Learning-enhanced 3D fiber orientation mapping in thick cardiac tissues

Abstract

Fibrous proteins, such as elastin and collagen, are crucial for the structural integrity of the cardiovascular system. For thin tissue-engineered heart valves and surgical patches, the two-dimensional mapping of fiber orientation is well-established. However, for three-dimensional (3D) thick tissue samples, e.g., the embryonic whole heart, robust 3D fiber analysis tools are not available. This information is essential for computational vascular modeling and tissue microstructure characterization. Therefore, this study employs machine learning (ML) and deep learning (DL) techniques to analyze the 3D cardiovascular fiber structures in thick samples of porcine pericardium and embryonic whole hearts. It is hypothesized that ML/DL-based fiber orientation analysis will outperform traditional Fourier transform and directional filter methods by offering higher spatial accuracy and reduced dependency on manual preprocessing. We trained our ML/DL models on both synthetic and real-world cardiovascular datasets obtained from confocal imaging. The evaluation used a mixed dataset of 1200 samples and a porcine/bovine dataset of 400 samples. Support vector regression (SVR) demonstrated the highest accuracy, achieving a normalized mean absolute error (nMAE) of 5.0% on the mixed dataset and 13.0% on the biological dataset. Among DL models, convolutional neural network (CNN) and residual network-50 (ResNet50) had an nMAE of 12.0% and 11.0% on the mixed dataset and 23.0% and 22.0% on the biological dataset, respectively. Attention mechanisms improved performance further, with the channel attention ResNet50 achieving an nMAE of 5.8% on the mixed dataset and 21.0% on the biological dataset. These findings highlight the potential of ML and DL techniques in improving 3D fiber orientation detection, enabling detailed cardiovascular microstructural assessment.

1. Introduction

Fibrous proteins, particularly collagen and elastin fibers, play a critical role in shaping the structural framework of the cardiovascular system [1]. These fibers are integral to the formation and function of cardiovascular tissues, including arteries, veins, and heart valves [2,3]. Except the baseline endothelial membrane, cardiovascular tissues are rarely 2D and complete mapping require a 3D analysis. Understanding the orientation of collagen fibers holds particular significance in thick cardiovascular tissues such as porcine pericardium and whole heart ventricles [4–7]. The integrity of the cardiac tissues depends on the precise alignment of its structural fibers, primarily collagen and elastin [8,9]. Moreover, quantitative mapping of microstructural fibers is essential in cardiovascular tissue engineering, e.g. artificial surgical patches, to track changes in mechanical properties in vivo [10] and to optimize fiber orientation in artificial constructs [11,12]. By ensuring accurate fiber alignment, these synthetic tissues can closely resemble the mechanical properties and functions of the biological cardiovascular tissues and enhance durability and surgical outcome.

In the literature, a myriad of 2D methods are proposed to determine the orientations of fiber structures. These include 2D Fourier transform [13,14], Hough transform [15,16], directional filters [17–19], intensity derivatives [20–22] or intensity variation [23], fiber tracking algorithms [24,25], and edge detection [26]. However, 3D fiber mapping, as focused on the present paper, is limited to our knowledge. Among the 2D methods, derivative-based techniques can provide pixel-level orientation information, but they often require additional algorithms to identify the edges of the fibers across the entire image [27]. Transform or filter-based methods such as Fourier Transform or Hough Transform typically involve defining an interrogation window to obtain fiber direction within that window [28]. For fiber tracking algorithms, it is necessary to develop an algorithm that considers the spread direction of each fiber family [29]. These traditional 2D methods have several disadvantages when applied to 3D fiber analysis. First, they often lack the ability to capture the full spatial complexity and orientation of fibers in 3D. Second, these methods typically require extensive preprocessing and post-processing steps, making them less efficient and more prone to errors. Additionally, they may not generalize well to different types of tissues or varying imaging conditions.

Advances in Machine Learning (ML) and Deep Learning (DL) offer new avenues for more accurate and efficient fiber analysis, as undertaken very recently [30–34]. For instance, Zeng et al. introduced FOD-Net, a deep learning method for fiber orientation distribution angular super-resolution [30]. Nath et al. demonstrated that deep learning techniques could capture more accurate diffusion fiber orientation distributions than constrained spherical deconvolution [31]. Similarly, Karimi et al. developed a model to estimate the fiber orientation distribution function from diffusion-weighted Magnetic Resonance Imaging (MRI) [32], while Lucena et al. enhanced fiber orientation estimation using convolutional neural networks [33]. Lin et al. presented a fast-learning approach for MR tractography using a convolutional neural network [34]. However, most of these studies have concentrated on 2D data analysis or utilized clinical imaging modalities like MRI, which are suited for macroscopic tissue assessments but lack the resolution needed for 3D fiber mapping. For example, Lee et al. [35] employed ML models on multiparametric quantitative MRI data to evaluate collagen fiber orientation and proteoglycan content in articular cartilage. While impactful, these approaches reveal a gap in methods for high-resolution 3D fiber analysis. This emphasizes the need for novel techniques tailored to complex biological samples, such as those analyzed through confocal microscopy. Pham et al. present a DL model based on convolutional neural networks (CNN) for the classification and characterization of histology images. The proposed CNN model achieves over 97% accuracy in classifying normal and scar tissue, providing quantitative insights into collagen fiber density and directional variance [36]. Current studies have highlighted the potential of deep learning in cardiovascular image analysis, including heart disease detection through cardiac sounds [37] and cardiac image segmentation [38,39].

In this study, we address this gap by introducing two novel approaches for 3D fiber orientation mapping. The proposed methods employ a robust local reconstruction technique, leveraging orthogonal 2D fiber analyses (xy and xz planes) to reconstruct comprehensive 3D fiber orientations. Additionally, the Fast Fourier Transform (FFT) algorithm is included as a benchmark to assess the comparative performance of our approaches. A significant aspect of our methodology lies in the integration of domain-specific preprocessing steps and the exploration of advanced ML/DL techniques, including attention mechanisms such as channel attention and Convolutional Block Attention Modules (CBAM). These attention mechanisms were incorporated to enhance the analysis and evaluate their potential impact on predictive accuracy for fiber orientation mapping in thick cardiac tissues, contributing to a comprehensive comparison of methodologies. To validate our methods, we utilized a combination of synthetic datasets generated via diffusion models [40] and real-world data acquired from 3D confocal microscopy. Synthetic datasets include diverse fiber arrangements, such as toroidal structures, while real-world samples encompass thick cardiovascular tissues and embryonic heart specimens. This approach allows us to benchmark the performance of our methods across a wide range of fiber orientations and imaging conditions. This manuscript is organized as follows: First, we detail the generation of synthetic datasets and the acquisition of real-world images, followed by a comprehensive description of our methodology, including the reconstruction process and integration of ML/DL techniques. We then present a comparative analysis of our methods against the FFT benchmark, evaluating their performance in terms of accuracy, computational efficiency, and adaptability to various fiber structures. Finally, the Discussion section critically evaluates the results, highlights potential limitations, and suggests avenues for future research.

2. Methodology

The given 3D image containing fiber information was divided into smaller volumetric interrogation volumes, or voxels, to facilitate analysis. Using at least two 2D fiber direction analysis the local 3D reconstruction is achieved based on the voxel cross-sectional images along the xy- and xz- axes of the 3D image volume in Fig. 1. The voxel data obtained from the xy- and xz- axes are aggregated the orientation information within each voxel, determining the resultant vector and primary orientation angle, θ, relative to a reference plane. This quantitative measure provides insight into the fiber orientation within the 3D space. To conduct this 3D analysis, we employed two new ML/DL models: Support Vector Regression (SVR) and CNN, described in Section 2.2, Section 2.3 and Section 2.4, respectively. The traditional FFT-based approach (Section 2.5), which does not involve ML/DL, is also included as a benchmark for comparisons. While FFT remains a well-established technique for frequency and orientation analysis, it primarily serves as a benchmark in this study. Existing ML/DL methods for fiber orientation mapping are limited to 2D analyses or clinical imaging modalities, such as MRI, which differ fundamentally in resolution and scope from the confocal microscopy datasets used in this research. Consequently, the methods proposed here represent a novel framework for 3D fiber orientation analysis in thick cardiac tissues, addressing challenges related to complex fiber arrangements and imaging noise.

Fig. 1.

Cartoon representation of a thick 3D cardiovascular tissue of the whole heart. (b,c) The pre-processed visualization along the xz and xy-axis using raw data. (d) 3D rendering highlighting the spatial organization of collagen fibers.

2.1. Datasets

2.1.1. Synthetic datasets

2D Data:

In our approach to synthesizing fiber-collagen images, a diffusion model was employed to generate diverse representations. Initially, key parameters such as fiber orientation, fiber density, and structural complexity were precisely selected, forming detailed textual descriptions for the diffusion model [31]. These descriptions served as inputs to the diffusion model, guiding the generation process to produce high-resolution images with resolutions typically exceeding 1024 × 1024 pixels. These prompts were crafted to reflect realistic microstructural properties observed in confocal images of biological tissues, including fiber orientation, density, branching complexity, and texture. Although no formal quantitative similarity metrics were used to validate the synthetic images, all outputs were visually reviewed by domain experts and qualitatively compared to representative biological samples to ensure morphological plausibility. By systematically varying these parameters, the creation of a comprehensive dataset encompassing a wide spectrum of fiber-collagen structures was ensured. This augmentation enriched our training corpus with a multitude of synthetic examples, facilitating a thorough exploration of fiber-collagen morphology. Ultimately, our approach yielded 8 high-quality synthetic images, later cropped by 50 × 50 to form a total of 800 training samples, providing desired diversity to our training dataset and resulted in robust model training.

3D Data:

In this study, we focused on the generation of data regarding a three-dimensional toroidal structure and its subsequent decomposition into a series of two-dimensional cross-sectional images. To achieve this, a customized algorithm was implemented, taking into consideration the geometrical properties of a torus, defined by the parametric equations [32]:

$$\text{x}(\mathrm{\theta },\mathrm{\phi })=(\text{R }+\text{ r }\ast \text{ cos}(\mathrm{\theta }))\ast \text{ cos}(\mathrm{\phi })$$ (1)

$$\text{y}(\mathrm{\theta },\mathrm{\phi })=(\text{R}+\text{r }\ast \text{ cos}(\mathrm{\theta }))\ast \text{ sin}(\mathrm{\phi })$$ (2)

$$\text{z}(\mathrm{\theta },\mathrm{\phi })=\text{r }\ast \text{ sin}(\mathrm{\theta })$$ (3)

The algorithm allows control over torus geometrical parameters, including its major and cross-sectional radii (R and r), as well as angular parameters (θ and φ). It generates a point cloud data of size MxN, where M represents the number of torus strings and N is the number of points in each string [33]. A torus gap with an angular extent is incorporated to introduce complexity for analysis and serve as a spatial marker. Additionally, the torus can be rotated in 3D to align its normal vector with a desired plane using rotation matrices.

2.1.2. Biological data

Early embryonic whole-heart samples:

Fertile white Leghorn eggs are incubated according to IRB approved guidelines. Microfil agent, 2 µl∶5 µl∶5 µL; dye: diluent buffer: curing agent, is given to the apex of the avian embryo heart in ovo culture (MICROFILInjection Compounds, Flow Tech, Inc) for vessel filling. The embryos were harvested in fresh chick ringer solution at Hamburger Hamilton (HH) stage 25 and fixed in 4% (wt/vol) paraformaldehyde [41]. This challenging dataset was specifically used as a Use Case of our ML algorithm.

Pericardium samples:

Healthy porcine hearts were obtained from Koc University Hospital RMK AIMES immediately post-mortem, adhering to ethical guidelines. The pericardium was carefully dissected, rinsed with sterile saline to remove blood and debris, cut into 1 × 1 cm pieces, and fixed in 10% formalin. In addition, clinically approved porcine (BioIntegral Surgical, Inc., Canada) and bovine pericardium (Edward Lifesciences) samples were cut into 1 × 1 cm sections. These sections were permeabilized with 0.1% Triton X-100 in PBS for 2 hours, then blocked with 5% BSA in PBS for 2 hours at room temperature to prevent non-specific binding. The sections were incubated overnight at 4°C with a primary antibody against collagen I (mouse anti-collagen I) diluted 1:200 in 1% BSA in PBS. After washing with PBS, sections were incubated with Alexa Fluor 488-conjugated anti-mouse IgG secondary antibody for 2 hours at room temperature in the dark. Stained sections were mounted on glass slides using an anti-fade mounting medium compatible with confocal microscopy.

Cardiac tissue imaging:

Confocal microscopy imaging was performed using a 488 nm laser for Alexa Fluor 488. Z-stack images were acquired to capture 3D representations of collagen I distribution within both porcine pericardium and embryonic heart. The in-plane resolution of the confocal images was approximately 2.15 µm/pixel for pericardial tissue and 0.65 µm/pixel for cardiac tissue, while the Z-step size (optical section thickness) was 1 µm per slice. Confocal microscopy were converted into 3D and visualized in xy- and xz-axes. For the algorithm, a total of 400 bovine and porcine samples were collected. This dataset was used to train and test the performance of both FFT and ML algorithms, with an 80/20 split for training and testing, respectively.

2.1.3. Training data

The training dataset comprises both biological and synthetic data to ensure robust model generalization, as shown in Supplement 1 ^{(3.3MB, pdf)} Fig. 1. A total of 11 distinct samples were obtained from a clinically approved porcine pericardium patch. Each sample was subdivided into 50 × 50 voxel regions, resulting in 400 biological samples. The voxel size of 50 × 50 pixels in the XY plane was empirically determined through iterative testing. Larger patch sizes tended to average out directional cues, while smaller patches lacked sufficient structural information to determine fiber orientation. This size provided a suitable balance between resolution and contextual fiber continuity. Along the Z-axis, local intensity profiles were assessed, and regions with weak signal across slices were excluded from training to ensure structural relevance. Additionally, a diffusion model was employed to generate 8 high-resolution synthetic images, which were subsequently divided into 50 × 50 voxel segments, yielding 800 synthetic samples. Collectively, the biological and synthetic data constituted a mixed dataset of 1200 samples. To ensure unbiased evaluation and avoid angular distribution skew, this mixed dataset was first balanced across fiber orientation angles before being split into training and testing subsets.

To increase model robustness and simulate real-world variability, data augmentation was applied to the training set, including random rotations, isotropic scaling, and Gaussian noise addition. This expanded the dataset to approximately 4,000 samples, allowing the model to generalize better to structural variations. For biological samples, additional preprocessing steps were necessary to remove irrelevant or misleading content. Non-fiber regions such as tissue edges, background voids, or saturated regions caused by uneven staining were excluded using a semi-automated pipeline based on intensity thresholding, contrast normalization, and morphological filtering. Regions with insufficient fiber density were filtered out using a combination of average pixel intensity and edge density metrics

This refinement step minimized noise and ensured that the model was trained on high-quality fiber orientation data. To prevent data leakage, the synthetic images used for training were completely distinct from those used in testing. These synthetic images were designed to replicate real-world fiber structures, enhancing the model’s ability to distinguish fiber orientations and adapt to complex tissue architectures. Ground truth fiber orientation angles used for training were manually annotated by the authors using the ImageJ software. These annotations were based on visual inspection of the fiber alignment in representative image regions, and angles were extracted by drawing orientation vectors directly on the confocal images.

2.1.4. Testing data

The testing dataset was designed for both 2D and 3D verification, incorporating synthetic and biological data. For 2D validation, MATLAB-generated linear structures with controlled orientations and two separate high-quality synthetic images from diffusion models (distinct from those used in training) were included, as shown in Supplement 1 ^{(3.3MB, pdf)} , Fig. 2. For biological validation, a total of eight samples were analyzed for each case, consisting of four samples from four different pericardia, with two different locations per pericardium, ensuring a comprehensive evaluation of fiber orientation variability across different anatomical sources and locations. These samples included clinically approved bovine and porcine pericardium as well as biological porcine pericardium, providing detailed insights into fiber orientation consistency and structural differences among tissue types. As the balancing was performed prior to the train-test split, the test dataset preserved a similar angle distribution, allowing fair evaluation across all methods. For biological test samples, an intensity-based filtering step was applied prior to evaluation to exclude regions lacking visible fiber structure. In RGB image channels, patches with low average intensity and limited contrast were identified as non-fiber regions and excluded from analysis. This ensured that model predictions were evaluated only in structurally meaningful areas, consistent with how ground truth angles were annotated. For 3D verification, the chick embryo heart dataset, which contains detailed 3D fiber structure information, was used to evaluate the model’s capability in reconstructing volumetric fiber orientations. No overlap existed between training and testing biological samples to ensure unbiased evaluation.

2.2. Support vector regression

Histogram of gradients (HOG) feature extraction technique was utilized to capture the fine details of fiber orientations within the images. HOG is renowned for its robustness in identifying edge structures by computing the gradient orientations of localized regions within an image [42]. For each image, the method involved dividing the image into small, connected regions called grid, and for each grid, compiling a histogram of gradient directions or edge orientations. By normalizing these histograms across larger regions of the image, invariance to the changes in illumination and shadowing was achieved. To determine the optimal grid size for feature extraction, various grid sizes such as 4 × 4, 8 × 8, 16 × 16, and 32 × 32 were tested. After extensive experimentation, the 32 × 32 grid size provided the best balance between detailed feature capture and computational efficiency for our image size (1024 × 1024). However, relying solely on a single large-scale grid risked missing finer structural variations. To address this, we adopted a multi-scale feature fusion strategy: HOG features computed at all four grid sizes were concatenated into a single composite feature vector. This enriched representation allowed the model to capture both coarse and fine-grained fiber orientation cues. Due to the high dimensionality of the resulting feature set, Principal Component Analysis (PCA) was applied to reduce redundancy while retaining the most informative components. This dimensionality reduction step was validated through hyperparameter tuning, where SVR models trained on PCA-compressed multi-scale features consistently outperformed those using single-scale or uncompressed features. The effectiveness of different grid size combinations and their trade-offs is further explored in Supplement 1 ^{(3.3MB, pdf)} Fig. 3.

Following feature extraction, SVR technique was employed to train the regression model. SVR is particularly adept at handling high-dimensional feature spaces and is capable of learning complex mappings between input features and target values. As illustrated in Fig. 2, the SVR model was trained to predict the actual fiber orientation angles from the extracted HOG features. By utilizing a kernel function, the non-linear relationships within the data were managed, enhancing predictive accuracy. A grid search was conducted to find the optimal hyperparameters for the SVR model, considering different kernel types, i.e. linear and radial basis function (rbf), regularization parameters (C), and kernel coefficients (gamma). This optimization approach, facilitated by cross-validation techniques, ensured robustness and generalization of performance, making the SVR model a reliable tool for analyzing and predicting fiber orientations even in test data.

Fig. 2.

Process of estimating fiber orientation using both synthetic and biological datasets. Synthetic images are generated through diffusion models, creating diverse fiber patterns, which are then compared with actual biological fiber images captured via microscopy. Feature extraction is performed on both datasets using HOG, emphasizing the directionality and distribution of fiber orientations. These features are subsequently input into a SVR model, where the input layer consists of feature vectors processed through kernel functions in the hidden layer. The output layer sums these contributions to predict fiber orientation. The analysis culminates in detailed orientation maps, exemplified by yellow arrows on a sample image, providing comprehensive insights into the structural organization of fibers in synthetic and biological samples.

2.3. Convolutional neural network training

In the deep learning phase, a CNN was utilized to analyze and discern complex spatial relationships within the fiber orientation data. CNNs are particularly well-suited for fiber image analysis task due to their ability to learn hierarchical representations of data through layers of convolutional filters [43]. Our CNN architecture included two convolutional layers, each followed by activation functions and pooling layers, which contributed to robust feature extraction and representation. Specifically, the model consisted of an input layer for 50 × 50 grayscale images, multiple convolutional layers with ReLU activation and max-pooling, followed by dense layers with dropout for regularization. We applied data augmentation techniques like random rotation, translation, and horizontal flipping to enhance the model's generalization. The model was trained with the Adam optimizer for 200 epochs and Mean Absolute Error (MAE) was used as a loss function.

2.3.1. Transfer learning

To further enhance the performance and efficiency of DL models, transfer learning was leveraged, incorporating pre-trained CNN models from well-established architectures such as ResNet50 [44]. Transfer learning involved using models that had been pre-trained on large image datasets, such as ImageNet, which contains millions of images across thousands of categories. Fine-tuning the pre-trained model involved selectively unfreezing and retraining specific layers, allowing the model's learned representations to adapt to the nuances of the fiber orientation dataset. This approach allowed for accelerated convergence, as the models required fewer epochs to adapt to the dataset.

2.3.2. Attention mechanisms

To enhance the model’s ability to focus on the most relevant regions and features of the images, attention mechanisms are incorporated into the architecture [45]:

Channel Attention:

This mechanism emphasizes critical feature channels by calculating a learnable scaling factor through global average pooling and dense layers. In our implementation, global average pooling is first applied to the input feature map to generate a channel descriptor, which summarizes the spatial content of each channel. This descriptor is then passed through a compact two-layer fully connected network. The first layer reduces the number of channels by a factor of eight, introducing a bottleneck structure that captures cross-channel dependencies while limiting computational cost. A ReLU activation is used to introduce non-linearity. The second layer restores the original channel dimension, and its output is passed through a sigmoid activation to produce normalized attention weights between zero and one. These weights are broadcast and applied to the input feature map via element-wise multiplication, enabling the model to selectively emphasize informative channels and suppress less relevant ones.

Spatial Attention:

Spatial attention highlights significant spatial regions within the feature maps. In our implementation, spatial attention is computed by first applying average pooling and max pooling operations independently across the channel dimension. These two spatial descriptors are then concatenated and passed through a two-dimensional convolutional layer with a kernel size of 7 × 7 and a single output channel. The convolutional layer captures contextual information over a relatively wide area, which is particularly beneficial for identifying fiber structures that span across multiple regions in the image. The resulting spatial attention map is activated with a sigmoid function and multiplied element-wise with the input feature map to selectively amplify or suppress spatial features.

2.4. Fast Fourier transform (benchmark)

Fiber orientation can be obtained based on the variability of voxel intensities in all directions within a 3D image stack using the 3D FFT [49]. In our approach, we divide a slice into typically 50 × 50 grids, resulting in smaller-sized images. Subsequently, a 2D FFT is applied to each of these smaller images. The vectors are then obtained using the 3D analysis method.

In the analysis of biological data, artifacts present in images can lead to the emergence of “bad” fiber directions (vectors) disrupting the accuracy of angle estimation in FFT analysis. To address this issue, we initially applied FFT to the entire image to obtain the frequency spectrum and identified the angle corresponding to the maximum amplitude. Vectors deviating within a range of 0-20 degrees from this dominant angle were classified as bad vectors. These vectors were removed, and the image was adjusted to align with the most dominant angle present. This vector exclusion step was applied only in the FFT benchmark to eliminate clearly spurious measurements caused by image artifacts. Machine learning models were evaluated across all regions to reflect end-to-end performance.

2.5. Performance evaluation

The primary performance metric for evaluating our regression models was the Normalized Mean Absolute Error (nMAE). nMAE offers a clear and intuitive measure of the average magnitude of errors between the predicted and actual fiber orientation angles, expressed as a percentage. It is calculated as the average of the absolute percentage differences between predicted values and the ground truth values, providing a straightforward assessment of prediction accuracy. Specifically, nMAE is defined by the formula:

$$MAE=\frac{1}{n}\underset{i=1}{\overset{n}{\sum }}|y_i-\widehat{y_i}|\ast 100$$ (4)

$$NormalizedMAE(\mathrm{\%})=\frac{MAE}{180}\times 100$$ (5)

where $y_i$ represents the actual fiber orientation angle, $\widehat{y_i}$ is the predicted angle, and n is the total number of predictions. Using nMAE as our primary performance metric allowed the overall accuracy of both FFT and ML models in predicting fine-grained fiber orientations. Lower nMAE values indicate better model performance, reflecting more precise and accurate predictions. By systematically analyzing the nMAE of our models, we could identify specific areas where our models excelled and where further improvements were necessary. This metric was instrumental in guiding the iterative refinement of our models, ensuring that we progressively enhanced their predictive capabilities and robustness.

2.6. Model output and orientation visualization

The machine learning and deep learning models in this study were trained to predict a single scalar angle value (θ) for each image patch, representing the dominant fiber orientation within that region. These angle values range between 0° and 179°, with all angles defined relative to the x-axis and measured counterclockwise. This consistent orientation convention ensures uniform interpretation across samples and datasets.

Since the model output is already a scalar angle (not a vector), no additional trigonometric transformation or projection was required during post-processing. For visualization purposes, each predicted angle was displayed as a straight-line segment or arrow centered on the corresponding patch location. These arrows illustrate the local fiber direction, enabling a spatially coherent orientation map. This approach is particularly useful in biological datasets where orientation patterns exhibit continuity or abrupt transitions.

All orientation visualizations presented in Supplement 1 ^{(3.3MB, pdf)} Fig. 4 were generated using this procedure. The visualization pipeline allows qualitative comparison between predicted fiber orientations and underlying image features, aiding both model interpretability and tissue analysis.

3. Result

3.1. 3D FFT approach (benchmark)

We create benchmark results using our FFT method with two different datasets: synthetically generated data and bovine/porcine data. The determination of angles for diverse linear structures was accomplished using a 2D FFT technique, enabling the analysis of signal components along various directions. For the synthetic dataset, lines were generated using a script and positioned at 45, 60, and 135 degrees, as illustrated in Fig. 3. The analysis revealed a slight 2-degree deviation from the anticipated 180-degree angle, suggesting that the method effectively discerns the angles formed by the linear structures with respect to the x-axis, achieving a notable accuracy rate of 98.9%.

Fig. 3.

FFT Analysis for 2D Synthetic Data. (a-d) Lines with 45, 60 and 135 degree angles are produced as binary scale using MATLAB, and the graph of the analysis results is shown using 2D FFT and x axes represent to angle of line, y axis represent to frequency spectrum.

The orientations of fiber structures in clinically approved and biological porcine slices were similarly analyzed using 2D FFT, as depicted in Fig. 4. For clinically approved bovine samples, a dominant fiber orientation at 130 degrees was recorded, with a deviation of 3.8% in Fig. 5. In contrast, clinically approved Porcine samples exhibited a dominant orientation at 140 degrees, with a deviation of 11.1%, indicating a 7.3% increase compared to clinically approved bovine. biological porcine showed a dominant fiber orientation at 135 degrees, with a deviation rate of 8.3%. These angles are measured with respect to the apicobasal direction of the heart.

Fig. 4.

Comparison of fiber orientation estimation in different tissue samples using FFT and SVR. The top row (a-c) shows fiber orientation maps (red arrows) overlaid on green fluorescence images for clinically approved bovine (a), clinically approved porcine (b), and biological porcine (c) tissues analyzed using FFT. The corresponding histograms (d-f) depict the distribution of fiber angles obtained from FFT analysis, with angles ranging from 20 to 160 degrees. The bottom row (g-i) displays fiber orientation maps (red arrows) for the same tissue samples analyzed using SVR. The associated histograms (j-l) show the distribution of fiber angles derived from SVR analysis, with angles concentrated around 100 degrees. This comparison highlights the differences in fiber orientation results between FFT and SVR methods across different tissue types.

Fig. 5.

Analysis of Fiber Orientation via 2D FFT for clinically approved bovine, clinically approved porcine, and biological porcine samples. Eight samples were analyzed for each case, illustratingthemeanfiberorientationangles,accompaniedbystandarddeviationbars. These eight samples consist of four samples from four different pericardia, with two different locations each, providing comprehensive insights into fiber orientation variability across different anatomical sources and locations

To further explore potential statistical differences among clinically approved bovine, clinically approved porcine, and biological porcine samples, an ANOVA test was conducted. The results suggested that there was no statistically significant variation in the dominant fiber orientations among the three groups.

3.2. Validation of the 3D representation

We validated the 3D vector integration method using FFT with a synthetic dataset. The 3D FFT method was applied to datasets of three-dimensional helical and toroidal structures to determine vector orientations. For the helical structure, the dataset with dimensions of 900 × 900 × 900 pixels was divided into 30 × 30 × 30 pixel grids, generating a total of 30 × 30 × 30 vector maps. Similarly, the toroidal structure, with the same dimensions, was processed to create 30 × 30 × 30 vector maps. Each vector was mapped to the nearest point on the respective structures and interpolated to ensure continuity. The method demonstrated a mean accuracy of 97% for the helix and 91.8% for the torus, as shown in Figs. 6(a) and 6(b).

Fig. 6.

3D Synthetic Torus Analysis Using 3D FFT. (a, b) Combined visualization showing the 3D structure of the helix and torus with detailed fiber orientation analysis using 3D FFT.

3.3. Performance of ML/DL models

In our study, we employed both SVR, CNN, ResNet50 with attention mechanism to analyze the orientation of collagen fibers in various tissue samples. To evaluate model robustness and stability, each model was trained and tested across five independent runs using different random seeds. All reported performance metrics in Table 1 reflect the mean ± standard deviation of these runs. In Table 1, SVR emerged as the most accurate Machine Learning model, achieving a nMAE of 5.5% on the mixed dataset, which corresponds to an average error of 10 degrees. This indicates that SVR can predict fiber orientation with a high degree of accuracy. However, its performance on the biological dataset was lower, with a nMAE of 13%.

Table 1. Performance comparison of different models used in our analysis across the mixed and biological datasets. The values represent the error rates (± standard deviation). SVR denotes Support Vector Regression, CNN represents Convolutional Neural Network, ResNet50 refers to Residual Neural Network, CBAM Attention CNN indicates the Convolutional Block Attention Module applied to CNN, and Channel Attention ResNet50 represents ResNet50 integrated with a channel attention mechanism.

Among the deep learning models, the CNN yielded a nMAE of 12 ± 3.7% on the mixed dataset, corresponding to an average error of approximately 21 degrees, and 23 ± 2% on the biological dataset, with potential for improvement through parameter tuning and augmentation. ResNet50 performed slightly better, achieving a nMAE of 11 ± 0.4% on the mixed dataset and 22 ± 1.1% on the biological dataset. Incorporating attention mechanisms further enhanced the models’ performance. The CBAM Attention CNN achieved a nMAE of 11 ± 0.6% on the mixed dataset and 18 ± 0.9% on the biological dataset, while the Channel Attention ResNet50 achieved the best performance among the deep learning models, with a nMAE of 5.8 ± 0.4% on the mixed dataset and 21 ± 1% on the biological dataset, highlighting the effectiveness of attention mechanisms in improving prediction accuracy. Compared to these, the SVR model demonstrated robust performance, achieving a nMAE of 5 ± 0.2% on the mixed dataset and 13 ± 0.7% on the biological dataset, making it the most accurate approach for further analysis.

As shown in Table 1, the standard deviations across five independent runs demonstrate clear differences in model stability. Models such as SVR (±0.2) and Channel Attention ResNet (±0.4) show relatively low variation, indicating high consistency across training instances. In contrast, the baseline CNN model exhibits a considerably higher standard deviation (±3.7 on the mixed dataset), which is over nine times larger than that of the SVR model and nearly double that of the ResNet variants. This suggests that the CNN model is more sensitive to initialization and training noise, leading to less reliable predictions under varying conditions. The attention-based models, particularly those incorporating channel-level mechanisms, consistently outperformed baseline CNNs not only in mean accuracy but also in robustness across runs.

3.4. Test of SVR model with real data

Finally, we validated the SVR method using two different datasets: synthetically generated data and bovine/porcine collagen data. To demonstrate the reliability of our model, we first analyzed synthetic collagen fiber structures generated by the diffusion model, using SVR to determine fiber orientations. Figures 7(a) and 7(d) depict the overall fiber structures, with red arrows indicating the orientations predicted by SVR. Detailed views in Figs. 7(b) and 7(e) focus on the specific fiber orientations within the yellow-highlighted areas of Figs. 7(a) and 7(d), respectively. The angle distribution histograms in Figs. 7(c) and 7(f) quantify the orientation angles of the fibers. In Fig. 7(c), the histogram reveals distinct peaks around 25° and 125°, indicating a strong preferential alignment of fibers at these angles in the synthetic model. This result suggests that the diffusion model effectively generates specific alignment patterns captured by SVR. Conversely, the histogram in Fig. 7(f) exhibits a more uniform distribution of fiber angles, reflecting the diverse and complex orientations in the synthetic dataset generated by the diffusion model. The circular structure of the image contributes to this uniform distribution of angles from 0° to 179°.

Fig. 7.

Visual representation and angle distribution of collagen fiber orientation. (a) and (d) show the collagen fiber structures obtained from the diffusion model. (b) and (e) are magnified views of the yellow highlighted areas in (a) and (d), respectively, providing a detailed view of fiber orientation within those regions. (c) and (f) are angle distribution histograms corresponding to the fiber structures shown in (a) and (d), respectively.

To further assess the accuracy of our models, we analyzed 2D collagen images from various sources. Figure 4 presents the results for nine images. The clinically approved bovine collagen sample displayed a predicted orientation marked by a red arrow, along with the corresponding angle distribution histogram.

Figure 4(j) illustrates a predominant orientation of approximately 120 degrees, with variations ranging between 100 and 140 degrees. The clinically approved porcine collagen sample shown in Fig. 4 h exhibited predicted orientations at 100 and 120 degrees, highlighted by the red arrow, while the angle distribution histogram in Fig. 4(k) displayed variations between 90 and 130 degrees. The biological porcine collagen sample presented in Fig. 4(i) showed a predominant orientation around 120 degrees, also indicated by the red arrow, with its angle distribution histogram in Fig. 4 l revealing variations between 100 and 140 degrees. These findings confirm the robustness and reliability of our models in accurately predicting collagen fiber orientations across different tissue types.

We extended our analysis to 3D collagen fiber orientation in porcine and bovine samples, leveraging advanced imaging and modeling techniques. Figure 8 presents the comprehensive results of this analysis. Figures 8(a) through 8c show 3D visualizations of collagen fiber orientations for clinically approved bovine, clinically approved porcine, and biological porcine samples, respectively. Figures 8(d) through 8f display the polar distribution visualizations obtained using SVR, while Figs. 8 g through 8i depict the results derived from FFT. For clinically approved bovine samples, the SVR results in Fig. 8(d) indicate predominant fiber orientations around 120 degrees along the xy-axis and 90 degrees along the xz-axis, whereas the FFT results in Fig. 8 g show predominant orientations at 130 degrees along the xy-axis and 90 degrees along the xz-axis. In clinically approved porcine samples, the SVR results in Fig. 8(e) reveal predominant fiber orientations at 120 and 130 degrees along the xy-axis and 90 degrees along the xz-axis, while the FFT results in Fig. 8 h confirm a predominant orientation at 120 degrees along the xy-axis and 90 degrees along the xz-axis. For biological porcine samples, the SVR results in Fig. 8(f) indicate predominant fiber orientations at 120 and 110 degrees, with some variation around 120 degrees along the xy-axis, and a consistent orientation around 90 degrees along the xz-axis. The FFT results in Fig. 8(i) similarly show predominant fiber orientations at 130 degrees along the xy-axis and 90 degrees along the xz-axis. These results demonstrate that our models effectively capture the complex 3D orientations of collagen fibers in porcine and bovine samples, showcasing their robustness and accuracy. This capability enhances our understanding of the structural organization in biological tissues, with significant implications for developmental biology and tissue engineering, where precise knowledge of fiber orientation is critical.

Fig. 8.

3D visualization and orientation analysis of fiber structures in clinically approved bovine, clinically approved porcine, and biological porcine tissues. a-c show 3D reconstructions of confocal microscopy slices, processed and visualized using Huygens, for clinically approved bovine (a), clinically approved porcine (b), and biological porcine (c) samples. d-f display the angular distribution of fiber orientations along the xy-axis (blue) and xz-axis (red), obtained through Fourier transform analysis in MATLAB. g-i provide the angular distribution of fiber orientations obtained from Support Vector Regression.

To further evaluate our approach, we applied it to predict the 3D collagen fiber orientation in early chick embryo heart samples as a challenging use case. Figure 9 provides the comprehensive results of this analysis. Figure 9(a) presents a 3D vector field visualization of collagen fibers in the chick embryo sample, with red arrows indicating the predicted orientations. Figure 9(b) shows a confocal microscopy image that details the structural organization of the collagen fibers throughout the ventricle. The polar distribution visualization in Fig. 9(c) indicates a predominant fiber orientation around 90 degrees. Figure 9(d) offers a volumetric rendering of the sample, highlighting the spatial distribution and organization of the collagen fibers. Additionally, a 3D vector field visualization in Fig. 9(e) illustrates regions with varied fiber orientations, which are confirmed by the corresponding confocal microscopy image in Fig. 9(f). The polar distribution visualization in Fig. 9 g reveals predominant orientations around 45 and 90 degrees for the region shown in Fig. 9(e) along the xy-axis, while the xz-axis consistently shows a predominant orientation at 90 degrees. These findings underscore our model’s effectiveness in capturing complex 3D fiber orientations, facilitating a deeper understanding of structural organization in biological tissues. This work has significant implications for developmental biology and tissue engineering, particularly in advancing our knowledge of collagen fiber arrangement and its functional roles.

Fig. 9.

Comprehensive analysis of 3D collagen fiber orientation in chick embryo heart samples using advanced imaging and modeling techniques. The first row focuses on the right ventricle (RV), showing a 3D rendering of the heart (first column), a high-resolution 2D confocal microscopy image of collagen fibers (second column), a 3D vector field visualization of fiber orientations (third column), and a polar distribution plot illustrating predominant fiber orientation around 90 degrees (fourth column). The second row provides similar analyses for the left ventricle (LV), with corresponding visualizations and orientation data.

4. Discussion

4.1. Synthetic data generation and utilization

Due to the inherent nature of biological data, which tend to have different fiber families concentrated at specific angles, model training naturally introduced biases, prioritizing these angles [46]. To address this issue, we generated synthetic data using a diffusion model and subsequently trained our models with this data. The synthetic dataset provided a controlled environment to ensure that the models were not biased towards a particular orientation. This was achieved by generating fibers at various angles. It was crucial to provide the diffusion models with accurate descriptions to obtain the required images. Therefore, the detailed description and quality of the dataset played a significant role in training robust models capable of generalizing to real-world application.

4.2. Feature extraction approaches

Models trained with features extracted from images using HOG are significantly affected by the grid size [47]. The grid size determines the structure of the feature map by affecting the granularity and scale of the captured features. A finer grid size results in more detailed feature extraction by capturing subtle variations in the image, which can be crucial for accurately modelling complex patterns such as collagen fiber orientations. Conversely, a coarser grid size can miss these details but reduces computational complexity and noise. Therefore, choosing the appropriate grid size is crucial and needs to be tailored the images being analyzed, with this study utilizing a grid size of 32 × 32. Moreover, the HOG parameters should be adapted to the specific characteristics of the dataset, such as the image resolution and the scale of the analyzed structures. This adaptability contributes to the overall effectiveness of the model by ensuring that the extracted features are both relevant and robust.

4.3. Comparative model performance

In this study, we employed both ML and DL techniques, including SVR, CNN, ResNet50, and attention-based DL models. Among these approaches, SVR demonstrated the most effective performance, excelling in terms of accuracy and computational efficiency. Its success can be attributed to its ability to handle high-dimensional feature spaces effectively while avoiding overfitting, particularly when applied to well-structured synthetic datasets. While DL models such as CNN and ResNet50 achieved competitive results, they did not surpass the performance of SVR in this context. This highlights that simpler, more interpretable machine learning techniques can sometimes outperform complex DL models for tasks where the feature space is well understood and relatively structured, such as fiber orientation analysis.

The DL models showed significant potential due to their advanced feature extraction capabilities but required extensive tuning, larger datasets, and advanced techniques like data augmentation and transfer learning to realize their full potential. The inclusion of attention mechanisms, for example, enhanced their performance, demonstrating the importance of architectural advancements in improving accuracy. However, the superior efficiency and robustness of SVR underline the critical need for algorithm selection based on the nature of the data and the specific requirements of the task.

Additionally, a comparison with FFT, used as a benchmark method, revealed notable advantages of SVR. While FFT is a reliable and well-established approach for analyzing frequency and orientation, it requires multiple preprocessing and post-processing steps for accurate results. In contrast, SVR simplifies the workflow by eliminating the need for these additional steps while achieving faster processing times. This efficiency, coupled with its strong performance, makes SVR a practical choice for applications involving large datasets and real-time analysis. These findings reinforce the importance of balancing model complexity, performance, and interpretability in the development of biomedical image analysis tools and other computational methods.

Furthermore, the broader angular distribution observed in SVR predictions can be attributed to the inclusion of all image patches, including structurally ambiguous or noisy regions. In contrast, the FFT method filters out spectrally incoherent vectors, resulting in narrower but less inclusive distributions. This distinction highlights a key trade-off between robustness and selectivity in the context of fiber orientation mapping.

In light of these findings, the observed advantage of SVR in our study reflects the effectiveness of classical machine learning models when applied to structured feature spaces and limited data scenarios. The use of hand-engineered HOG features allowed SVR to efficiently capture fiber orientation patterns without requiring large-scale data or complex architectures. However, this should not be interpreted as an inherent limitation of deep learning. Given access to larger and more diverse biological datasets, advanced DL architectures such as transformer-based encoders or deeper attention modules are expected to surpass SVR by leveraging their ability to learn high-level spatial representations and contextual information. Additionally, while our DL architectures were intentionally kept lightweight to mitigate overfitting, more expressive designs could improve performance provided by sufficient training data. Hyperparameter exploration in our study focused on standard components (e.g., learning rate, dropout), but further tuning of attention-specific parameters such as the channel reduction ratio, kernel size, and the number of attention heads may unlock additional performance gains. As such, model selection should remain data-driven and application-specific, with future work exploring how data-efficient deep learning methods can bridge this gap in biomedical imaging tasks.

4.4. Fiber orientation across porcine tissues

The ANOVA results indicated no statistically significant differences in the dominant fiber orientations among clinically approved bovine, clinically approved porcine, and biological porcine tissues in FFT analyses. This finding suggests that these tissue types share a similar primary fiber alignment. Given this similarity, clinically approved bovine and porcine tissues may be considered interchangeable in applications where fiber orientation is a key structural parameter. However, this does not imply complete clinical equivalence. Fiber orientation is only one of many factors that determine tissue suitability. Mechanical properties such as elasticity, anisotropy, fatigue resistance, and compliance must also be thoroughly evaluated to assess clinical applicability and long-term performance.

In tissue engineering and cardiovascular repair, this consistency in fiber alignment supports the use of porcine pericardium as a scaffold or decellularized matrix, offering both scalability and practicality. When biological porcine tissue is not readily available, clinically approved bovine or porcine alternatives may serve as viable substitutes, assuming their mechanical profiles align with clinical requirements.

Additionally, 3D FFT analyses helped reveal the broader architectural organization of these tissues, confirming that the primary fiber alignment remains unchanged regardless of tissue type. This structural consistency could be valuable for designing engineered constructs that replicate the mechanical properties of native tissues. From a clinical perspective, understanding fiber orientation is essential for optimizing surgical patch designs and improving tissue-engineered heart valves. The ML/DL-based approach presented in this study provides a more refined method for analyzing fiber alignment, which could aid in the development of personalized cardiovascular implants and regenerative therapies. Furthermore, high-resolution fiber mapping may enhance computational models used in surgical planning and disease diagnostics, particularly in conditions affecting collagen organization.

5. Conclusion

This study compared the effectiveness of traditional FFT with advanced ML and DL models for analyzing collagen fiber orientations in various tissue samples. The findings emphasized the strengths and limitations of each approach, demonstrating the advantages of ML and DL models over the traditional FFT method in handling complex scenarios. While FFT remains effective for basic 2D and 3D fiber orientation analyses, it encounters challenges in processing noise and structural variations present in complex tissue architectures. Although FFT performed well in synthetic and biological datasets, its applicability diminishes as tissue complexity increases due to its reliance on extensive preprocessing and assumptions about uniformity.

In contrast, ML and DL models, including SVR, CNN, ResNet50, and attention-enhanced architectures, exhibited superior robustness and accuracy in analyzing intricate fiber patterns. These models excelled in their ability to learn from diverse datasets, adapting to variations in tissue structures and reducing the impact of noise. Among them, SVR consistently provided precise and interpretable results, highlighting its efficiency in characterizing fiber orientations. DL models further demonstrated their potential for deeper tissue analysis, especially with advanced techniques like transfer learning and attention mechanisms, which improve performance in challenging cases.

In conclusion, while FFT serves as a reliable tool for basic analyses, ML and DL models significantly advance the field by offering improved accuracy, automation, and adaptability to complex biological structures. These methods deepen our understanding of tissue architecture and hold promise for applications in biomedical research, tissue engineering, and computational modeling. Future efforts should focus on refining these models further, exploring novel architectures, and extending their use to other intricate biological systems.

6. Future work

This study lays the groundwork for data-driven 3D fiber orientation analysis, but several exciting directions remain to be explored. On the methodological side, more advanced architectures such as transformer-based models [48] or lightweight attention networks [49] could further improve accuracy and robustness, particularly in noisy or low-resolution biological data. In parallel, expanding the approach to unsupervised or self-supervised learning could reduce the dependency on labeled training data, which is often scarce in biomedical imaging. From an application perspective, the current pipeline can be adapted for clinical and bioengineering use cases such as surgical patch design, valve scaffold engineering, or fibrosis monitoring. Mapping fiber orientation in tissues affected by disease or mechanical stress can provide meaningful insight into remodeling processes. One promising direction is the development of a real-time analysis framework that can be integrated directly with confocal or SHG imaging systems. Optimizing the model for faster inference and deploying it on edge devices would make it feasible to use during surgeries or intraoperative planning. Furthermore, the modular design and rapid inference capabilities of the present model make it highly suitable for high-throughput implementation in large-scale tissue engineering and clinical screening workflows. Lastly, a longer-term goal is to track changes in fiber orientation over time, allowing for longitudinal studies of tissue remodeling or implant integration. Tracking changes in fiber architecture across different time points or treatment conditions can support the development of predictive models of tissue behavior. In turn, this brings AI closer to real-time, in vivo applications in biomedical research.

Funding

The Scientific and Technological Research Council of Türkiye 10.13039/501100004410 (TUBITAK) (grants 2247A, 2211A); HORIZON EUROPE European Innovation Council 10.13039/100018703 (EIC) Transition project HeartWise ( 101214454).

Disclosures

The authors declare no conflicts of interest.

Data availability

The datasets supporting the findings of this study are publicly available at [50]. The repository contains both synthetic and biological confocal microscopy data. Specifically, the biological dataset includes:

• •Biological Porcine: 12 different patch images, with one including 3D slice scans.
• •Chick Embryo: Heart slice scans in 2D.
• •Clinically Approved Bovine: Nine patches, with three 3D slice scans.
• •Clinically Approved Porcine: Seven patches, with four having 3D slice scans.

All raw and preprocessed data used in training, testing, and benchmarking are available alongside code for loading, visualization, and reproduction of the main results. No access restrictions apply.

The code used in this study is publicly available at [51]. This repository contains all necessary scripts, model implementations, and dataset processing pipelines used for fiber orientation mapping.

Supplemental document

See Supplement 1 ^{(3.3MB, pdf)} for supporting content.