+) 0.093 (0.001)	(+) 0.106 (<0.001)
Collagen Helical status	∼I1670/I1640	(−) 0.289 (<0.001)	(−) 0.325 (<0.001)

As mentioned earlier, we defined two distinct regression problems with different target values: K_init prediction and J-int prediction. For each problem, we developed a pool of ML algorithms to identify the model that minimizes prediction error (Table 3). To ensure consistency, each model was tested on the same fixed training and test datasets. This approach enabled us to accurately assess the contribution of each MMR feature as well as the additional features from the MP and OMP categories (Fig. 1).

3.2. Regression model results for predicting crack initiation toughness (K_init)

3.2.1. Selecting the best MMR feature in predicting crack initiation toughness

In the first step, datasets consisting of CSP features along with one MMR feature were used to identify the best MMR feature for predicting fracture toughness properties. As such, four different datasets were evaluated with respect to age and sex of the donor and porosity and vBMD of the specimen (Table 5).

Table 5.

Model performance results for CSP features combined with each individual MMR feature for prediction of K_init. Bold indicates the optimal algorithms among the ML algorithms tested. The RMSE, MAE and MAPE scores of the best models were considered to determine the best MMR feature among the four MMR features.

		$R^2$	RMSE	MAE	MAPE
CSP	ETR	0.103	2.036	1.641	0.230
	XGB	0.220	1.898	1.501	0.199
	SVR	0.272	1.833	1.484	0.206
	Ensemble	0.323	1.768	1.449	0.196
CSP + v1PO4/Amide I	ETR	0.560	1.426	1.122	0.154
	XGB	0.519	1.491	1.092	0.143
	SVR	0.494	1.528	1.199	0.171
	Ensemble	0.586	1.383	1.050	0.141
CSP + v1PO4/Proline	ETR	0.438	1.610	1.237	0.176
	XGB	0.163	1.966	1.492	0.201
	SVR	0.453	1.590	1.223	0.174
	Ensemble	0.445	1.601	1.215	0.167
CSP + v1PO4/Amide III	ETR	0.240	1.873	1.524	0.213
	XGB	0.332	1.756	1.377	0.184
	SVR	0.421	1.636	1.351	0.182
	Ensemble	0.423	1.633	1.312	0.179
CSP + v1PO4/CH2-wag	ETR	0.158	1.972	1.659	0.229
	XGB	0.107	2.03	1.605	0.21
	SVR	0.277	1.827	1.457	0.202
	Ensemble	0.308	1.788	1.467	0.195

For the CSP model, the ETR model exhibited the lowest performance followed by the XGB algorithm. The SVR model showed notable improvement in prediction while the ensemble approach outperformed the individual algorithms (i.e., highest R² and lowest error metrics). The performance of the CSP models suggests that, without additional features, the predictive capability is limited, as evidenced by the relatively low R² values and moderate error metrics (Table 5 and Supp. Fig. 1).

We tested all four MMRs individually to identify the one that provided the greatest improvement in predicting K_init. Among them, the inclusion of the v₁PO₄/Amide I significantly improved model performance, regardless of the algorithms used (Table 5 and Supp. Fig. 1). Moreover, the ensemble model achieved the highest performance in the prediction of K_init. The superior performance of the ensemble model underscores its effectiveness in integrating complementary information from different models. While other MMRs (v₁PO₄/Proline, v₁PO₄/Amide III and v₁PO₄/CH₂-wag) also led to some improvements (Fig. 2), the overall improvements were less pronounced compared to the v₁PO₄/Amide I feature (Table 5 and Supp. Fig. 1). The moderate increase in R² and the reduction in error metrics of other MMRs emphasize the importance of selecting highly informative features to enhance model performance. These findings emphasize the need to identify and incorporate relevant features to optimize ML models for predictive tasks.

Fig. 2.

Predictions of ML algorithms versus actual values of K_init. Incorporating the MMR feature in place of the CSP feature improved prediction performance. Based on R² and MAPE scores, the v₁PO₄/Amide I with the ensemble algorithm provides the best model for predicting K_init.

3.2.2. Evaluation of additional features on predicting crack initiation toughness

We expanded our analysis to assess the impact of additional features and feature combinations on the performance of various ML models. After selecting the best MMR feature (i.e., v₁PO₄/Amide I), we applied the same methodology to evaluate the contribution of the OMP and MP features (Fig. 1). The same models were tested on the same split datasets, with the following feature combinations: CSP + v₁PO₄/Amide I + MP, CSP + v₁PO₄/Amide I + OMP, and CSP + v₁PO₄/Amide I + OMP + MP. The results were again evaluated using R², RMSE, MAE, and MAPE and were reported in Table 6 and Fig. 3.

Table 6.

Performance of the models for each combination of feature sets in predicting K_init. Bold indicates the optimal ML algorithm, which provided the most accurate prediction of K_init.

		R2	RMSE	MAE	MAPE
CSP + V1PO4/Amide I + MP	ETR	0.577	1.397	1.111	0.149
	XGB	0.478	1.553	1.154	0.148
	SVR	0.561	1.424	1.173	0.151
	Ensemble	0.601	1.358	1.006	0.130
CSP + V1PO4/Amide I + OMP	ETR	0.621	1.323	0.995	0.132
	XGB	0.544	1.451	1.125	0.145
	SVR	0.432	1.619	1.328	0.175
	Ensemble	0.582	1.389	1.065	0.139
CSP + V1PO4/Amide I + OMP + MP	ETR	0.623	1.320	1.015	0.134
	XGB	0.491	1.533	1.184	0.145
	SVR	0.396	1.669	1.302	0.163
	Ensemble	0.557	1.431	1.121	0.142

Fig. 3.

Predictions of the best performance of ML algorithms versus actual values of K_init. Based on the R² and MAPE scores, the ETR and ensemble algorithms provide the most accurate models for predicting K_init.

For the combination of v₁PO₄/Amide I and the MP features (carbonate substitution and crystallinity), the ETR and SVR models achieved comparable performance in predicting K_init (Table 6 and Supp. Fig. 2). Moreover, the ensemble model achieved the highest performance with the highest R², and the lowest values of RMSE, MAE, and MAPE. The addition of the MP features to v₁PO4/Amide I improved the models in predicting K_init. When combining v₁PO₄/Amide I with the OMP features (collagen structure), the ETR model showed substantial improvement while the XGB, SVR and ensemble models achieved lower performance compared to the ETR model (Table 6 and Supp. Fig. 2). The inclusion of the OMP features alongside v₁PO₄/Amide I led to notable performance improvements, especially for the ETR model, which achieved the highest R². Interestingly, ETR and XGB provided higher R² values and lower error metrics than SVR and ensemble when OMP features were added to v₁PO₄/Amide I, while the opposite was the case when MP features were added to v₁PO₄/Amide I (Table 6 and Supp. Fig. 2).

For the combination of v₁PO4/Amide I, OMP, and MP features, the ETR model achieved the highest R² and the lowest RMSE, MAE and MAPE error metrics, while the ensemble model had the second-best performance in the prediction of K_init. On the other hand, the SVR model showed the worst performance (Table 6 and Supp. Fig. 2). Including all three feature sets, best MMR (v₁PO₄/Amide I), OMP, and MP,generally resulted in improved performance across all models (Fig. 3). The ETR and ensemble models performed the best, achieving higher R² values of 0.623 and 0.557, respectively. However, the slight drop in performance for the SVR model suggests that while adding more features can improve accuracy, it may also introduce additional complexity that requires careful handling. Therefore, these results emphasized the critical role of feature selection and combination in enhancing ML model performance. The comparison of model predictions for all feature combinations is presented in Fig. 3.

3.3. Regression model results for predicting J-integral

As with the K_init prediction, before training the SVR, XGB, and ETR algorithms, we performed parameter optimization using the grid-search method to identify the optimal parameters. Additionally, at each stage, 20 % of the dataset was consistently used as the test set, while the remaining 80 % was allocated as the training set throughout all steps.

3.3.1. Selecting the best MMR feature in predicting J-integral

As we conducted in the K_init prediction, the first step involved creating datasets consisting of CSP features and one MMR feature to identify the best MMR feature (Table 7 and Supp. Fig. 3).

Table 7.

Model performance results for CSP features combined with each individual MMR feature for prediction of J-int. Bold indicates the optimal algorithms among the ML algorithms tested. The RMSE, MAE and MAPE scores of the best models were considered to determine the best MMR feature among the four MMR features.

		$R^2$	RMSE	MAE	MAPE
CSP	ETR	0.048	5.258	4.314	0.442
	XGB	0.029	5.061	4.130	0.418
	SVR	0.214	4.551	3.712	0.364
	Ensemble	0.120	4.817	3.835	0.386
CSP + V1PO4/Amide I	ETR	0.411	3.939	3.094	0.309
	XGB	0.423	3.901	2.919	0.295
	SVR	0.478	3.710	3.062	0.288
	Ensemble	0.487	3.677	2.946	0.289
CSP + v1PO4/Proline	ETR	0.052	5.000	3.916	0.394
	XGB	0.027	5.065	4.049	0.393
	SVR	0.116	4.829	3.592	0.318
	Ensemble	0.117	4.826	3.776	0.359
CSP + v1PO4/Amide III	ETR	0.108	4.849	3.817	0.385
	XGB	0.053	5.270	4.305	0.441
	SVR	0.219	4.537	3.517	0.330
	Ensemble	0.133	4.782	3.778	0.375
CSP + v1PO4/CH2-wag	ETR	0.344	4.158	3.321	0.343
	XGB	0.490	3.665	2.802	0.276
	SVR	0.457	3.785	3.101	0.314
	Ensemble	0.467	3.747	2.874	0.290

In the ability of CSP features to predict J-int, the ETR and XGB algorithms exhibited poor performance (Table 7 and Supp. Fig. 3). The SVR algorithm provided the best prediction achieving the highest R² and lowest RMSE, MAE, and MAPE error metrics. The predictive performance of the ensemble algorithm was between XGB (or ETR) and SVR. Overall, the predictive capability of age, sex, porosity, and vBMD was limited without additional features (Fig. 4).

Fig. 4.

Predictions of ML algorithms versus actual values of J-int. Incorporating the MMR feature in place of the CSP feature improved prediction performance. Based on R² and MAPE scores, the v₁PO₄/CH₂-wag with the XGB algorithm provides the best model for predicting J-int, while the v₁PO₄/Amide I with the ensemble algorithm shows a comparable R² but a higher MAPE score.

When the v₁PO₄/Amide I feature was incorporated, the models showed significant improvements (Table 7 and Supp. Fig. 3). The ETR and XGB models showed similar performance while the SVR model demonstrated further improvement (Supp. Fig. 2). The ensemble model performed the best, achieving the highest R² and lower RMSE, MAE, and MAPE error metrics. The superior performance of the ensemble model demonstrates its ability to integrate complementary information from different models, suggesting that the v₁PO₄/Amide I feature captures important aspects of the underlying data.

While the v₁PO₄/Proline feature contributed to some improvements, the increases were less significant compared to the v₁PO₄/Amide I feature (Fig. 4). The inclusion of the v₁PO₄/Amide III feature produced mixed results, indicating variability in how different models process complex feature sets. This underscored the importance of both careful feature selection and understanding model compatibility. Finally, the inclusion of the v₁PO₄/CH₂-wag feature resulted in significant performance improvements across all models (Supp. Fig. 3). The v₁PO₄/CH₂-wag feature significantly enhanced the predictive accuracy, particularly for the XGB model (Table 7 and Fig. 4), which demonstrated outstanding performance in prediction of J-int. This suggests that the v₁PO₄/CH₂-wag feature captures critical predictive information and is highly valuable for the model's performance. The comparison of predicted values across the models with different MMR feature combinations is shown in Fig. 4.

3.3.2. Evaluation of additional features on predicting J-integral

Once selecting the best MMR feature, a similar methodology was applied to evaluate the contribution of the OMP and MP features to the J-int prediction. The same models were used on the same split datasets, with different combinations of features: CSP + v₁PO₄/CH₂-wag + MP, CSP + v₁PO₄/CH₂-wag + OMP, and CSP + v₁PO₄/CH₂-wag + OMP + MP. The results for all feature combinations are presented in Table 8 and Fig. 5 below.

Table 8.

Performance of the models for each combination of feature sets for prediction of J-int.

		R2	RMSE	MAE	MAPE
CSP + v1PO4/CH2-wag + MP	ETR	0.454	3.795	2.964	0.304
	XGB	0.485	3.686	2.821	0.279
	SVR	0.457	3.784	3.067	0.301
	Ensemble	0.492	3.659	2.867	0.285
CSP + v1PO4/CH2-wag + OMP	ETR	0.699	2.815	2.400	0.240
	XGB	0.737	2.634	2.283	0.240
	SVR	0.653	3.023	2.480	0.238
	Ensemble	0.733	2.652	2.296	0.227
CSP + v1PO4/CH2-wag + OMP + MP	ETR	0.719	2.723	2.349	0.238
	XGB	0.672	2.939	2.463	0.253
	SVR	0.658	3.004	2.356	0.216
	Ensemble	0.719	2.720	2.299	0.229

Fig. 5.

Predictions of the best performance of ML algorithms versus actual values of J-int. Based on the R² and MAPE scores, the XGB and ensemble algorithms provide the most accurate models for predicting J-int.

For the combination of the best MMR feature (i.e., v₁PO₄/CH₂-wag) and the MP feature, the ensemble model provided the best performance in predicting J-int. The addition of the MP feature to v₁PO₄/CH₂-wag improved the models' predictive capabilities. The ensemble model's superior performance, with the highest R² and the lowest MAPE, suggests that the MP feature provides valuable supplementary information, improving overall accuracy.

The inclusion of the OMP features alongside v₁PO₄/CH₂-wag led to performance improvements across all models (Table 8 and Supp. Fig. 4). Yet, the XGB and the ensemble model achieved the highest performance (i.e., highest R² and lowest error metrics). The consistent increase in accuracy and reduction in error metrics demonstrate the OMP features' substantial contribution to capturing complex data relationships.

For the combination of v₁PO₄/CH₂-wag, OMP, and MP features, the ETR and the ensemble model achieved the best performance with the highest R² and lowest RMSE, MAE and MAPE error metrics (Fig. 5). The inclusion of both MP and OMP features, enhanced the accuracy of the models, as evidenced by higher R² values and lower error metrics. However, slight variations in performance across models indicate the need for tailored feature selection and model tuning to achieve optimal predictive accuracy. The comparison of model results is shown in Fig. 5.

4. Discussion

To the best of knowledge, this study is the first attempt to combine RS with clinically relevant compositional and structural features (such as age, sex, cortical bone porosity and bone mineral density) in a machine learning framework to predict the mechanical properties of human cortical bone using femoral mid-diaphysis cortical bone from donors aged 21–101 years. By integrating molecular-level features derived from Raman spectra with clinically relevant parameters, we have demonstrated an approach to enhancing the predictive accuracy of fracture toughness prediction of human cortical bone. This study sets a new approach for using ML to predict complex bone mechanical properties, offering an innovative, multi-dimensional method to enhance the accuracy and reliability of predictions.

For the K_init prediction, the v₁PO₄/Amide I feature was identified as the most effective parameter for improving model accuracy over CSP features (Fig. 2). While the inclusion of mineral properties/MP features (e.g., carbonate substitution and crystallinity) and organic matrix properties/OMP features (e.g., collagen cross-links and collagen helical status) led to incremental improvements (Fig. 3), it was clear that the primary driver of model performance was v₁PO₄/Amide I. The most significant improvement in prediction, ranging from an R² of 0.323 to 0.586, based on the ensemble approach, was observed after incorporating this feature into the models (Table 5). This suggests that its specific molecular characteristics are most pertinent to the K_init prediction in bone-related materials. The v₁PO4/Amide I feature reflects key biochemical properties associated with bone mineralization regarding collagen structure (Unal et al., 2021; Mandair and Morris, 2015), two critical main components influencing bone mechanical behavior (Currey, 1969; Wang et al., 2001). This outcome is of great significance as it highlights the potential of RS to capture detailed biochemical information, which is directly linked to bone's structural integrity and fracture resistance. The combination of these features with the ETR or ensemble algorithms results in creating a more robust and accurate model (Fig. 3).

For J-int prediction, v₁PO₄/CH₂-wag is the most suitable feature for creating an accurate model (Fig. 4). Among all models and feature combinations, the best prediction performance was achieved with the XGB and ensemble algorithms (Fig. 5). The v₁PO₄/CH₂-wag feature emerged as a key predictor of J-int, as the most significant improvement in prediction, ranging from an R² of 0.214 to 0.490, was observed after incorporating this feature into the models (Fig. 5). This further underscores the importance of integrating both biochemical and clinically relevant features to fully capture the complexity of bone material properties. The inclusion of Raman based-mineral quality parameters and organic matrix properties demonstrated additional improvements in the predictive capability of the models (Table 8 and Fig. 5), suggesting that a comprehensive approach that accounts for both the mineral and organic components of bone is crucial for accurate predictions. This finding has important implications for bone research, as the J-int measures the amount of energy dissipation by bone during crack propagation under increasing displacement (Unal et al., 2023; Willett et al., 2019). The integration of v₁PO₄/CH₂-wag into predictive models adds an insight to understanding the toughness and resistance of bone under mechanical loading, highlighting the critical role of biochemical features in the modeling of mechanical properties of bone, a focus that is often underexplored in traditional mechanical testing and simulation studies (Unal et al., 2018a). Overall, the best-performing algorithm using CSP alone yielded an R² of 0.323 for K_init and 0.214 for the J-int (Table 5, Table 7), compared with R² values of approximately 0.623 and 0.737 when RS-derived features are included. These substantial drops in explained variance further underscore the critical contribution of RS features to predictive accuracy.

In the past, several studies have showed the moderate to strong correlations between mechanical properties of murine bone and RS-based measures of bone composition (Akkus et al., 2004; Bi et al., 2011; Raghavan et al., 2012; Ramasamy and Akkus, 2007; Maher et al., 2011; Inzana et al., 2013; Massie et al., 2021), highlighting the potential of RS in predicting bone mechanical properties. In our previous study, using a similar set of variables (age, vBMD, and bone matrix quality properties derived from RS), general linear regression models were able to predict K_init (R² of 0.502) and the J-int (R² of 0.539) of human cortical bone (Unal et al., 2019). Unlike our prior study, the current study applies advanced ML algorithms to a larger cohort of 118 cadaveric femoral mid-diaphysis samples. In these models, we integrate demographic variables (age and sex), structural measurements (cortical porosity and vBMD), and an extensive suite of RS-derived compositional metrics into a unified predictive framework (See Supplemental Table 1). 5-fold cross-validation within the training set and evaluation on an independent 20 % hold-out test set demonstrate consistent model performance across diverse specimens. Collectively, these methodological and cohort enhancements establish this study as the first to leverage AI/ML techniques with combined clinical, structural, and spectroscopic data for robust prediction of human cortical bone's fracture toughness properties.

The integration of MP and OMP features with the MMR feature also demonstrated notable improvements in model performance for both K_init and J-int predictions (Fig. 3 and Fig. 5). The addition of these features enhanced the models' ability to capture variation in the target variables, offering insights into the potential of including multiple molecular and material characteristics in predictive modeling. However, one of the key insights from our analysis is the importance of feature selection and dimensionality reduction techniques in improving ML model performance. By identifying informative features from RS-derived bone quality properties and clinically relevant variables, we were able to mitigate overfitting and enhance the generalization capabilities of our models. The results suggest that while adding multiple features can enhance accuracy, careful consideration must be given to avoiding unnecessary complexity and overfitting. This is particularly important in bone research, where the goal is to balance model precision with computational efficiency and generalizability.

The differences in performance observed between the various ML algorithms can be attributed to several factors, including the ability to handle non-linear relationships, model complexity, and feature selection. For example, XGB excelled in capturing complex interactions and feature importance (Chen and Guestrin, 2016), while SVR and ETR were more limited by their simpler structures and sensitivity to parameter tuning (Vapnik, 1999; Geurts et al., 2006). Despite the complexity of the models, less complex algorithms were able to provide comparable accuracy, indicating that selecting the most informative features can lead to more efficient and accurate predictions (Table 5, Table 6, Table 7, Table 8). The ensemble strategy, which combines multiple ML models, demonstrated its power to improve predictive performance by capturing different aspects of the data, thus ensuring robustness. By integrating multiple models, the ensemble method helps mitigate the risk of overfitting and provides a more stable solution that generalizes well to unseen data. This is particularly crucial in biomedical applications where data can be noisy or sparse, and model reliability is paramount. Therefore, the ensemble strategy's ability to combine complementary strengths from different models makes it an invaluable tool in the development of predictive models for bone research. Furthermore, our study highlights the role of model interpretability in translational research. While complex DL models such as neural networks often yield superior predictive performance in biomedical applications (Baldi, 2018; Zemouri et al., 2019), their black-box nature limits their interpretability and clinical utility. In contrast, simpler models such as SVR, ETR, XGB based linear regression models offer greater transparency, allowing clinicians to understand the underlying factors contributing to fracture risk prediction. The application of these advanced techniques in bone research is still relatively new, but it holds great promise for improving the understanding of bone properties and predicting fracture risks.

The ability to quantify these features non-invasively provides a valuable tool for assessing bone quality in both clinical and research settings, further expanding the applicability of RS-based techniques in bone biomechanics (Massie et al., 2023). Therefore, the results presented in this study also highlight the tremendous potential of RS, specifically techniques like Spatially Offset Raman Spectroscopy (SORS) for in vivo assessment of bone health (Buckley et al., 2015; Matousek et al., 2005; Matousek, 2006). SORS allows for non-invasive, real-time measurements of bone composition, offering a unique advantage in clinical applications (Gautam et al., 2023; Ahmed et al., 2023). It could enable clinicians to monitor bone quality continuously and evaluate treatment effectiveness without needing invasive procedures (Nicolson et al., 2021). The combination of SORS with ML models could revolutionize how we assess bone strength and fracture risk, accelerating more personalized and effective treatment strategies.

However, several challenges and limitations warrant consideration in future research. Firstly, the generalizability of our models may be influenced by the heterogeneity of the study population and variations in data acquisition protocols. Second, while our cohort of 118 cadaveric femoral cortical specimens represents one of the largest Raman datasets to date, assembling such a sample necessitated merging measurements from two different instruments. To minimize instrument-related variability, we balanced donor allocation across both devices, performed daily silicon-wafer calibrations to align wavenumber and normalize intensity, and ensured equal representation of spectra from both instruments in the training and test sets. Nonetheless, residual batch effects may still influence model performance. Addressing such issues will require larger, more diverse datasets and standardized methodologies for data collection and preprocessing. Moreover, the combination of additional factors obtained from various imaging modalities could further enhance the predictive capabilities of our ML models by capturing the other structural and material properties of bone tissue at different length scales. Although 5-fold cross-validation within the training data helps mitigate overfitting, the absence of an external validation cohort may limit the models' generalizability. Future work should include independent datasets for further validation.

In conclusion, this study demonstrates the potential of integration of AI/ML and RS in bone biomechanics research. By combining molecular-level features with clinically relevant parameters, we developed a predictive ML-based framework that may enhance our understanding of bone mechanical properties and fracture resistance as well as may facilitate personalized risk assessment strategies for fracture prevention and management in clinical settings.

CRediT authorship contribution statement

Mustafa UNAL: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Ramazan UNLU: Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Methodology, Formal analysis, Conceptualization. Sasidhar UPPUGANTI: Writing – review & editing, Software, Methodology, Investigation, Formal analysis, Data curation. Jeffry S. NYMAN: Writing – review & editing, Writing – original draft, Supervision, Project administration, Funding acquisition, Conceptualization.

Declaration of competing interest

The authors declare that they have no conflict of interest related to this work.

Appendix A. Supplementary data

Supplementary material

Data availability

Data will be made available on request.