Method for automatic quantification of vasodilation in patients undergoing flow-mediated dilation (FMD) examination

Description

1 / 17 METHOD FOR AUTOMATIC QUANTIFICATION OF VASODILATION IN PATIENTS UNDERGOING FLOW-MEDIATED DILATION (FMD) EXAMINATION FIELD OF THE INVENTION [1] The present invention falls within the technical field of artificial intelligence applied to the analysis of medical examinations, more specifically in the processing of ultrasound images for the evaluation of flow-mediated dilation (FMD). [2] In this sense, the image processing method of the present invention has clinical and research applications, and can be used in hospitals, laboratories and specialized centers to automate and optimize the analysis of ultrasound examinations of the brachial artery, reducing dependence on manual interpretation and improving the reproducibility of diagnoses. In addition, the method can be adapted for other image-based medical analyses, such as the evaluation of carotid artery intima-media thickness in vascular ultrasound examinations. FUNDAMENTALS OF THE INVENTION [3] Flow-mediated dilation (FMD) is a medical procedure used to assess endothelial function. The endothelium acts as an interface between the blood and the vascular wall, through endothelial cells (ECs). The study by Furchgott and Zawadzki (1980, doi: 10.1038 / 288373a0) proposed that the function of ECs was to release a substance responsible for the dilation of blood vessels; this substance was later identified by the authors as nitric oxide (NO). This discovery allowed the creation of new medications for the treatment of cardiovascular diseases (CVDs). [4] The FMD technique was introduced in a clinical trial by Celermajer et al. (1992, doi: 10.1016 / 0140- 6736(92)93147-f) and has been applied as a marker of Petition 870250012127, dated 02 / 14 / 2025, p. 8 / 37 2 / 17 Vascular health. The authors presented evidence that their FMD technique was NO-dependent, therefore there was an adaptation of the internal diameter of the arteries in response to changes in blood flow. By quantifying the variation in artery diameter, it is possible to assess the health of the vascular response, something that is not possible in currently available routine examinations. Low vasodilation capacity indicates the presence of CVDs in their early stages. [5] CVDs are the leading cause of death worldwide, responsible for the loss of 17.9 million lives every year. CVD consists of a group of disorders related to the heart and blood vessels. In addition, more than four out of five CVD deaths occur due to heart attacks and strokes, and one third of these deaths occur prematurely in people under 70 years of age (WHO, 2013, ISBN: 978-92-4-150623-6). [6] FMD consists more precisely of using ultrasound images to identify patients at high risk of atherosclerosis before clinical evidence of any vascular disease. During the test, the brachial artery is identified by the ultrasound device for computational analysis (THIJSSEN et al., 2011, doi: 10.1152 / ajpheart.00471.2010). [7] The target of ultrasound analysis is the lumen diameter in response to increased blood flow during reactive hyperemia, induced by inflation and then deflation of a cuff. This diameter measurement occurs during three conditions: at rest (baseline), after inflation, and after deflation of the cuff. This process allows for increased shear stress along the blood vessel and promotes the release of NO. In healthy patients, greater dilation of the arteries is observed in response to increased blood flow in the arterial walls. Petition 870250012127, dated 02 / 14 / 2025, page 9 / 37 3 / 17 (RAITAKARI; CELERMAJER, 2000, doi:10.1046 / j.13652125.2000.00277.x). [8] Patient preparation is an important step to ensure the reproducibility of the FMD method. Several factors can influence artery measurements, such as diet, alcohol use, smoking, drugs, and physical activity. To minimize these effects, it is highly recommended to follow certain guidelines. The test should be performed in a calm environment with controlled temperature for a period of 10 to 15 minutes (THIJSSEN et al., 2011, doi: 10.1152 / ajpheart.00471.2010 & THIJSSEN et al., 2019, doi: 10.1093 / eurheartj / ehz350). [9] Another important factor for measuring FMD is the cuff position. The study by Doshi et al. (2001, PMID: 11724650) identified that small changes in position can result in a different stimulus. Dilation was significantly greater after occlusion of the upper arm compared to occlusion of the wrist. Standardization of cuff position is crucial for comparison between studies.

[10] Initially, analyses of ultrasound images generated by the FMD technique were performed manually using visual inspection of the video frames. Four cardiac cycles were analyzed in the final period of diastole for each observer, the final measurements were constituted by the average of all observations. This method was highly operator-dependent and subject to significant error (CELERMAJER, et al. 1994, doi: 10.1016 / 07351097(94)90141-4).

[11] Subsequently, computerized analyses allowed the measurement of multiple points along the blood vessel. These methods consist of edge detection and wall-tracking software for artery segmentation. Studies comparing validity and reproducibility Petition 870250012127, dated 02 / 14 / 2025, page 10 / 37 4 / 17 of computerized systems showed smaller variations between observers than manual methods (PREIK, 2003, DOI: 10.1055 / s-2000-7989).

[12] However, despite being a consolidated method applied for over 20 years in human research, it still requires high technical skill from the observer and appropriate training time. There are many reasons that make the FMD technique attractive, such as the fact that it is non-invasive and provides a direct measurement of arterial function. However, different methodological approaches limit its validity, comparability, and potential use as a clinical tool (JARRETE; ZANESCO; DELBIN, 2016, doi: 10.1590 / S1980- 65742016000100001).

[13] Performing FMD consistently is a decisive factor in improving measurements in predicting future clinical risks and in its use as a robust investigative tool. This approach not only reinforces the scientific basis of FMD, but also highlights the need for continuous refinement in its methodology. Addressing unresolved challenges in FMD practice is fundamental to advancing its usefulness as a widely adopted measurement technique in research and clinical practice (JARRETE; ZANESCO; DELBIN, 2016, doi: 10.1590 / S1980-65742016000100001 & THIJSSEN et al., 2019, doi: 10.1093 / eurheartj / ehz350).

[14] As an example, some state-of-the-art documents that address related methodologies will be presented below:

[15] The document “MNET-10: A ROBUST SHALLOW The study “CONVOLUTIONAL NEURAL NETWORK MODEL PERFORMING ABLATION STUDY ON MEDICAL IMAGES ASSESSING THE EFFECTIVENESS OF APPLYING OPTIMAL DATA AUGMENTATION TECHNIQUE” (2022, doi:10.3389 / fmed.2022.924979) reveals the challenges in interpreting medical images using systems of Petition 870250012127, dated 02 / 14 / 2025, page 11 / 37 5 / 17 Computer-aided diagnosis (CAD), including the complexity of cancerous lesions, the similarity between classes, variations within the same class, scarcity of medical data, and the presence of artifacts and noise. To overcome these difficulties, researchers developed a shallow convolutional neural network (CNN) model called MNet-10, optimally configured through an ablation study, altering the layer and hyperparameter structure. Thus, although the article describes a neural network for medical image classification based on convolutional layers and pooling, it does not consider the comparison between different images, as is done by the present invention. While in diagnoses such as melanoma and tumors a single image may be sufficient, in FMD examination it is necessary to analyze at least 12 minutes of video, where the artery's behavior varies over time.The present invention proposes a method that concatenates convolutional networks to compare features of different images in a unified model. Furthermore, unlike this article, the present invention solves the technical problem of analyzing the variation in arterial diameter throughout the examination by extracting features considering different time periods, organizing the learning process so that the comparison between images occurs before the extraction of individual features.

[16] The document TEMPORAL CONVOLUTIONAL NETWORKS: A UNIFIED APPROACH TO ACTION SEGMENTATION” (2016, doi:10.48550 / arXiv.1608.08242) reveals Temporal Convolutional Network (TCN) as a unified approach for action segmentation in video, capturing temporal relationships across multiple scales. TCN integrates feature extraction and quantification, enabling better capture of long-range spatial and temporal relationships. Petition 870250012127, dated 02 / 14 / 2025, page 12 / 37 6 / 17 The article describes performing image segmentation based on temporal characteristics, transforming video data into a two-dimensional representation and applying convolution and pooling to segment objects. Unlike the present invention, which quantifies the variation in diameter over time, TCN generates segmented images. In FMD examination, TCN could segment the artery, but would require processing 12 minutes of video (approximately 18,000 images) and applying another model to extract and classify the arterial diameter, resulting in high computational cost. Therefore, the present invention proposes a more efficient approach, using fewer image units, sufficient to accurately assess the artery's behavior, avoiding full video processing and the need for additional processing techniques.

[17] Document WO2023077239A1 discloses a method for training a neural network for segmenting a low-information image in order to identify a plurality of atherosclerotic plaque features in that image. The method involves receiving a plurality of image pairs, where each pair comprises a low-information image of a specific vasculature and a high-information image of the same vasculature. The images are then registered to map both onto the same coordinate system. The low-information image is segmented based on the regions identified in the high-information image, thus allowing the identification of atherosclerotic plaque features in the low-information image. Finally, the segmented image is compared to a reference pattern based on the high-information image to calculate a loss, which is backpropagated through the neural network to train it.Although neural networks share fundamental operations, a. Petition 870250012127, dated 02 / 14 / 2025, page 13 / 37 7 / 17 The present invention differs from the document in two main aspects: the extraction of features at different instants of the video, performed by a concatenation block, and the result produced, which in the claimed invention is the categorization of patients, while the document described here generates segmented images. The problem in WO2023077239A1 is the need to integrate other models to classify patients and the manual work required for segmentation of the artery images, which can generate inaccuracies. In this sense, the present invention overcomes these limitations by quantifying brachial artery vasodilation with fewer images, eliminating the processing of complete videos and additional techniques.

[18] Thus, it is clear that, although different proposals for the analysis of brachial artery ultrasound examinations have been discussed in the state of the art, none of them presents a unified approach capable of extracting characteristics at different moments of the examination and quantifying vasodilation without the need for manual segmentation or complete video processing. The present invention proposes a more efficient method, which reduces the dependence on manual analyses and optimizes the reproducibility of diagnoses, overcoming the limitations of the analyzed documents. BRIEF DESCRIPTION OF THE INVENTION

[19] The present invention relates to a method for automatic quantification of vasodilation in patients undergoing flow-mediated dilation (FMD) examination, comprising: (i) receiving a set of ultrasound images extracted from an FMD examination over time; (ii) converting the set of images to grayscale and applying normalization; (iii) processing the images using a convolutional neural network (CNN), applying operations of Petition 870250012127, dated 02 / 14 / 2025, p. 14 / 37 8 / 17 convolution to generate feature maps; (iv) calculate the dimension of the resulting feature map and apply a ReLU activation function; (v) reduce the dimensionality of the feature map using a Max-Pooling layer; (vi) determine the dimension of the feature map after pooling; (vii) convert the feature maps into a one-dimensional vector and send them through a fully connected layer; (viii) apply a softmax activation to quantify vasodilation in patients and concatenate the outputs of the different convolutional networks; (ix) pass the concatenation through a fully connected layer and perform backpropagation of the error separately for each processed image; and (x) determine the final activation to obtain the probability of quantifying vasodilation. BRIEF DESCRIPTION OF THE FIGURES

[20] Figure 1 illustrates the architecture of the convolutional neural network of the present invention.

[21] Figure 2 shows the training flow of the proposed architecture. In this process, the weights of the multiple neural networks are adjusted to minimize the final error, without the need to provide the features that should be extracted for each of the images.

[22] Figure 3 is a representation of the functioning of the neural network, according to an embodiment of the present invention.

[23] Figure 4 on the left shows the original image collected from the ultrasound examination and on the right the pre-processed image, extracting the region of interest by the concentration of white pixels in the image, according to an exemplary embodiment of the present invention.

[24] Figure 5 is a graph that presents the result of training and validation throughout the training of 400 Petition 870250012127, dated 02 / 14 / 2025, page 15 / 37 9 / 17 epochs of the neural network, according to an exemplary embodiment of the present invention.

[25] Figure 6 presents the confusion matrix of FMD quantification in all available brachial artery videos, according to an exemplary embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[26] In general, the present invention consists of a method based on temporal convolutional neural networks (TCNs) for the automatic quantification of vasodilation in patients undergoing FMD examinations. Unlike traditional methods that rely on artery segmentation, the proposed approach uses multiple convolutional neural networks (CNNs) to extract spatial features from ultrasound images and then employs a sequential neural network to capture temporal relationships between different frames of the examination.

[27] The model architecture is designed to directly process FMD examination videos, eliminating the need for conventional edge tracking and arterial diameter measurement techniques. The model output consists of a percentage quantification. The response can be a positive, negative, or zero percentage change, i.e., there may be dilation, paradoxical vasoconstriction, or no response.

[28] More specifically, the proposed neural network initially receives an input image represented by Xe / ? / / .ru.ví; , where X represents the values ​​of the input image, W is the width, H the height, and C the number of color channels of that image. Furthermore, these values ​​of X are limited to the set of real values ​​(R). Then, convolution operations are applied to the image to generate a feature map, which can be represented by the Equation Petition 870250012127, dated 02 / 14 / 2025, page 16 / 37 10 / 17 (eq.1). ^i,j,k Σμ=1Ση=1Σε=1Wm,n,c,kXi+m-1,j+n-1,c +bk(eq.1)where Zijk is the resulting output at position (i,j) of the feature map 'k', Wm,n,c,k is the convolutional filter of size FHxFwxC, which operates on small image windows, Xi+m-1j+n-1,c is the input pixel value at position (i + m — 1,j + n — 1) in the c channel of the image and bk is the bias for the feature map k.

[29] Based on the adjustment of the convolutional filter and bias values, the network performs the adjustment of the prediction results. This convolution operation traverses the entire image and generates a feature map ZE rh'xW'xK, where Z are the network output values, K is the number of filters, and H'xW are the resulting height and width of the image after the operation, obtained by Equation (eq.2). In this equation, F represents the size of the filters (kernel) applied to the image. Generally, these are values ​​such as 3x3, 5x5, etc., indicating the height and width of the filter used in the convolution. S is the convolution step (stride), which is the number of pixels the filter moves horizontally and vertically at each step during the image convolution. If the stride is 1, the filter moves one pixel at a time; if it is 2, it moves two pixels at a time, and so on.

[30] After + 1,W = the convolution, W — FwS (eq.2) an activation function is applied to add nonlinearity to the network to allow the extraction of complex features. This feature map AE RH xW xK is given by Equation (eq.3), where A represents the output values ​​after applying the activation function: Petition 870250012127, dated 02 / 14 / 2025, page 17 / 37 11 / 17 ^i,j,k,t = ReLUÍZij^t) ​​= max(0,ZiJ^t) (eq.3)

[31] The pooling layer is then used to reduce the spatial dimensionality of the feature maps and is applied after the convolutions. The max pooling operation (dimensionality reduction) takes the maximum value in local regions of the image, with the pooling window being P x P, the pooling operation is described by Equation (eq.4). Pi,j,k>t =maXm,nEPxP^i+m-1 ,j+n-1 ,k )

[32] This operation results in a feature map given by PE rhxWxKxT, where P are the output values ​​of the Pooling layer, the dimensions of the images are then adjusted. H'' x W'' which represent the new dimensions are given by Equation (eq.5). ,,H' w W' H = peW =v(eq.5)

[33] After the convolutional and pooling layers, the feature maps are flattened into a one-dimensional vector and passed to a fully connected layer, this flattening (flatten(P)) consists of transforming a matrix into a vector. If PE rhxWxK, then the fully connected layer is described by Equation (eq.6). zFC = WFCflatten(P) + bFC (eq.6) where WFC is a weight matrix with dimensions Nx(H''W''K), where N is the number of neurons in the fully connected layer multiplied by the resulting dimensions of the previous pooling layer and bFC is the bias represented by bFCERN. The resulting output of the fully connected layer will then be zFCE RN. Finally, a final activation is applied to extract different classes from each image, described in Equation (eq.7). Petition 870250012127, dated 02 / 14 / 2025, page 18 / 37 12 / 17 eZFC / / = / ^ for each j = 1, 2, 3..., N (eq.7) where yj is the probability of each class j, the output of this activation can be expressed by yE RN. The Euler constant is represented by the letter “ee zFC represents the output of the fully connected layer. Figure 1 shows the layers and hyperparameters used to construct the neural network.

[34] The next step is the concatenation operation of the neural network outputs, represented by the term concat. Let y E Rn be the output vector of each convolutional network; to concatenate this information, a vector with dimensions of N x T is created, where N is the number of classes predicted for each image and T is the number of images evaluated for each video. Finally, this one-dimensional N x T vector is filled with the outputs of all t convolutional networks as described in Equation (eq.8). H = cancat(yi,y2,...,yT) E RNxT(eq.8)

[35] After concatenating the outputs of the different images, the resulting vector is passed to the next layer of the network. The next fully connected layer is described by Equation 9. ZFCWnll + bFC(eq.9) where: WFCE RWxT is the weight matrix of the fully connected layer; hFC E RN is the bias associated with the fully connected layer; and zFCE Rné is the resulting vector for the next layer.

[36] The concatenation of neurons does not directly alter the backpropagation process, but the Petition 870250012127, dated 02 / 14 / 2025, page 19 / 37 13 / 17 gradients need to be calculated separately for each concatenated part, as shown in Equation (eq.10). dL _ [dL dL — — — . — H Ltfi H2 dLA (eq.10) L (Loss): Represents the loss function used to train the neural network. It can be, for example, the cross-entropy for classification or the mean squared error for regression. H (Concatenated activations): Represents the activation vector resulting from the concatenation of different parts. T (Number of concatenated components): Represents the number of concatenated subsets to form H.

[37] With this, each image will receive a different gradient value, allowing each convolutional network to update independently. The main objective of the proposed network is to quantify the patient's vasodilation between 0 and 1. To make quantification possible, a 2-neuron output layer was used, followed by a softmax activation. This activation function modifies the output values ​​so that the sum of all neurons in this layer equals 1. In this way, each neuron represents a normalized quantification of vasodilation. Equation (eq.11) shows how the activation function z FC\eZia — σ(ζ^^)ί — -^--Zj (eq.11)Σί=1e is calculated.

[38] The term a_i represents the probability associated with class i. The function σ indicates that the softmax is being applied to the zFC logit vector, which contains the activations of the last fully connected layer before the output. The numerator quantifies the relevance of neuron i to one of the groups of Petition 870250012127, dated 02 / 14 / 2025, page 20 / 37 14 / 17 patients, while the denominator normalizes the values, ensuring that the sum of the probabilities equals 1. Thus, instead of simply classifying, this probability can be used to quantify the uncertainty or intensity of a patient's association with different groups.

[39] Figure 2 shows the layers used to construct the MultiConvNet architecture. MultiConvNet is a neural network that uses multiple CNNs to extract and combine different image features. The term Multi highlights the use of multiple convolutional networks, Conv refers to convolutions, which are essential for image processing, and Net indicates that it is a neural network. The ConvNet blocks shown are equivalent to the architecture shown in Figure 1. The output of each ConvNet is a layer of 64 neurons that will be concatenated to form a layer of 320 neurons for training and validating the network.

[40] In this sense, the method for automatic quantification of vasodilation in patients undergoing flow-mediated dilation (FMD) examination comprises: (i) receive a set of ultrasound images extracted from an FMD examination over time; (ii) convert the set of images to grayscale and apply normalization; (iii) process the images using a convolutional neural network (CNN), applying convolutional operations to generate feature maps; (iv) calculate the dimension of the resulting feature map and apply a ReLU activation function; (v) reduce the dimensionality of the feature map by means of a Max-Pooling layer; (vi) determine the dimension of the feature map after pooling; (vii) convert the feature maps into a vector Petition 870250012127, dated 02 / 14 / 2025, page 21 / 37 15 / 17 one-dimensional and send them through a fully connected layer; (viii) apply a softmax activation to quantify vasodilation in patients and concatenate the outputs of the different convolutional networks; (ix) pass the concatenation through a fully connected layer and perform backpropagation of the error separately for each processed image; and (x) determine the final activation to obtain the probability of quantifying vasodilation. EXAMPLE OF IMPLEMENTATION

[41] The implementation of the proposed method for the automatic analysis of flow-mediated dilation (FMD) examinations was based on the use of convolutional neural networks and temporal convolutional neural networks (TCNs). Initially, 186 ultrasound examinations were collected, each approximately 12 minutes long and recorded at 25 frames per second. In the example, the examinations were separated into two categories, distinguishing between those that presented reduced levels or paradoxical vasoconstriction in arterial dilation and those that remained within normal parameters. To ensure balanced model training, the database was divided equally, with 93 samples in each category.

[42] Image preprocessing was performed to isolate the region of interest, corresponding to the brachial artery, using Gaussian pixel intensity distribution analysis to define an appropriate segmentation boundary. After this step, five images spaced throughout the examination were extracted to be used in model training. The dataset was then divided into 80% for training, totaling 148 samples, and 20% for validation, with 38 examinations.

[43] The architecture developed for quantifying vasodilation in patients, as presented in Petition 870250012127, dated 02 / 14 / 2025, page 22 / 37 16 / 17 Figure 2 shows a modification of traditional convolutional neural networks, incorporating TCN models to capture the temporal evolution of arterial dilation throughout the examination. Each extracted frame was individually processed by a CNN, which received images resized to 32x32 pixels and converted to grayscale. The first convolutional layer used 3x3 and 32-channel filters, generating a 30x30 pixel output. Then, a MaxPooling layer reduced the resolution to 15x15 pixels. This convolution and pooling process was repeated once more, reducing the image dimension to 6x6 pixels. To avoid overfitting and improve generalization, dropout layers were applied before converting the resulting matrix into a fully connected layer with 2304 neurons. Subsequently, this layer was reduced to 128 neurons and, finally, to 64 neurons representing the spatial features extracted from each image.

[44] In the temporal modeling stage, the CNN output vectors were concatenated into a single linear layer of 320 neurons, allowing the combination of spatial information from the different images throughout the examination. This layer was processed by a new hidden layer of 128 neurons, followed by another dropout stage for regularization. The last layer contained two output neurons, corresponding to the patient classes, where each neuron represented the confidence level of the vasodilation quantification. Softmax activation was applied to ensure that the sum of the probabilities of the classes was equal to 1, allowing the model to select the most probable category based on the learned patterns.

[45] Figure 4 on the left shows the original image collected from the ultrasound examination and on the right the pre-processed image, extracting the region of interest by Petition 870250012127, dated 02 / 14 / 2025, page 23 / 37 17 / 17 concentration of white pixels in the image.

[46] To optimize model training, Stochastic Gradient Descent was used with a learning rate of 0.06 and a cross-entropy-based loss function. The model was trained for a total of 400 epochs, continuously adjusting the network weights to minimize loss and improve the accuracy of vasodilation quantification.

[47] As can be seen in Figure 5, the results of training and validation over 400 epochs demonstrated a high effectiveness of the model in quantifying vasodilation in FMD examinations. The best performance was recorded in epoch 397, with an accuracy of 97.37% in the validation set and a loss function equal to 0.1967. The confusion matrix analysis over the 186 available examinations indicated an overall accuracy of 95.16%, as can be seen in Figure 6, validating the model's ability to correctly distinguish cases of excessive arterial dilation from those with normal responses. Furthermore, the implementation of the architecture demonstrated a low computational cost, allowing complete training in a reduced time and without the need for specialized GPUs.

[48] ​​The application of the proposed method represents a significant advance in the automation of FMD examination analysis, eliminating the need for manual segmentation of the artery and reducing dependence on observer skill, allowing for faster and more accurate analysis, facilitating the adoption of the technique in clinical settings and expanding its potential for applications in medical research. Furthermore, the approach can be adapted for other vascular ultrasound assessments, such as carotid artery analysis, contributing to the improvement of diagnostic methods for cardiovascular diseases. Petition 870250012127, dated 02 / 14 / 2025, page 24 / 37

Claims

1 / 4 CLAIMS 1. A method for automatic quantification of vasodilation in patients undergoing flow-mediated dilation (FMD) examination, characterized by comprising the following steps: (i) receiving a set of ultrasound images extracted from an FMD examination over time; (ii) converting the image set to grayscale and applying normalization; (iii) processing the images using a convolutional neural network (CNN), applying convolution operations to generate feature maps; (iv) calculating the dimension of the resulting feature map and applying a ReLU activation function; (v) reducing the dimensionality of the feature map using a Max-Pooling layer; (vi) determining the dimension of the feature map after pooling; (vii) converting the feature maps into a one-dimensional vector and sending them through a fully connected layer;(viii) apply a softmax activation to quantify vasodilation in patients and concatenate the outputs of the different convolutional networks; (ix) pass the concatenation through a fully connected layer and perform backpropagation of the error separately for each processed image; and (x) determine the final activation to obtain the probability of quantifying vasodilation.

2. Method, according to claim 1, characterized in that the convolution operations are represented by: Zi,;,k = Σμ=1 Ση=1 Σϋ=1 ^m,n,c,k^i+m-1,j+n-1,c + &k (eq.1), where Zij,k is the resulting output at position (i,j) of the feature map 'k', Wm,n,c,k is the convolutional filter of size FHxFwxC, which operates on small windows of the images, Xi+m-1,j+n-1,c is the value of the input pixel at position (i + m — 1,j + n — 1) in the c channel of the image and bk is the bias for the feature map k.

3. Method, according to claim 1, characterized in that the calculation of the dimension of the resulting feature map is given by H' and W', where: H' = £-^+1,^-=^-^+1, (eq.2) where the convolution operation traverses the entire image and generates a feature map ZE rh'xW'xK, where Z are the output values ​​of the network, K is the number of filters and H! x W' are the resulting height and width of the image after the operation; in equation 2 F represents the size of the filters (kernel) applied to the image and S is the step (stride) of the convolution.

4. Method, according to claim 1, characterized in that the activation function ReLU generates a feature map AE rH xW xK given by: Aw = ReLU(ZiJ,kit) = max(0, ZlJik,t) (eq.3) where A represents the output values ​​after applying the activation function.

5. Method, according to claim 1, characterized in that the dimensionality reduction of the feature map by means of a Max-Pooling layer is given by: Pi,j,k,t maxm,nePxP^í+m-1,j+n-1,fc (eq.4) this operation results in a feature map given by PE rhxWxKxT, where P are the output values ​​of the Pooling layer, the dimensions of the images are then adjusted.

6. Method according to claim 1, characterized in that the height and width of the feature map are given by: H' ίλτΙΙ Wf H = — and W = — (eq.5). Petition 870250012127, dated 14 / 02 / 2025, p. 26 / 37 3 / 4 7. Method, according to claim 1, characterized in that the conversion of feature maps into a dimensional vector is given by the function: zFC = WFC flatten(P) + bFC (eq.6), where WFC is a weight matrix given by WFC E rNxHwk and bFC is the bias represented by bFC ERN and the resulting output of the fully connected layer is zFC.

8. Method, according to claim 1, characterized by the softmax activation function for quantifying vasodilation in patients comprising: ezFC tí=.^X for each j = 1, 2, 3..., N (eq.7), where yj is the probability of each class j, the output of this activation can be expressed by y E RN, the Euler constant is represented by the letter “ee zFC represents the output of the fully connected layer.

9. Method, according to claim 1, characterized in that the concatenation (H) of the outputs of the softmax activation function is given by: H = concat(y1,y2,...,yT) E RNxT (eq.8) where y E RN is the output vector of each convolutional network, N is the number of classes predicted for each image and T the number of images evaluated for each video, and the one-dimensional vector N x T is filled with the outputs of all t convolutional networks.

10. Method, according to claim 1, characterized in that the concatenation by a fully connected layer is given by the function: ZFC = WFCH + bFC (eq.9) where: WFC e rNxt is the weight matrix of the fully connected layer; Petition 870250012127, dated 14 / 02 / 2025, p. 27 / 37 4 / 4 hFC g rN is the bias associated with the fully connected layer; and ZFC g rN is the resulting vector for the next layer.

11. Method, according to claim 1, characterized by performing error backpropagation separately for each processed image being given by the gradient of the function (L): dL FôL dL dLl where LHi H2 HT. (eq.10) L (Loss) represents the loss function used to train the neural network, H (concatenated activations) represents the activation vector resulting from the concatenation of different parts and T (number of concatenated components) represents the number of concatenated subsets to form H.

12. Method, according to claim 1, characterized in that the determination of the final activation to obtain the probability of quantifying vasodilation is given by the function: σ(ζρε)ί ezi (eq.11) ^ / =1 ° where a_i represents the probability associated with class i, the function σ indicates that the softmax is being applied to the logit vector Z^, the numerator quantifies the relevance of neuron i to one of the patient groups, while the denominator normalizes the values, ensuring that the sum of the probabilities equals 1. Petition 870250012127, dated 14 / 02 / 2025, p. 28 / 37

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