The confluence of advances in compute and deep model architectures Rumelhart et al. (1986); He et al. (2016); Chollet (2017); Krizhevsky et al. (2012); Simonyan and Zisserman (2014) has offset a stream of research in automated medical image analysis in the recent past Shen et al. (2017). Bioimaging techniques such as Computed Tomography (CT), Magnetic Resonance Imaging (MRI), Functional Magnetic Resonance Imaging (fMRI), Positron Emission Tomography (PET), Mammography, Ultrasound, and X-ray have been predominately interpreted by radiologists and physicians for timely detection, diagnosis, and treatment of diseases Litjens et al. (2017). However, the healthcare industry is an ever-changing field that requires extensive training as there exist wide variations to pathologies that keep evolving. Due to the high demand for skilled labor, human experts potentially experience fatigue which necessitates computer-aided diagnostic tools. Thus, the maturation of deep learning is accelerating the intervention of computer-assisted tools for human experts, doctors, and researchers to reduce the labor-intensive and time-consuming work of manual medical image analysis.
Deep learning is poised to dramatically democratize healthcare, especially in the Global South where expertise in medical image analysis remains inadequate and prohibitively expensive Murtaza et al. (2020). But the success or failure of adopting and using these systems in clinical settings profoundly hinges on the assured trust of stakeholders in the robustness and interpretability of inference mechanisms of these deep models that are crucial in safety-critical sectors like healthcare Reyes et al. (2020).
Despite the inherent complexity of deep learning models, we present in this work a roadmap toward understanding the inference mechanisms that lead to predictions using adaptive path-based integrated gradient techniques. We have systematically studied and experimented with a class of these techniques using standard state-of-the-art convolutional neural network (CNN) architectures to classify brain tumors from MRI with regions of interest segmented and verified by medical experts. These attribution techniques give information about salient features in the input that corresponds to a specific predicted class. They can improve model understanding, build trust, and lead to system verification by clinical experts to adopt deep learning-based computer-aided diagnostic tools.
The remaining outline of this paper is as follows: Section 2 discusses related interpretability approaches in deep learning-based medical image analysis. Section 3 describes the adopted methodology and the proposed approach. Section 4 discusses the dataset and explains the experimental results, and Section 5 concludes the work and present future research directions.
2 Related Literature
Varied interpretability methods have been recently proposed for medical image analysis tasks. Research in this direction is growing primarily to help build trustworthy artificial intelligence (AI) systems that use a human-in-the-loop approach to complement domain experts. Concept Learning techniques have been used inKoh et al. (2020); Sabour et al. (2017); Shen et al. (2019) to manipulate high-level concepts to train models that can perform multi-stage predictions from high-level clinical concepts which provide input to the final classification task of disease categories. However, these methods have a significant annotation costs, and concept-to-task mismatches can lead to considerable information leakage Salahuddin et al. (2022).
Another class of technique is Case-Based Models, where class discriminative disentangled representations and feature mappings are learned, and the final classification is performed by measuring the similarity between the input image and the base templates Bass et al. (2020); Kim et al. (2021); Li et al. (2018). But this class of techniques is not susceptible to corruption by noise and compression artifacts. It is also difficult to train models using this paradigm. Counter Factual Explanation is another approach where input medical images are perturbed in pseudo-realistic ways to generate an opposite prediction. They have the problem of generating unrealistic perturbations with respect to the input images which can often be low resolutions as opposed to the original images Baumgartner et al. (2018); Cohen et al. (2021); Lenis et al. (2020); Schutte et al. (2021); Seah et al. (2019); Selvaraju et al. (2017); Simonyan et al. (2013); Singla et al. (2021). Visualization of the internal network representation of learned features of kernels in CNNs is another technique that is used in model understanding. But this approach has a limitation of difficulty in interpreting feature maps in medical image analysis settings Bau et al. (2017); Natekar et al. (2020).
An attribution map provides a post-hoc explanations whereby regions of the input image are highlighted as indicated saliency method based on the model prediction. In their paper, Böhle et al. (2019) proposed Layer-wise relevance propagation for explaining deep neural network decisions in MRI-based Alzheimer’s disease classification. A deep CNN-based model with Gradient Class Activation Map (Grad-CAM) was trained to classify oral lesions for clinical oral photographic images Camalan et al. (2021). In Kermany et al. (2018), a similar CNN-based Grad-CAM technique for the classification of Oral Dysplasia is proposed. However, our approach is different from Böhle et al. (2019); Camalan et al. (2021); Kermany et al. (2018) as we utilize adaptive path-based integrated gradients techniques to address the problem of noisy saliency masks which hinders former methods Kapishnikov et al. (2021).
3 Proposed Method
We present the CNN models utilized to carry out experiments in this study for the classification task. Characterizations of these CNN architectures are presented, indicating their inductive prior, strengths, and limitations in learning visual representations. We give a detailed description of the adaptive path-based integrated gradients techniques and their direct applications to deep learning-based models in medical image analysis. To achieve this, we have summarized the mathematical notation convention in Table 1 used in this work.
|Set of real numbers|
-dimensional real-valued vector
|Set of real-valued matrix|
real-valued tensor which is a single channel image input to a neural network
A corresponding one-hot encoded label for an image input
|Cardinality of the set of medical image classes.|
|The kernels for the -th layer of a CNN|
Non-linear transformation of inputat layer given a parameter
|Activation function at layer|
Non-negative real-valued regularization hyperparameter
|The squared norm|
|and||A training and testing samples of task respectively. is sampled from the distribution of task|
|A neural network that produces latent representation for each input|
|An attribution operator that takes a trained model to produce a saliency map|
|Computed saliency map for a given input image|
We have utilized 8 standard CNN architectures: Visual Geometric Group (VGG 16 and VGG 19 Simonyan and Zisserman (2014)), Deep Residual Network-50 (ResNet-50, ResNet-50V2) He et al. (2016), Densely Connected Convolutional Networks Huang et al. (2017), Deep Learning with Depthwise Separable Convolutions (Xception) Chollet (2017)), Going deeper with convolutions (Inception)Szegedy et al. (2015), and Efficientnet: Rethinking model scaling for convolutional neural networks Tan and Le (2019)
for classifying brain tumors from the T1-weighted MRI slices. The choice of these deep models is explained by the fact that they are widely used in medical image features extraction for prediction and/or classification.
VGG was first introduced in the ImageNet Large Scale Visual Recognition Challenge (ILSVRC) 2014 challengeRussakovsky et al. (2015) mainly to evaluate the effect of increasing depth in a deep neural network architecture with very small (
) convolution kernels. The results showed that increasing depth to 16-19 weight layers is a significant factor in improving the prior-art configurations. Increment in neural architectural depth leads to more expressive models that learn better representations, thus, improve generalizations across training tasks. However, deeper networks are hard to train because of the vanishing gradient problemHochreiter (1991); Bengio et al. (1994); Glorot and Bengio (2010). In that regard, the deep residual learning; ResNets was introduced in He et al. (2016) to facilitate training routines for massively deeper neural networks. Results inHe et al. (2016)
empirically showed that ResNets converge faster using local search methods such as stochastic gradient descent (SGD) and can achieve higher accuracy from considerably increased depth of several layers. The primary way the vanishing gradient problem is tackled in this framework is by introducing identity mappings that create shortcut connections to maximally exploit information flow in the network architecture thus solving the vanishing gradient problem. As depth is addressed by the residual network framework, another key concern is how wide can we go and in what variety of kernel sizes?
Thus, a natural solution would be to learn, within computational limits as many factors of variations as possible. This is the main idea introduced in the depth-wise separable layers based on the Inception architecture Szegedy et al. (2015). In contrast to a standard Inception model that performs cross-channel correlations followed by spatial correlations, in the Xception model, spatial convolutions are performed independently Chollet (2017). This consists of a spatial convolution performed independently for each channel of the input followed by a point-wise convolution across channels for dimensionality reduction of the computed features. In their work Huang et al. (2017), introduced the idea of dense connectivity; DenseNet where each layer is connected to every other layer in a feed-forward fashion in neural networks. Their approach is a natural extension of the successes made by ResNets. A DenseNet comprises dense blocks which implement dense connectivity to reduce the computational cost of channel-wise feature concatenation. This architectural design is robust to gradient flow as it provides robust signals for gradient propagation in the layers of a substantially deeper network which results in gainful generalization performance. With a small growth rate, this architectural design is computationally efficient. The EfficientNet Tan and Le (2019) introduced a principled study of model scaling considering the impact of depth, width, and resolution on model performance. A new compound scaling method was proposed that uniformly scales all three dimensions of an input image: depth, width and resolution using a compound coefficient that is derived from a grid search method.
The above architectures as described are known in the context of supervised deep learning for which the optimization uses gradient-based local search methods. The goal of the optimization is to find an optimal fitted function that minimizes the empirical risk; measured from the training samples with a defined loss function :
where compacts the parameters of the trainable neural network , N the number of training examples, and associated are the features vector and label for sample respectively. To prone generalization, a regularization term is imperatively added
in the norm regime with the learning rate. In order words for with , at layer
we want to interpolatesuch that
predicts the label for . In this notation, is the output interpolation of layer , is the activation function at layer , is the learnable parameters at layer with and
the weight matrix and bias vector respectively. In the expression in Equation3 the weights matrix is introduced as a sort of regularization that activates the connections which contribute to the interpolation of at layer ; this is known as the dropout regularization.
Adopting a gradient flow training method with variable learning rate at layer , in the meta learning regime as we adopted in this work, the update of follows two procedures. If is assumed to be the distribution of task where each task is sampled as with the aim to learn prior knowledge from all these . As discussed in Finn et al. (2017) the main goal is to encapsulate the prior knowledge of all as the initial weight of the fitted function which can now be used as initial weight for quick adaptation to a new task. The first attempts is to find the parameter of a task with training sample ; where is the number of sample in . At the iteration, is updated as:
which is now followed by a proper update of using the direction of the gradient and the test samples of the task ; where is the number of sample in . Assume that is obtained after several update as discussed in Equation 4 for each task , the proper update of follows:
where and are the number of tasks and the learning rate at layer respectively.
3.2 Proposed Visual Interpretability Framework
To help interpret a model inference mechanism, which is crucial in building trust for clinical adoption of deep learning-based computer-aided diagnostic systems, we have proposed an interpretability framework depicted in Figure 1 that gives an overview of an attribution mechanism. Sundararajan et al. (2017) posited fundamental axioms: Sensitivity and Implementation Invariance that attribution methods must satisfy are adhered for all selected saliency methods in this study. For a macro-scale attribution, a model that has learned statistical regularities of any given bioimaging dataset that has an arbitrary number of classes to produce a representation for each medical image slice
that is a compact latent representation in a vector space. With this representation, any arbitrary dimensionality reduction method can map the latent representation onto a lower-dimensional space for analysis and visualization. This could be a Gaussian Mixture Model (GMM)Duda et al. (1973), t-Distributed Stochastic Neighbor Embedding (t-SNE) Van der Maaten and Hinton (2008)
or Principal Component Analysis (PCA)Wold et al. (1987) technique to understand the latent space projection.
To attain local information about an attribution scheme because of the limitations of global attribution as it does not give contextual information of feature importance in the input space. We therefore, propose the use of gradient information since neural models are differentiable functions. We propose a framework of an adaptive path-based gradient integration method that utilizes the Guided Integrated Gradient (GIG) Kapishnikov et al. (2021) as shown in Equation 8 and a region-based saliency method (XRAI) Kapishnikov et al. (2019). The core idea of Integrated Gradient (IG) is that given a non-linear differentiable function defined as:
which represents a deep neural network and an input . A general attribution of the prediction at the input relative to some baseline input is a vector where is the contribution of the vector component to the function . In a medical image analysis context, the function represents a deep neural network that learns a disentangled non-linear transformation of given medical image slices. The input vector is a simple tensor of the mono channel image, where the indices correspond to pixels. The attribution vector serves as a mask over the original input to show the regions of interest of the model for the given predicted score. This information gives us insight into regions of interest for any given 2D image slice:
where is the difference between the input image and the corresponding baseline input at each pixel.
Computing and visualizing the saliency maps involve the following steps:
We initialize a baseline with all zero. This baseline input remains prediction-neutral and has a crucial role in the interpretation and visualization of the input pixel feature importance.
Linear interpolations are generated between the baseline and the original image that are incremental steps in the feature space between the baseline and the input image .
The gradient in Equation 8 is computed to measure the relation between the features
and changes in the model class predictions. It gives a criterion for pixels with the most relevance to the model class probability scores. This gives a basis for quantifying feature importance in the input image with respect to the model prediction.
Using a summation method, an aggregate of the gradients is computed.
The aggregated saliency mask is scaled to the input image to ensure feature attribution values are accumulated across multiple interpolated images that are all on the same scale that represents the saliency map on the input image with the pixel feature saliency.
4 Experimental Results
This section presents an overview of the dataset used in the present work including the annotation procedure for segmentation of regions of interest in each MRI image. We further explain the training regime for all the models and elaborate on the proposed framework for computing interpretable features using adaptive path-based gradient integration techniques for scoring pixel-wise feature relevance as discussed in Section 3.2. Results show that deep neural network models trained on medical images can give prediction confidence through softmax scores as well as use interpretability techniques to infer feature attribution maps.
Data for this study is from Cheng (2017). It comprises 2D slices of brain contrast-enhanced MRI (CE-MRI) T1-weighted images consisting of 3064 slices from 233 patients. It includes 708 Meningiomas, 1426 Gliomas, and 930 Pituitary tumors. Representative MRI image slices that have large lesion sizes are selected to construct the dataset. In each slice, the tumor boundary is manually delineated and verified by radiologists. We have plotted 16 random samples from the three classes with tumor borders depicted in red as shown in Figure 2.
These 2-D slices of T1-weighted images are used to train standard deep CNNs for a 3-class classification task into Glioma, Meningioma, and Pituitary tumors.
4.2 Implementation Performance
(Left-panel) Performance measure of the 8 CNN architectures used in this experiment all trained for 20 epochs. Overall, DenseNet-121Chollet (2017) showed the highest
Score reaching of .981. (Right-panel) The confusion matrix for test samples which represent 20% of the dataset. The model was able to generalize well with 5, 4, and 3 misclassification for Meningioma, Glioma, and Pituitary tumor respectively. Because of the distinctness of both Meningioma and Pituitary tumor, the model has 0 false positives between both classes.
As the primary objective of this study is to build a framework for understanding the visual interpretability of deep models in medical images, we limit our experiments to 8 standard vision-based deep neural architectures. We train and test the 8 standard CNN architectures; results are shown in Figure 3 and summarised in Table 2 with training parameters depicted in Table 3. The input to each model is a tensor that is a resized version of the original image slices primarily due to computational concerns. We conducted all experiments on an Nvidia K80/T4 GPU. In Section 4.3 several saliency methods are applied to understand model interpretability.
|Parameters||Depth||Top 1 % Accuracy|
|Number of epochs||20|
|Optimizer||Stochastic Gradient Descent with Momentum (SDGM)|
The DenseNet-121 model showed the best overall test performance reaching 98.10%. The test results indicate the high confidence and stability of model prediction. This is the basis of selection for further feature attribution given that it is the best performing model implying it has learned a more robust and generalizable representation of the data distribution as shown in Figure 4. The clear distinction between Figure 4 (top-panel) and Figure 4 (bottom-panel) gives an evident indication that the model has learnt inherent factors of variation in the signals which have been disentangled into nearly separable manifolds in the learnt representation space. This figure supports the results of the confusion matrix above as Glioma and Meningioma have small overlap in the embedding space thus the 9 misclassified samples between both classes. However, this ability of learning necessitates the notion of what has the model learnt about the data space and how can it be interpreted by domain experts? Thus, the notion of feature attribution is investigated to make sense of mapping between the model input and the predicted class.
Our proposed attribution approach is predicated on the notion that visual inspection has a major role in medical image analysis decision making. Naturally, an automated visual attribution method is vital in human-centred AI medical image analysis pipeline. Given that many attribution methods have been proposed, we have, however, used gradient-based adaptive path integration methods because of their robustness to noise and smoother pixel-level feature saliency mappings as depicted in the Figures 5, 6, and 7 for the three brain tumor classes. These methods are: Vanilla Gradient Sundararajan et al. (2017), Guided Integrated Gradient (GIG) Kapishnikov et al. (2021) and XRAI Kapishnikov et al. (2019). The visual attribution was implemented using the three best models as shown in Figure 3 (Left-panel).
Xception shows the least visual explainablity as indicated in Figure 5. From the input image, Pituitary tumor located in the pituitary gland, a region below the hypothalamus is faintly attributed by all but XRAI. The attribution masks give little meaningful information about the region of interest where the tumor is present. Though other factors such as the dataset size, batch size, annotation quality, data augmentation technique can considerably lead to the emergence of such characteristics, the model architecture and optimization objective have a large effect as they introduce stronger inductive priors on the space of learning functions. Moreover, this result indicates the difference between statistical correlations learned by CNNs being different from the way humans perceive and process visual stimuli.
From Figures 6 and 7, we observed that XRAI gives the best saliency maps as shown in the masked MRI images. VG and SG have coarse and partially noisy saliency maps, and can not be used to infer meaningful explanations of the model inference mechanism. As stated in the original papers, the baseline choice has a major effect on the obtainable saliency map Sundararajan et al. (2017); Kapishnikov et al. (2019, 2021). We used a baseline of zero pixels for all attribution methods primarily because it is information neutral. XRAI demonstrated higher interpretability compared to vanilla gradient and guided integrated gradients methods because it is more suited to deep learning-based medical image analysis tasks where the emphasis is to understand the region of interest from which a model inferred its prediction. We observed that a combination of XRAI and Blur IG can deduce feature saliency from the medical scans as 35% of saliency maps of XRAI highlights important features that are in a close approximation of expert segmentation for the DenseNet-121 model. So, utilizing multiple attribution methods can improve model interpretability for domain experts.
These results, therefore, open the possibility of not only accelerating visual interpretability of deep neural models in medical image analysis but as well offset prepossessing such as human-in-the-loop segmentation, model debugging, and debiasing which are all crucial in real-world application use cases. The latter has an important role in low-decision risk and highly regulated domains such as healthcare. In sum, these stated use cases can rapidly advance access to needed but affordable healthcare for low-resource settings.
However, Table 2 in tandem with 5, 6 and 7 show that the inductive architectural priors have to most impact on the selectivity of the receptive fields of CNNs for visual saliency analysis. CNNs perform spatial weight sharing where each filter is replicated across the entire visual field of the input Luo et al. (2016), thus, the resolution of this receptive field matters. Unlike humans, CNNs have texture and shape biases that are evident across all the model architectures Geirhos et al. (2018); Baker et al. (2018). Visual attribution methods must consider raise this notion in a human-in-the-loop AI systems to ameliorate the pitfalls of the wrong attribution in deep models for real-world healthcare applications.
Deep learning models are gaining traction in ubiquitous healthcare applications from the application of vision techniques to language models. However, the inference mechanisms of these models is still an open question. In this paper, we posed the question: What do these models learn in medical images? Our findings show that the robust statistical regularities learned between input-output mappings differ from biological visual stimuli processing done by humans. We show that different input attribution methods have varied degrees of explainability of the input signal. A robust representation learner and the right attribution approach are crucial to getting interpretable saliency maps of deep CNNs in medial image analysis. This is important because it will help in building human-in-the-loop computer-aided diagnostic models that not only generalize well to unseen samples but are also explainable to domain experts. Our findings indicate that deep models can complement the efforts of medical experts in efficiently detecting and diagnosing diseases from medical images. Thus, a human-in-the-loop approach can accelerate the adoption of neural models in medical decision-making. It provides a path toward building stakeholder trust given that healthcare requires critical evaluation of assistive technologies before adoption and general usage. Finally, we encourage further research into quantifying the explainability of these visual attribution methods, developing benchmarks against which new visual attribution methods can be measured to accelerate model explainability research, and the provision of open access tumor boundary segmented dataset so as to test new saliency algorithms in ground truth expert segmented datasets.
This research received no external funding.
Availability of data and materials
This research used the brain tumor dataset from the School of Biomedical Engineering Southern Medical University, Guangzhou, which contains 3064 T1-weighted contrast-inhanced images with three kinds of brain tumor. The data is publicly available at https://figshare.com/articles/dataset/brain_tumor_dataset/1512427. The code is available at https://github.com/yusufbrima/XDNNBioimaging for reproduciblity.
The authors declare that they have no competing interests.
All the authors contributed to this work.
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