Collaborative Screening of COVID-19-like Disease from Multi-Institutional Radiographs: A Federated Learning Approach

Abstract

COVID-19-like pandemics are a major threat to the global health system have the potential to cause high mortality across age groups. The advance of the Internet of Medical Things (IoMT) technologies paves the way toward developing reliable solutions to combat these pandemics. Medical images (i.e., X-rays, computed tomography (CT)) provide an efficient tool for disease detection and diagnosis. The cost, time, and efforts for acquiring and annotating, for instance, large CT datasets make it complicated to obtain large numbers of samples from a single institution. However, owing to the necessity to preserve the privacy of patient data, it is challenging to build a centralized dataset from many institutions, especially during a pandemic. Moreover, heterogeneity between institutions presents a barrier to building efficient screening solutions. Thus, this paper presents a fog-based federated generative domain adaption framework (FGDA), where fog nodes aggregate patients’ data necessary to collaboratively train local deep-learning models for disease screening in medical images from different institutions. Local differential privacy is presented to protect the local gradients against attackers during the global model aggregation. In FGDA, the generative domain adaptation (DA) method is introduced to handle data discrepancies. Experimental evaluation on a case study of COVID-19 segmentation demonstrated the efficiency of FGDA over competing learning approaches with statistical significance.

1. Introduction

The Internet of Medical Things (IoMT) has been an essential contributor to the enhancement of the accuracy, reliability, and productivity of healthcare services provided in smart cities. The scientific community has expressed a significant amount of enthusiasm over the computerization of the IoMT in relation to conventional medical facilities and medical care services [1]. Through the establishment of a seamless connection between patients and medical staff, as well as the transmission of diagnostic and treatment data, the IoMT has the potential to eliminate unnecessary actions and responsibilities of health organisations [2].

The social and physiological problems that have been brought on by pandemic diseases pose a threat to the global health system. Every time a pandemic disease breaks out, it presents the world’s healthcare systems with new and difficult problems and responsibilities. It is widely believed that COVID-19 is the most dangerous and deadly pandemic disease that is having a severe impact on healthcare all over the world. Therefore, in order to battle pandemics caused by COVID-19-like viruses, it is necessary to have an IoMT system that can collect and evaluate diagnostic and treatment data pertaining to patients. In this regard, the screening and diagnosis of COVID-19-like pandemics is a first line of defence in the fight against a pandemic disease [3]. As a result of this, a significant amount of research attention has recently been dedicated to the screening and detection of COVID-19 from radiological images such as computed tomography (CT), X-rays, and ultrasound frames as a supplement to the RT-PCR test [4].

In recent years, Deep Learning (DL) has shown impressive performance in diagnosis activities (i.e., identification, localization, categorization, etc.) utilising x-ray images. Several convolutional neural networks (CNNs) have been trained to distinguish between COVID-19 patients, other types of pneumonia patients, and normal cases based on radiographic images [5]. In contrast, segmentation methods attempt to autonomously localize/detect and segment diseased areas in chest radiography images, with the primary goal of reducing the workloads associated with performing manual segmentation and helping to overcome the issues of inter- and intra-observer variance. Most current DL research, however, takes for granted that all data can be found in a single, centralised hub. Cloud servers are commonly used in cloud-based IoMT to do this. Nevertheless, it is challenging, if not unachievable, to have a big training dataset at a central area due to the decentralized architecture of the IoMT environment (i.e., institution, hospital, etc.). In the IoMT setting, the labelled data are typically shared throughout multiple organisations. Therefore, it is time-consuming and fraught with latency concerns to move these data to a centralised place. There is also the possibility that hospitals and clinics will not divulge patients’ personal health data. Because of this, radiographic image screening for COVID-19-like pandemics in IoMT is not something that can be accomplished with centralised DL [6].

In response, Google announced Federated Learning (FL) to facilitate a data-private collaborative learning solution. With FL, multiple coworkers can train a machine/deep learning network locally using their own data and then send their training updates to a centralised server, where they will be consolidated into a global model [7]. The global updates are then transmitted by the aggregation server to all participating universities for use and further education. Since the data are stored locally by the participating universities in the IoMT, their confidentiality is protected throughout the learning process. Fog computing, a middleware interface to cloud computing, was developed to move data storage and processing closer to the point of origin [8]. It is a paradigm shift that directs the development of new fields of study in content distribution, data dissemination, and service management. More promising IoMT applications can be achieved through fog computing by establishing interdependencies of network elements using existing practise and methodology [9]. In this model, fog servers located in different parts of the world handle the various computing and communication tasks. Thus, this paper recommends utilising FL and fog computing to strengthen IoMT capabilities for collaborative screening of COVID-19-like pandemics from radiography images [10].

Despite the numerous studies aimed at enhancing the AI method’s capability in screening COVID-19-like pandemics, the application of these techniques remains restricted, particularly for multi-site data, for the explanations that follow [11]. First, patients are anxious about the security of their data, and healthcare centres are afraid that sharing patients’ data may cause them to lose the trust of their patients. Concern that rival organisations would use their data for their own commercial or scholarly advantage is a common source of anxiety for healthcare organisations from a purely business perspective. Second, the medical images that come from a variety of institutions are often drawn from a wide variety of data distributions [12]. This fluctuation poses a risk to the training stability and places restrictions on the capacity to achieve the greatest screening performance.

This work was inspired by the recent achievement of deep learning in COVID-19 diagnosis, and it helps solve the problems listed above. First, this paper presents an FL framework that enables interactive screening of COVID-19-like diseases from medical imagery in fog-assisted IoMT. The concept of fog computing is presented to provide the training phase with more robust and convenient resources.

Second, multi-institutional samples are exploited to align the source domain with the target using a novel task-agnostic domain aligner that is regularized via a single discriminator that first checks the distribution of the source information with those of the target and later enforces the two domains to match each other, aiming to reduce the impact of domain shift in the global updates of the proposed FL framework. Third, to preserve the privacy of data through the domain adaption, an intelligent local differential privacy (LDP) mechanism is redesigned to protect the privacy of discriminator’s and generators’ information during the communication of learning updates between client side and server side. Finally, the effectiveness of the suggested framework was validated by empirical analysis and evaluation using a specific example of multi-source COVID-19 segmentation as a test subject. The results showed significant performance increases.

The remainder of this study is structured as follows: Related studies are overviewed in Section 2. The design of the proposed system is given Section 3. The proposed FL framework is discussed in Section 4. The experimental configurations are given in Section 5. Then, the discussion of empirical results is introduced in Section 6. Section 7 summarizes and concludes our work at the end of the manuscript.

2. Literature Review

In this part, a comprehensive assessment of the recent and relevant research literature for the radiographic image-based diagnosis of COVID-19-like pandemics is provided.

• Deep learning for screening of COVID-19-like diseases

The recent literature contains many studies for screening COVID-19-like disease from medical images. These studies cover one or more tasks such as classification, segmentation, localization, reconstruction, etc.

To classify COVID-19 from other pneumonia, the authors of [13] presented an open-source framework, called CovidCTNet, that integrated multiple DL models to realize accurate classification from CT images. In a similar way, the authors of [14] presented a lightweight, approachable, professional DL model for classifying different types of infection from lung ultrasound images. The authors of [15] proposed three models (i.e., DenseNet, InceptionV3, and Inception-ResNetV4) for the diagnosis of different pneumonia from X-ray radiographs of patients. Moreover, the authors of [16] presented a multi-kernel-size spatial-channel attention technique for detecting COVID-19 from chest X-ray radiographs. The design of this method comprises three phases: (1) feature extraction; (2) pairing of parallel multi-kernel-size attention blocks to gather and learn the cross-channel and cross-spatial interrelatedness in manifold spaces using many convolutional kernels of diverse magnitudes to attain channel- and spatial-attentive feature maps; and (3) classification decision block.

For segmentation tasks, the authors of [17] developed an automated approach for segmenting respiratory parenchyma in CT radiographs and analyzing consistency characteristics from the segmented pulmonary parenchyma areas to support radiotherapists in COVID-19 diagnosis. To achieve this, the study presented a segmentation model that incorporates a 3D V-Net shape-deformation block based on a spatial transform network for pulmonary parenchyma segmentation from lung CT scans.

B.

Federated Learning for Domain Adaption

Recently, multiple research efforts have been devoted to promoting collaborative training for screening COVID-19-like pandemics from image data. The authors of [18] presented a data-driven FL framework, called Auto-FedAvg, to immediately learn the model aggregation updates from data making use of the Dirichlet distribution, in a way adaptive to the distribution of training data during learning. The authors of [19] presented an effective reinforcement learning (RL) mechanism for searching for the optimal hyperparameter of FL during training on multi-site medical images. The authors of [20] focused on managing both local and global drifts while also introducing a new harmonising framework, in which the authors proposed mitigating the local update drift by normalising the amplitudes of pictures that have been translated into the frequency domain to approximate a uniform imaging environment. Second, using the harmonised features, the authors built a client weight disturbance that leads each local model to a flat optimum. A smooth optimum is one in which a neighbourhood region surrounding the local optimal solution has a loss that is consistent over the entire neighbourhood. In addition, the authors of [21] proposed an FL approach that can perform inside and outside model personalization via an insubstantial-gradient method to make use of the local customized model by gathering global updates for general expertise and local updates for client-given optimization. Moreover, the authors of [22] identified and solved a novel issue setting known as federated domain generalization to enable learning a federated model from several remote source domains in such a way that it can directly generalise to domains that have not been encountered before. Episodic Learning in Continuous Frequency Space (ELCFS) was proposed to allow each client to leverage multi-source data distributions while adhering to the difficult restriction of data decentralisation.

To sum up,

Table 1. Summary of the related works.

Methods	Task	COVID-like	Data	Multi-Domain	Privacy	Unlabeled Target	Federated	Source
Auto-FedAvg [18]	Segmentation	✓	CT	✓	✗	✗	✓	Free
HarmoFL [20]	Segmentation	✗	MRI	✓	✗	✗	✓	Exist
IOP-FL [21]	Segmentation	✗	MRI	✓	✗	✗	✓	Exist
FedDG [22]	Segmentation	✗	MRI	✓	✗	✗	✓	Exist
Auto-FedAvg [18]	Segmentation	✓	CT	✓	✗	✗	✓	Free
Fed MoE [23]	Classification	✗	fMRI	✓	✓	✗	✓	Exist
Fed Align [23]	Classification	✗	fMRI	✓	✓	✗	✓	Exist
MS-SFDA [24]	Classification	✗	fMRI	✓	✗	✓	✗	Free
TMJDA [25]	Classification	✗	fMRI	✓	✗	✗	✗	Exist
FED [26]	Segmentation	✓	CT	✗	✗	✗	✓	Exist
COVID-Net [27]	Classification	✓	CT	✗	✗	✗	✗	Exist
DECISION [28]	Classification	✗	RGB	✓	✗	✓	✗	Exist

presents an insightful conclusion about the literature studies discussed above.

3. System Design

This section describes the system model for screening of COVID-19-like pandemics from distributed multi-institutional medical images in IoMT. Expanding from centralized computing at the cloud, fog computing accommodates geographically dispersed fog servers so as to bring computational resources closer to participating institutions. Figure 1 depicts the proposed system model. Notably, the system model’s three main tiers each comprise a different set of devices. The three tiers are described as follows.

• Edge tier: In IoMT, the edge tier comprises medical devices and instruments used to capture medical/patient information necessary for diagnosis. This includes implanted sensors, laptops, scanners, mobile devices, etc. These devices may have various quantities of data and various computational resources, capacities, power capabilities, acquisition techniques, and protocols leading to an many gaps. Some of these data might be private and cannot be revealed by medical institutions because of privacy concerns. Thus, these data are securely moved over the secure communication channel to a local fog server to be safely stored.
• Fog tier: It acts as a bridge to connect cloud servers to edge devices, as it has more robust computational resources than the edge devices and is closer to the edge of the IoMT network. Hence, it can alleviate the resource-restriction issue of edge devices, while affording better communication efficiency than a cloud environment. In our IoMT system, the fog tier takes the responsibility of aggregating institutional patients’ data (e.g., CT or X-rays) from the neighbouring edge devices to be safely stored, annotated, and prepared without threatening the privacy of the data. Then, the fog servers also act as the training participants that host the local DL models that are collaboratively trained using their corresponding local institutional data. In each round of federated learning, the participating fog nodes upload their local parameters $W_L$ to the cloud for aggregation. Once the aggregation is complete, they receive the global parameters $W_G$ from the cloud and update the local parameters $W_L$ accordingly. To protect privacy, the fog servers apply differential privacy to the local parameters before uploading them.
• Cloud tier: It contains the cloud server that acts as the training coordinator, sometimes called a parameter or aggregation server. It is primarily responsible for initializing global model parameters before training, broadcasting initial values to the local models ${ℳ}_L$ on the fog nodes, and selecting the training participants. More importantly, it also aggregates the local parameters/gradients $W_L$ from the participating fog nodes to calculate the new global parameters $W_G$. It then broadcasts the global parameters back to the participants.

4. Methodology

In this section, we provide a comprehensive overview of the FL framework for cross-site screening of COVID-19 from CT scans at multiple institutions using IoMT, while protecting patients’ right to privacy. For the sake of brevity, we will use COVID-19 infection segmentation and/or quantification as an example of a typical use case for COVID-19 screening in this and subsequent sections. We explain how data privacy is established and how various data domains can be aligned in the next section.

4.1. Problem Formulation

Given matrix $D_i$ representing the CT data held by site $i$, $N$ sites $\left\{S_1,....S_N\right\}$ seek to train their DL models by combining their corresponding CT data $\left\{D_1,....,D_N\right\}$. For COVID-19 analysis from CT scans, the number of scans at each site is insufficient to build and train an efficient DL approach. Traditionally, this issue could be solved by joining all data in a single site and employing $D=\left\{D_1{\displaystyle \cup }{D}_2....{\displaystyle \cup }{D}_N\right\}$ to train ${ℳ}_{Blend}$. Some of these CT data may be annotated, and others not. The input space $X$, ground-truth (GT) space $Y$, and sample-identity space $I$ are the main constituents of the entire training data. For multi-site COVID-19-lesion segmentation, $D_i$ consists of CT data aggregated from institution $S_i$, and X represents acquired CT features, which, with ground-truth $Y$, are used to segment and quantify the infection area. These datasets have a common feature space, yet their samples differ. For instance, heterogeneous sites have diverse patients. Nevertheless, the CT features are extracted and learned from the same pipeline. Consequently, the data distribution can be formulated as in (1),

$$X_i=X_j, Y_i=Y_j, I_i=I_j \forall D_i{D}_j i\ne j$$

(1)

which is a type of horizontal FL in which a variety of datasets have feature intersection and trivial sample-space intersection.

Rules and policies prohibit the sharing of data by clinical organizations. An FL scheme is a training schema in which institutions $S_i$ cooperatively train a model ${ℳ}_{FED}$ without disclosing their data $D_i$. In our case, a centralized cloud server is used to compute the global model ${ℳ}_G$, while fog participants (i.e., from various institutions) employ the identical DL architecture for segmentation. The model is trained using the local data at each fog server, and the training parameters are regularly updated and transferred to the centralized server. The transmission of parameters between the fog nodes and the cloud coordinator server makes the model and data prone to parameter-reversal attacks. As soon as all parameters reach the server, the server performs average aggregation to compute the new global parameters $W_G$, then broadcasts them back to the local participants.

4.2. Privacy-Maintaining FL

The basic FL system has the phases of local upgrading and server communication in distributed optimization. This section presents the proposed privacy protection segmentation along with the steps of training, using Dice loss to train segmentation at any institution $n$,

$$L=1-\frac{2{{\displaystyle \sum }}_{x_i}{z}_i·y_i}{{{\displaystyle \sum }}_{x_i}{z}_i+{{\displaystyle \sum }}_{x_i}{y}_i},$$

(2)

where $z_i$ and $y_i$ are the model prediction and GT, respectively, for input $x_i$, and the training set is arbitrarily selected from the feature space $X_n$ and GT space $Y_n$.

4.3. Local Differential Privacy

LDP [29,30] is a popular method for privacy protection in artificial intelligence (AI) and constitutes a robust standard for privacy assurance for data-driven AI solutions. LDP seeks to offer a limit ϵ such that adversaries might learn almost nothing more about a participant than if it were missing from the training data since the participant’s critical data are almost unrelated to the model’s outputs. $ϵ$ signifies the level of privacy that can be managed by various parties. Several studies have tried to maintain DP at the data level in a centralized training scenario. To safeguard data from a reversal attack that exploits the local parameters $W_L$ to deduce the training data, the DP was introduced to inject noise into the local parameters before sending them to the parameter server for aggregation. In this way, an adversary becomes unable to infer anything about the private patient data in the IoMT environment.

With a definite mapping method $f:D\to {ℝ}^m$, the sympathy $s_h$ is the supreme absolute difference ${||f\left(D\right)-f\left(D^{\prime }\right)||}_1$, where ${||D-D^{\prime }||}_1=1$, which represents a single element of variance separating $D$ and $D^{\prime }$ [14]. Herein, the $f$ is a function that calculates the parameters $\mathcal{W}$ in the segmentation model. Presenting “noise” through the training procedure (i.e., input samples, parameters, or segmentation results) can restrain the granularity of common information and guarantee to realize the LDP for all $S \subseteq Range \left(f\right)$ as follows:

$$Pr\left[f \left(D\right)\in S\right]\le e^{ϵ} Pr \left[f \left(D^{\prime }\right)\in S\right],$$

(3)

$$Pr\left[f\left(D\right)\in S\right]\le e^{ϵ}Pr\left[f\left(D^{\prime }\right)\in S\right]+\delta ,$$

(4)

where δ is the failure probability and $ϵ$ denotes the privacy budget. The lesser the value of δ, the tighter the distribution of the data production by $f$ in both datasets. This work considers two LDP techniques to realize efficient privacy assurance [31] by incorporating noise in the shared network parameters.

First, Gaussian-based LDP [32] injects noise $N\left(0,s_f^2{\sigma }^2\right)$ with average $0$ and $s_f^2{\sigma }^2$ variance of a Gaussian distribution for the task $f\left(D\right)$ as follows:

$$\tilde{f}\left(D\right)\cong f\left(D\right)+N\left(0,s_f^2{\sigma }^2\right)$$

(5)

where the sensitivity $s_f^{}$ of the random function $f$ is defined as follows:

$$\Delta f=\underset{D,D^{\prime }}{\max }{||f\left(D\right)-f\left(D^{\prime }\right)||}_1$$

(6)

Hence, the random function $f$ will satisfy the definition of LDP with $\left(ϵ,\delta \right)$ when $\delta \ge \frac{4}{5}exp\left(-{\left(\sigma ϵ\right)}^2/2\right)$ and $ϵ<1$. This implies that the parameter of Gaussian noise $\sigma$ can be associated with the privacy parameters $ϵ,$ and$\delta$.

Second, Laplace-based LDP [33] positions a Laplace distribution around zero, with scale $b$ that represents the corresponding probability density function,

$$Lap\left(b\right)=Lap(x|b)=\frac{1}{2}exp\left(-\frac{\left|x\right|}{b}\right).$$

(7)

The Laplace variance is ${\sigma }^2=2b^2$. This technique includes noise $Lap \left(s_f/ϵ\right)$ in $f\left(D\right)$ with universal sympathy $s_f$, and conserves LDP with $\left(ϵ,0\right)$. Hence, we associate the parameter $b$ with the privacy parameter $ϵ$. In the COVID-19 segmentation scenario, f is implemented using the DL segmentation network, and the sympathy $s_f$ cannot be calculated; hence we set $s_f$ to 1.

To sum up, the notion behind LDP techniques is to combine a specific quantity of noise in the query output while maintaining the value of the original gradient. This noise is typically determined based on the privacy arguments $\left(ϵ, \delta \right)$. Therefore, it regulates the parameters according to privacy obligations by associating the privacy and noise parameters.

4.4. Domain Adaption for Multi-Site FL-Based Screening

Despite the improved, efficient privacy realized by FL, there is an extra challenge in segmenting COVID-19 infections from CT scans that have heterogeneous data presented in the IoMT system, which causes a domain shift between institutions [34]. The key notion is that DA techniques can improve the segmentation performance of multi-site data in the IoMT and remain efficient even if noise is applied for privacy protection, particularly for institutions whose data distributions are completely different from those of other institutions. The following section presents the proposed DA technique, in which adaptation is performed at the level of learned knowledge representation.

4.5. Federated Generative Domain Adaption (FGDA)

CT scans are institutionally maintained in FL setups in order to safeguard patients’ right to confidentiality. In order to meet the requirements of the DA challenge, we will attempt to generalise from disparate source domains to the common domain space of target data. It is impossible to train a specialised segmentation model that can use both the source domain and the target domain simultaneously because an IoMT system constrains the exchange of data. These restrictions make it impossible to use both domains at the same time. We solve this problem by employing an adversarial alignment methodology [35,36,37] with two components, namely an institutional domain-relevant feature extractor and a universal discriminator, by means of segmentation models and by separating optimization into two stages that are independent of one another. Then the institutional extractor $G_s$ is trained for the source institution $D_s$, and the institutional extractor $G_t$ for the target institution $D_t$. For every pair ($D_s$, $D_t$), an adversarial domain discriminator $D$ is trained to align the distributions. Once these are trained to recognize the domain from which the features originated, the discriminator $D$ is confused by feature generators ($G_s$, $G_t$). Hence, in the situation of privacy preservation, $D$ can use the noisy output representations generated from $G_s$ and $G_t$ with no leakage of private CT data. The discriminators of source domains receive inputs $M\circ G_t\left(x^t\right)$and $M\circ G_s\left(x^s\right)$, where $M(·)$ is the noise producer (See Figure 2). Thus, data penetration at the target institution is prohibited during discriminator training at the source institution. With $X^S \mathrm{and} X^T$ indicative of the source and domain data, correspondingly, the source domain can be perceived from the others using the following formula:

$$L_{Discriminator}({\mathit{X}}^S,{\mathit{X}}^T,G_s,G_t)=-{\mathbb{E}}_{x^s~{\mathit{X}}^S}\left[log(D_s\left(G_s\left(X^s\right)\right))\right]-{\mathbb{E}}_{x^t~{\mathit{X}}^T}\left[log(1-D_s\left(M\circ G_t\left(X^{\mathit{t}}\right)\right))\right].$$

(8)

$L_{\mathit{Discriminator}}$ is kept constant, and $L_{\mathit{Generator}}$ is updated as follows:

$$L_{Generator}({\mathit{X}}^S,{\mathit{X}}^T,G_s,G_t)=-{\mathbb{E}}_{x^s~{\mathit{X}}^S}\left[log(D_s\left(G_s\left(X^s\right)\right))\right]-{\mathbb{E}}_{x^t~{\mathit{X}}^T}\left[log(D_s\left(M\circ G_t\left(X^{\mathit{t}}\right)\right))\right]$$

(9)

Once the training of the FL model is combined with an alignment component, the divergence between the source and target domains can be reduced. Algorithm 1 presents the implementation of FGDA.

Algorithm 1: FGDA
Input: (1) $X=\left\{X_1,...,X_N\right\}$, COVID-19 CT data from $N$ institutions; (2) $G_{w_G}=\left\{G_{w_{G_1}},...,G_{w_{G_N}}\right\}$$\mathrm{represents}\mathrm{institutional}\mathrm{generators}\mathrm{at}N\mathrm{sites},\mathrm{with}\mathrm{parameters}{w}_{G_i}$; (3) ${SG}_{w_S}=\left\{{SG}_{w_{s_1}},...,{SG}_{w_{s_N}}\right\}$ $\mathrm{represents}\mathrm{segmentation}\mathrm{models}\mathrm{with}\mathrm{parameters}{w}_{S_i}$; (4) $D_{w_D}=\left\{D_{w_{D_1}},...,D_{w_{D_N}}\right\}$$\mathrm{represents}\mathrm{discriminators}\mathrm{at}N\mathrm{sites},\mathrm{with}\mathrm{parameters}{\theta }_{D_i}$; (5) $Y=\left\{Y_1,...,Y_N\right\}$ represents COVID-19 infection GTs; (6) M(·) is the noise originator; (7) K is the number of optimization phases; (8) $\tau$ is a universal updating step, i.e., for every optimization phase, the universal and institutional parameters are communicated in $\tau$ steps; (9) $\left\{G_{{\overline{w}}_1},C_{w_{\mathrm{c}}}\right\}$ is the universal model.
1:	$\mathrm{Initialize}\mathrm{parameters}\left\{w_G,w_C,w_D\right\}$
2:	$\mathbf{for}k=1$ to $K$ do:
3:	t = 0
4:	$\mathbf{for}i=1, j=1$ to $N$ do:
5:	${\left\{\left(X_i^S,Y_i^S\right)\right\}}_{i=1}^N$ sample from source institution
6:	${\left\{\left(X_j^T\right)\right\}}_{j=1}^N$ sample from target institution
7	$\mathrm{Calculate}\mathrm{gradient}\mathrm{with}\mathrm{Dice}\mathrm{loss}(\mathrm{Equation}(2))\mathrm{to}\mathrm{update}{w}_{G_i}^{\left(k\right)}{\mathrm{and}w}_{S_i}^{\left(k\right)}$
8	Domain Adaption:
9	$\mathrm{Upgrade}{w}_{D_i}^{\left(k\right)}$, {$w_{G_i}^{\left(k\right)}, w_{G_j}^{\left(k\right)}$} with Equation (8) and Equation (8), respectively
10:	Terminate for loop
11:	$t\leftarrow t+1$
12:	If $t\%\tau =0$ then:
13:	${\overline{w}}_G^{\left(k\right)}=\frac{1}{N}{\displaystyle \sum }_N^{}\left(w_{G_i}^{\left(k\right)}+M\left(w_{G_i}^{\left(k\right)}\right)\right)$
14:	${\overline{w}}_S^{\left(k\right)}=\frac{1}{N}{\displaystyle \sum }_N^{}\left(w_{S_i}^{\left(k\right)}+M\left(w_{S_i}^{\left(k\right)}\right)\right)$ universal parameter upgrade after $\tau$ steps
15:	for n = 1 to N do:
16:	$w_G^{\left(k\right)}={\overline{w}}_G^{\left(k\right)}$
17:	$w_S^{\left(k\right)}={\overline{w}}_S^{\left(k\right)}$
18:	Terminate for loop
19:	Terminate if
20:	Terminate for loop
21:	$\mathbf{Return}:\mathbf{universal}\mathbf{model}\left\{G_{{\overline{\theta }}_G}{,}_{}{SG}_{{\overline{\theta }}_S}\right\}$.

5. Experiments and Analysis

5.1. Dataset Description

We assessed the performance of the proposed framework on heterogeneous multi-source data using three publicly available COVID-19 CT datasets: (1) 829 slices from nine CT volumes with 372 infected slices, which we refer to as Institution 1; (2) COVID-19-CT-Seg [38], comprising 20 public COVID-19 CT volumes from the Coronacases Initiative and Radiopaedia, with more than 1,800 annotated slices, which we refer to as Institution 2; and (3) a 50 CT volume published in the MosMedData dataset [39], aggregated from municipal hospitals in Moscow, Russia, which we refer to as Institution 3.

5.2. Evaluation Metrics

We assess the segmentation performance of the proposed model according to three performance indicators: the Dice similarity coefficient (DSC), normalized surface distance (NSD), and Jaccard Similarity (JS). The mathematical definition of the above indicators is given as follow:

$$\begin{array}{c}\mathrm{DSC}=\frac{2 \ast TP}{\left(FP + TP\right) + \left(TP + FN\right)}\end{array}$$

(10)

$$\begin{array}{c}\mathrm{JS}=\frac{TP}{FP + TP + FN}\end{array}$$

(11)

$$\mathrm{NSD}=\frac{2\left|\partial S{\displaystyle \cap }{B}_{\partial S}^{\tau }\right|+2\left|\partial S{\displaystyle \cap }{B}_{\partial G}^{\tau }\right|}{\left|\partial S\right|+\left|\partial G\right|}$$

(12)

In the last formula, the symbols $B_{\partial S}^{\tau }\mathrm{and}{B}_{\partial G}^{\tau }$ represent the boundary area of segmentation maps and GT, respectively.

5.3. Implementation Setup

All the simulation experiments were performed on a Dell server equipped with NVIDIA Quadro GPU, Intel (R) Xeon (R) CPU E5-2670 0@ 2.60 GHz CPU (32 processors), 256 GB memory, and Windows 10 64-bit operating system. The implementation of the FL framework was coded with the PySyft and Pytorch libraries running on Python 3.7. The standard BiSeNet [40] was employed as the segmentation network. The output of the BiSeNet was a segmentation map indicating the COVID-19-infection regions. Dice loss was used as the cost function, and 5-fold cross-validation was adopted for training. The Adam optimizer was applied to the segmentation network. The learning rate of 1 × 10⁻³ was decreased by 0.5 after every 25 epochs and stabilized after the 75th epoch. Through all epochs, an institutional upgrade was carried out several times, depending on the interaction stride $R$, to replace a one-time upgrade, and 100 steps were used per epoch.

5.4. Numerical Results

To validate the efficiency and effectiveness of the proposed FL framework (FL-Cov) at fine-tuning the COVID-19 segmentation performance of multi-institutional CT data in IoMT, we compared it (with $\tau =15$ and $\alpha =0.01)$ to four non-federated learning schemas. The segmentation network was trained on each institutional dataset (Independent). The segmentation model was used on samples from one institution and tested on CT data from another institution (Cross). All data from different institutions were aggregated in a single location and used for training and testing (Blend). An ensemble DL framework was constructed using private models at diverse institutions (Ensemble). The Ensemble schema took the mean of outcomes of the independent schema trained inside the institution and a Cross schema trained using data from different institutions. The Independent and Cross schemas usually protect the privacy of CT data but cannot include data from other institutions. The Blend schema utilizes all CT data from various institutions but cannot ensure data privacy. The segmentation performance of the Blend schema is expected to improve compared to FL-Cov, as it uses a complete set of CT data.

To achieve a fair comparison, we selected the optimal parameters for diverse learning schemas by changing the network as little as possible. Considering the heterogeneity of the data distribution, we attempted to employ the previously discussed DA methods to fine-tune the segmentation performance of FL-Cov as discussed in the FGDA schemes. As a consequence of applying randomization techniques to FL-Cov, the generated feature representation distorted by Gaussian noise ${\epsilon }_n\left(0,0.01\sigma \right)$ was used as the input to discriminators $D$. The universal network was the concatenation of the generator $G$ and segmentation network. The parameters of the private $G\mathrm{and}C$ are only shared with the universal network. We first trained the $G\mathrm{and}SG$ models for 10 epochs and broadcast the generative loss (Equation (8)). The entire framework was then trained using the settings employed for FL-Cov.

The segmentation results are presented in Figure 3, where the training data used in the Cross schema are written as “Cross-<dataset site>.” The test result on the training dataset is not reported, as all data from this site were used for training. When testing CT scans from the remaining institutions, we do not report a standard deviation (std) for Cross learning experiments. The segmentation results for the remaining schemas are stated in the form of “mean (std).” According to the comparison of the average DSC and NSD, we spotlight the optimal DSC and NSD scores in Figure 3. It can be noted that the Cross-learning schema realizes higher DSC and NSD values than the independent schema with less training data. This is obvious for training on Institution 1 data. When Cross-training is performed on Institution 3 data, the performance is improved by 1.3% and 0.7% over the independent learning schema on Institution 1 and Institution 2, respectively. DSC and NSD of the Ensemble schema do not improve over segmentation results of the independent schema, possibly because it might not take advantage of decisions taken by a variety of segmentation networks (i.e., private models), which impairs its predictive capability.

With respect to FL-Cov, average DSCs show great improvements of 2% for Institution 1, 2% for Institution 2, and 3.5% for Institution 3 over the Cross-learning schema for every institution, and DSC improvements of 2–5% over the Independent and Ensemble schemas. Similarly, the average NSDs achieved by FL-Cov present significant improvements (2.1% for Institution 1, 2.5% for Institution 2, 3.25% for Institution 3) over Ensemble learning. NSD of FL-Cov was greatly improved (2–3%) over the Independent and Ensemble schemas. Compared to FL-Cov, FGDA improved DSC on Institution 1 and Institution 2 by 1.7% (p-value: 0.04416) and 0.7% (p-value: 0.02227), respectively, and reduced the DSC of Institution 3 by 1%. Similarly, the NSD of FGDA was improved by 1.9% (p-value: 0.03562) and 0.2% (p-value: 0.01463) on Institution 2 and Institution 3, respectively, but decreased by 1.5%. Compared to Ensemble settings, FGDA improved DSC by 3.4% (p-value: 0.04085) on Institution 1, and realized equal and less DSC on Institution 1 and Institution 2, respectively. Similarly, the FGDA improved the NSD by 1% on both Institution 1 (p-value: 0.03735) and Institution 2 (p-value: 0.03678) and was comparable on Institution 3 when compared to FL-Cov. The observed behaviour of the DA technique might depend on the data distribution at different institutions.

5.5. Comparative Analysis

To validate the efficiency of the proposed framework, a set of fair experimental comparisons were made between the proposed solution and cutting-edge approaches. The experimental comparisons on each institutional COVID-19 dataset were performed and the corresponding results are given in

Table 2. Statistical significance of proposed FGDA against other learning schemas using DSC and NSD measures.

	Institution 1				Institution 2				Institution 3
	DSC	NSD	JS	p-Value	DSC	NSD	JS	p-Value	DSC	NSD	JS	p-Value
Fed MoE [23]	86.14	82.28	89.11	1.87 × ${10}^{-7}$	86.17	86.44	89.34	1.34 × ${10}^{-8}$	88.96	89.36	91.52	3.46 × ${10}^{-9}$
MS-SFDA [24]	86.36	82.38	87.91	1.34 × ${10}^{-2}$	86.19	86.54	88.93	2.06 × ${10}^{-3}$	89.60	87.71	91.46	7.09 × ${10}^{-10}$
Fed Align [23]	87.46	82.51	89.34	6.11 × ${10}^{-6}$	87.56	85.69	89.41	1.27 × ${10}^{-6}$	88.02	88.63	93.58	2.88 × ${10}^{-3}$
FED [26]	84.98	81.07	85.40	3.73 × ${10}^{-9}$	85.06	84.12	84.52	5.41 × ${10}^{-7}$	84.19	82.89	81.60	6.33 × ${10}^{-11}$
COVID-Net [27]	86.58	83.22	89.24	4.56 × ${10}^{-7}$	86.43	86.07	89.44	3.19 × ${10}^{-9}$	87.03	89.46	93.14	7.86 × ${10}^{-5}$
FGDA	88.8	84.92	90.77	/	88.83	88.61	91.73	/	90.72	89.91	93.66	/

. It is notable that the proposed FGDA can overcome all the competing methods with considerable margins (DSC: 1.34, NSD: 1.7, JS: 1.43) in all performance metrics in the case of Institution 1. Similarly, the proposed FGDA can overcome rall the competing methods with considerable margins (DSC: 1.27, NSD: 2.07, JS: 2.29) in all performance metrics in the case of Institution 2. Moreover, the proposed FGDA can overcome all the competing methods with considerable margins (DSC: 1.12, NSD:1.28, JS:2.14) in all performance metrics in the case of Institution 3.

To validate the robustness of the proposed FGDA against competing learning approaches, the statistical paired t-test was performed with a threshold of p-value < 0.05 (Confidence Interval: 95%). Scipy, which is a public scientific tool [41], was employed to perform this experiment, and the resultants p-values are presented in Table 2. The p-value < 0.05 means that the results from FGDA are statistically significant. It is notable that almost all p-values < 0.05 This further demonstrates the efficiency of the FGDA and supports our findings in the comparative analysis.

5.6. Privacy Analysis

This section discusses and evaluates the impact of the privacy budget on the performance of the proposed framework. In Figure 4, we plot the relationship between the privacy budget of Gaussian DP and segmentation performance. Similarly, in Figure 5, we plot the relationship between the privacy budget of Laplace DP and segmentation performance. It is obvious that there is a significant tradeoff between the performance and privacy of the model, and it can be noted that the performance considerably decreased after the privacy budget exceeded 0.001. This tradeoff necessitates a careful choice of the amount of injected noise during training, which might negatively affect the domain-adaption process.

5.7. Convergence Analysis

This subsection analyses the impact of the synchronisation stride $\tau$ on segmentation performance. To determine the optimal value $\tau$, the performance of the proposed FGDA was evaluated under different values of $\tau$ and the segmentation results are presented in Figure 6. It is worth noting that the performance starts convergence after $\tau =20$, which indicates rapid convergence. This also indicates less communication overhead during the training, as little server–fog interaction is required.

5.8. Stability Analysis

The previous experiments only explored an IoMT federated application that trained ten participants. However, real-world IoMT applications often include thousands of nodes. Experiments were performed to investigate the scalability of the proposed framework. Figure 7 shows the relationship between segmentation performance and the number of fog nodes, ranging from three to 15. It can be seen that when more participants are engaged in federated training, the segmentation performance improves, then stabilizes after the number of fog nodes reaches ten participants. This further explains the ability of the proposed framework to be efficiently trained and applied in a large-scale IoMT environment.

6. Limitations

Though the experimental trials demonstrate that the communication stride, used to regulate the number of times the parameters of the private and global network are upgraded, did not influence the segmentation performance, it is difficult to conclude that the stride parameter is unrelated. Moreover, an extra number of stride values must be scrutinized based on the application. Also, we employed applied methods to study and analyse different LDP techniques (i.e., Gaussian and Laplacian). Nevertheless, the sympathy of the mapping function $f:D\to {\mathrm{R}}^{\mathrm{m}}$ (i.e., the BiSeNet in our situation) is difficult to estimate. Thus, we could not specify the limit. Recent literature [23,24,25,26,27,28,29,30] has established that Laplace and Gaussian noise higher than a particular degree might offer perfect protection from data recovery invasion. Based on certain datasets or applications, it is possible to experimentally approximate an appropriate noise degree according to the attacking viewpoint.

Approaches such as a forest of randomization trees can be used to further improve performance in the Ensemble schema. According to the system model, a central coordinator is responsible for aggregating the local parameters, which makes the overall system vulnerable to a single point of failure and server-side attacks. The number of FL contributors could have an influential role, particularly when an averaging policy is employed to upgrade the global model. Integrating a further-improved network-election mechanism and incentive-updating policy might help to avoid the inclusion of erroneous private networks in updating procedures.

7. Conclusions and Future Work

To conclude, this study takes advantage of fog and cloud computing to design a collaborative FL framework for screening COVID-19-like pandemics from multi-institutional medical images in IoMT networks. The privacy of local parameters is protected using local differential privacy. A domain adaption method (i.e., FGDA) is introduced to tackle the problem of heterogeneous data distribution of the IoMT system. FGDA lessened the impact of heterogeneity and showed acceptable performance. The results showed that FGDA extensively improved segmentation performance on multi-institutional data. The FGDA could be generalized as a medical imaging tool to screen COVID-19-like pandemics.

In future work, several directions can be explored to realize improvements: (1) experiment with the proposed framework on different medical images and diseases; (2) extend the framework to semi-supervised training to enable learning from unlabeled CT scans, and (3) using a decentralized blockchain ledger to improve the security and privacy of federated training.