Web-Based Graphical User Interface Design Integrating MATLAB Server for the Mathematical Model of Human Cardiovascular-Respiratory System

Abstract

A mathematical model of the human cardiovascular-respiratory system is proposed in several MATLAB graphical user interface (GUI) designs. However, it is observed that the latter are not web-based designed, making it hard for users to use them anywhere. This article proposes a web-based GUI design that integrates MATLAB server as a computational tool, worldwide accessible by users, upon subscription. The proposed web-based GUI design has been tested using a small sample of customers, males and females having different attributes relative to the model. After testing across normal and abnormal medical conditions in Rwanda, our findings demonstrate that the proposed web-based GUI design is highly efficient. This suggests robust usability, indicating that users worldwide can securely utilize it to assess pressures on the human cardiovascular-respiratory system.

Keywords

graphic user interface cardiovascular-respiratory system mathematical model MATLAB server web-based

Introduction

Cardiovascular and respiratory diseases represent a major global health burden, driven by multiple factors such as rapid urbanization, lifestyle changes, and increasing environmental pollution.^1-3 These diseases remain among the leading causes of morbidity and mortality worldwide, highlighting the urgent need for effective, accessible, and scalable tools to support diagnosis, monitoring, and analysis. Recent advances in information technology (IT) have significantly contributed to medical research and clinical practice by enabling computational modeling, physiological signal processing, and decision-support systems. In particular, the integration of computational software with intuitive graphical user interfaces (GUIs) has proven effective for analyzing complex biological systems, including the cardiovascular-respiratory system.^4,5 MATLAB has long been used as a powerful computational platform in cardiovascular research. Several studies have employed MATLAB-based GUIs for pulse analysis, heart rate variability assessment, and electrocardiographic signal processing.^6,7 Additional MATLAB toolboxes, such as CEPS and CARE-rCortex, have been developed for advanced analysis of physiological and cardio-respiratory signals.^8-10 Although these tools provide accurate and flexible computational capabilities, they typically require local installation of MATLAB, thereby limiting accessibility, scalability, and widespread adoption. More recent MATLAB developments have improved usability and workflow efficiency, including standalone GUIs for electrocardiogram (ECG) signal quality assessment.¹¹ Nevertheless, these solutions remain largely desktop-oriented and do not address the growing demand for globally accessible, web-based platforms. To overcome the limitations of local desktop environments, some studies have explored client-server and web-oriented architectures, where a graphical interface communicates with a remote computational engine.^12,13 While these approaches represent an important step toward remote access, they often remain limited in terms of full web deployment, ease of use, and worldwide availability.

Novelty and Contributions

In contrast to existing MATLAB GUI tools and previously proposed client-server systems, this article presents a fully web-based GUI that integrates a MATLAB server as a centralized computational engine for the mathematical modeling of the human cardiovascular-respiratory system. The main contributions of this work are as follows:

The design and implementation of a professional web-based medical platform that enables worldwide access without requiring local MATLAB installation by end users. The computational accuracy is the same as that of the desktop version of MATLAB.

The integration of a MATLAB server as a remote computational backend for simulation, parameter estimation, and analysis of a cardiovascular-respiratory mathematical model.

A clear separation between the computation layer and the user interface, improving scalability, maintainability, and usability for researchers and medical professionals.

An experimental evaluation demonstrating the feasibility, reliability, and practical applicability of the proposed web-based system.

By addressing the accessibility and deployment limitations of existing desktop-based and partially web-enabled solutions, the proposed approach provides a novel and practical contribution toward globally accessible tools for cardiovascular-respiratory system modeling. A secure real-time MATLAB computation setup within a web platform is achieved using a client-server architecture.

The work is organized into several key sections. After the introduction that establishes the research context and the need for global IT tools in medical diagnostics, this article presents the mathematical model for cardiovascular-respiratory disease, detailing the equations and parameters used. The next section covers the Web Design and GUI Layout, explaining the technological framework and user interface. This is followed by the evaluation and testing of the system, which includes functional, security, and clinical tests. Finally, this article provides a conclusion, recommendations for future implementations, and limitations.

Methodology

Mathematical Model Equations

The mathematical model of cardiovascular-respiratory system presented is the one developed in Ntaganda et al,¹⁴ which focuses on cardiovascular-respiratory parameter outputs during physical exercise. For a short time, the human body receives the energy anaerobically thanks to the metabolic oxygen consumption rate [MR_O₂(t)] modeled by the following equation

M R_{O_{2}} (t) = M R_{O_{2}}^{r} + (M R_{O_{2}}^{e x} - M R_{O_{2}}^{r}) (1 - e^{- t / τ_{a}}),

where $M R_{O_{2}}^{r}$ denotes the metabolic oxygen consumption rate at rest, $M R_{O_{2}}^{e x}$ is the metabolic oxygen consumption rate during physical exercise, and τ_a denotes the time constant of MR_O₂. In Zhang et al,¹⁰ it is given by the following expression

M R_{O_{2}}^{e x} = M R_{O_{2}}^{r} + ρ W,

where ρ is the parameter describing the physical condition of the exercising person and W is the imposed workload. We consider the constant τ_a = 0.5. Note that in 4τ_a minutes, the momentary oxygen supply reaches 98% of the total oxygen demand. As for the metabolic rate of carbon dioxide production, we have

M R_{C O_{2}} (t) = R Q M R_{O_{2}} (t),

where RQ denotes the constant respiratory quotient. Klabunde¹⁵ yields the systemic arterial blood pressure (P_as) described by the following equation

P_{a s} = P_{d i a s} + \frac{1}{3} (P_{s y s} - P_{d i a s}),

(1)

where P_sys is the systolic blood pressure, and P_dias denotes the diastolic blood pressure. As for the systemic venous blood pressure, we consider

P v s = P a s - F s \times R s,

(2)

where R_s is the peripheral resistance in the systemic circuit, and F_s denotes the blood flow perfusing the tissue compartment. In Crapo,¹⁶ the alveolar ventilation ( $. V_{A}$ ) is formulated as

. V_{A} = f \times (V T - V D),

(3)

where V T is the tidal volume, V D denotes the physiologic dead space, and f represents the number of breaths/minutes (in BPM: breaths per minute). In addition, Crapo¹⁶ has shown that

V T = V C - (I R V + E R V),

(4)

where V C is the vital capacity (in cm³), IRV (in mL) is the inspiratory reserve volume, and ERV (in mL) denotes the expiratory reserve volume. It is known that vital capacity depends on sex, height (h in cm) and age (a in years) as follows (see Vital Capacity¹⁷ for more details)

V C_{f e m a l e} = (21.78 - 0.101 a) h,

(5)

V C_{m a l e} = (27.63 - 0.112 a) h .

(6)

Moreover, the gas concentrations and the corresponding partial pressures are related by the following dissociation laws (for details, see Timischl¹⁸)

C_{a O_{2}} (t) = K_{1} {(1 - K e^{- K_{2} P_{a O_{2}} (t)})}^{2},

C_{a C O_{2}} (t) = K_{C O_{2}} P_{a C O_{2}} (t) + k_{C O_{2}},

where K₁ and K₂ are the constants for the O₂ dissociation curve, K_CO₂ denotes the slope of the physiological CO₂ dissociation curve, and k_CO₂ is the constant for the physiological CO₂ dissociation curve.

The developed mathematical model also involves pressures and concentrations of respiratory gases. Furthermore, PaO₂ is the arterial pressure of oxygen, PaCO₂ denotes the arterial pressure of carbon dioxide, CvO₂ refers to the concentration of bound and dissolved oxygen in the mixed venous blood entering in lungs, and CvCO₂ is the concentration of bound and dissolved carbon dioxide in the mixed venous blood entering in lungs. The regulation of cardiac and respiratory output is insured by heart rate (H) and alveolar ventilation ( $. V_{A}$ ) which play a crucial role in controlling cardiovascular-respiratory system. It is common practice to represent the exchange between different components by arrows, as shown in Figure 1. The model equations relative to the above diagram displaying the exchanges between different components of the system are as follows:

{\begin{matrix} \frac{d P_{a s} (t)}{d t} & = & - γ_{a s} P_{a s} (t) + P_{v s} (t) f_{1} ({\dot{V}}_{A}), \\ \frac{d P_{v s} (t)}{d t} & = & - γ_{v s} P_{v s} (t) + P_{a s}^{α} (t), \\ \frac{d P_{a O_{2}} (t)}{d t} & = & - γ_{O_{2}} P_{a O_{2}} (t) + P_{a C O_{2}} (t) f_{2} (H), \\ \frac{d P_{a C O_{2}} (t)}{d t} & = & - γ_{C O_{2}} P_{a C O_{2}} (t) + P_{a O_{2}}^{β} (t), \\ V_{T O_{2}} \frac{d C_{v O_{2}} (t)}{d t} & = & - M R_{O_{2}} (t) + \\ (\frac{P_{a s} (t) - P_{v s} (t)}{R_{s}}) \times \\ (C_{a O_{2}} (t)) - C_{v O_{2}} (t), \\ V_{T C O_{2}} \frac{d C_{v C O_{2}} (t)}{d t} & = & M R_{C O_{2}} (t) + \\ (\frac{P_{a s} (t) - P_{v s} (t)}{R_{s}}) \times \\ (C_{a C O_{2}} (t) - C_{v C O_{2}} (t)) . \end{matrix}

(7)

where γ_as, γ_vs, γ_O₂, γ_CO₂, α, and β are the constants, and f₁ and f₂ are the logistic functions, and they are in the following form:

f_{1} ({\dot{V}}_{A}) = \frac{C_{1} f_{1, 0}}{f_{1, 0} + (C_{1} - f_{1, 0}) e^{- k_{1} {\dot{V}}_{A}}},

(8)

and

f_{2} (H) = \frac{C_{2} f_{2, 0}}{f_{2, 0} + (C_{2} - f_{2, 0}) e^{- k_{2} H}},

(9)

where k₁ and k₂ are the rate of maximum growth of alveolar ventilation and heart rate, respectively, while C₁ and C₂ are the carrying capacity of alveolar ventilation and heart rate, respectively. Note that at the beginning of the evolutionary process, we have

f_{1} (. V_{A}) = f_{1, 0} and f_{2} (H) = f_{2, 0}

(10)

In Vital Capacity,¹⁷ the value of IRV and ERV are given in Table 1, while Table 2 shows collected parameters from the literature (see Timischl¹⁸). The estimated parameters in Ntaganda et al¹⁴ are in Table 3.

Figure 1.

Diagram of exchange of pressures for a 4-compartmental mathematical model of human cardiovascular-respiratory system, where f₁ and f₂ denote the logistic functions. The parameters MR_O₂ and MR_CO₂ represent the metabolic oxygen consumption rate and the metabolic carbon dioxide production rate, respectively. F_s denotes the blood flow perfusing the tissue compartment. APC and VPC stand for the arterial pulmonary and venous pulmonary compartments, respectively, while ASC and VSC denote the arterial systemic and venous systemic compartments, respectively.

Table 1.

Value of IRV and ERV (in Vital Capacity¹⁷) Used in the Model.

Sex	Parameter	Value
Female	IRV	2100
Female	ERV	800
Male	IRV	3000
Male	ERV	1100

Table 2.

Value of Parameters Collected from Literature (in Timischl¹⁸) to be Used in the Model.

Parameter	Value	Unit	Parameter	Value	Unit
VTO ₂	6	liter	f	15	BPM
VTCO ₂	15	liter	V D	150	mL
ρ	−0.002	-	CaO ₂	0.197	liter_STPD/liter
RQ	0.88	-	K ₁	0.2	-
MROr ₂	0.350	liter_STPD/Min	K ₂	0.046	-
W	75	Watt	$K_{C O_{2}}$	0.0065	-
R_s	14.6	mm Hg.min/liter	$k_{C O_{2}}$	0.244	-
Q = F_s	6	liter/Min

Table 3.

Estimated Model Parameters¹⁴ to be Used in the Model.

Estimated parameter	Male	Female
α	0.0512	0.0621
β	0.2511	0.2341
k ₁	1.0007	1.2147
k ₂	0.1081	0.2018
γ_as	0.4217	0.4342
γ_vs	0.1903	0.1873
γ_O ₂	32.2687	33.2902
γ_CO ₂	0.3045	0.2825

Technological Tools

The proposed web-based GUI requires the following IT tools: MATLAB software to facilitate the estimation of the parameters of the model and MATLAB server to allow numerical estimates or results to be displayed on the webpage of the proposed web-based GUI. Using the widgets in App Designer, user interfaces were created to enable users to provide the input and output within the web-based environment while all computations are performed via the MATLAB server hosting the MATLAB software. The aim of the process is to allow users who do not have MATLAB software to access the outputs of the customer’s results via the proposed website. Figure 2 shows the scheme demonstrating the workflow scenarios intended.

Figure 2.

MATLAB web apps workflow. Step 1 shows that the graphical user interface is designed and programmed using the App Designer from MATLAB. Step 2 indicates how the designed and programmed application can be compiled into a package and transferred to step 3, where the mathematical model application can be hosted and deployed on the MATLAB web app server. The end user can access the system without having MATLAB on their machines. A web-based GUI offers the ability to access the system from anywhere as long as there is Internet access.

The reporting of this study follows the Enhancing the QUAlity and Transparency Of health Research (EQUATOR) Network guidelines, specifically adhering to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) checklist and reporting standards.¹⁹

Web-Based Graphical User Interface Layout

The current web-based GUI proposed for the mathematical model of cardiovascular-respiratory system is designed as follows: users sequentially, starting with the receptionists, followed by the nurse, and then the doctor, each opens the website https://matwebgui.com and access a webpage portal presenting the users with 2 options, including Login and Register. For registration, the following inputs are required: First name, Last name, Email, Contact, Username, Password, Gender, and Position, while the login, if registered, requires only Username, Password, and Position. To log in to the system, the receptionist, accessing the webpage, employs his or her username, password, and position and then accesses the customer registration page, where he or she inputs the customer’s physiological characteristics: First name, Last name, Phone, Gender, Age, and press on the Register button. Upon this registration, the customer data is saved in the system database, and the receptionist is ready to register a new customer using the customer registration page. This service is administered for every new customer present at the reception’s desk. To log in to the system, the nurse uses his or her credentials, ie, username, password, and position and then accesses the customer database page, which displays the status “Pending” for every customer in the system. He or she requires to process each customer by pressing on the button “Pending.” This leads the nurse to a customer-measured parameters page, where he or she inputs the customer’s eight parameters as discussed on the mathematical model (height, P_sys, PaO₂, CvO₂, heart rate, P_dias, PaCO₂, CvCO₂) and then submits them into the customer database. Likewise, to log in to the system, the doctor uses his or her username, password, and position and accesses where he or she starts processing each customer by pressing the button “Compute.” This action pushes customer’s data into MATLAB server for computation tasks required. Whenever the tasks of computation are completed, estimates from MATLAB server are sent and displayed in the web-based GUI page for each customer processed.

Web Design Components

In this section, a succinct description of the web design components is presented step by step whose users include, namely, a receptionist, a nurse, a medical doctor, and an administrator.

Front-end web interface and login page. The front-end web page displayed in Figure 3 is obtained via the link https://matwebgui.com, which is the website proposed in this article. New users click on the sign-up button and proceed to the next sign-up page. The sign-up app is displayed in Figure 4. On the left-hand side, credentials for new users (Receptionist, Nurse, Doctor, and Admin) are required, while on the right-hand side, a dropdown menu for selecting gender and role (Position) is provided. When every item therein is filled, the new user presses the “Register” button and moves to the login web page displayed in Figure 5 and proceeds to the next web page.

Figure 3.

A front GUI allowing any users to login or signup, prior to feeding in the system necessary credentials that identify the users.

Figure 4.

Necessary credentials that are required for new users, including first name, last name, email, contact (cell phone number), username, and a password. The user should select his or her gender and work position.

Figure 5.

The required information for users to log into the system includes a username, password, and job position.

New customer’s web receptionist page. After the login, the receptionist assesses the customer web page described in Figure 6a, which shows 2 options: New Customers and Recorded Customers. For the first option (see Figure 6b), the receptionist has to provide inputs, including “First name, Last name, Phone number, Age, ID/Passport number, Cell, and Village” and select the “Gender, District, Sector, and Insurance type” of the customer. Once all the inputs have been collected, the receptionist presses the button “Save” and he or she would then be ready to attend to the next new customer. When the save button has been activated, data recorded are automatically sent to “Database.” The button “Close” is clicked if the receptionist does not wish to record the customer’s data. For the second option, pressing on the button “Recorded customers,” the receptionist displays the designed web list of customers with registration number, first name, name, and phone. The sample of this list is shown in Figure 6c.

Figure 6.

The ‘Customer Form’ is completed by the receptionist, who clicks on ‘New Customer’ (a) to enter all the required customer information (b). Thereafter, a list of recorded customers is displayed (c).

The customer’s web nurse page. Once the nurse logs into the designated website, they can access the pending customers recorded by the receptionist or view the list of recorded customers. The nurse’s window, showing these 2 options, is depicted in Figure 7a. By clicking the “Pending” button, a new window (see Figure 7b) will appear. As shown in Figure 7c, the nurse is required to enter the cardiovascular parameters, which are then saved in the database after pressing the “Submit” button. These parameters include height, heart rate, systolic arterial pressure, diastolic arterial pressure, arterial pressure of oxygen, arterial pressure of carbon dioxide blood pressure, concentration of bound and dissolved oxygen in the mixed venous blood entering in lungs, and concentration of bound and dissolved carbon dioxide in the mixed venous blood entering in lungs. When this is done, this window is closed, and from the database, the nurse can process a new customer. By pressing the “Reports” button, the nurse can search the list of all recorded customers. The search is based on the specified start and end dates, as shown in Figure 7d.

Figure 7.

The main page of the nurse (a), list of the customers to enter the parameters of the cardiovascular-respiratory system (b), list of the parameters to set (c), and the search functionality (d).

The customer’s web medical doctor page. After accessing the website via its URL, the doctor logs in and selects their work position as “Medical Doctor.” He or she then gains direct access to the database, which contains customer information that has been sequentially entered by the “Receptionist” and the “Nurse.” He or she presses the ”Compute” button, which runs the computation of the model and produces the outputs, which are estimates of the following quantities:

P_{a s} E, P_{v s} E, P_{a} O_{2} E, P_{a} C O_{2} E, C_{v} O_{2} E, C_{v} C O_{2} E

Each one of these estimates is then compared to a medical threshold confidence interval, which allows the doctor to forward to the patient a medical diagnostic of his or her cardiovascular and respiratory disease. When this is done, an option to “save” and/or to “print” the patient’s results can be selected by the doctor for record-keeping purpose and then “close” the web. At this level, the medical doctor is ready to open the window (Figure 8a), showing 3 main buttons: “Pending,” “Consulted,” and “View-List.” Pressing on the “Pending” button, the window of the parameters sent by the nurse is displayed (see sample in Figure 8b). To access Figure 8c and d, the medical doctor must click on the “Consulted” and “View-List” buttons, respectively. The figure illustrates the list of consulted customers and the search functionality, which allows users to specify start and end dates to retrieve data for the consulted customers.

Figure 8.

The main page of the medical doctor (a), list of the customers to proceed the cardiovascular-respiratory system test (b), sample of the consulted customers (c), and the search functionality (d).

The outputs expected using the web are comprised estimated parameters along with their immediate medical scale indicating the patient’s plausible health diagnostic. The parameter estimates include the systemic arterial blood pressure (P_as), the systemic venous blood pressure (P_vs), and the values of PaO₂, PaCO₂, CvO₂, and CvCO₂.

The interface design follows a structured, sequential workflow aligned with real hospital operations. By separating responsibilities across receptionists, nurses, and doctors, the system minimizes cognitive overload and reduces data entry errors. Clear navigation pathways, guided parameter input fields, and immediate visualization of computed results enhance usability for medical professionals with varying levels of technical expertise.

A MATLAB Graphical User Interface Design Components

In this work, the design under consideration deals with both genders. For each case, the cardiovascular-respiratory parameters of the customer are entered in the GUI, as shown in Figure 9.

Figure 9.

MATLAB design of output for cardiovascular-respiratory system.

In the GUI, the medical practitioner is expected, on one hand, to capture first the customer’s cardiovascular-respiratory initial parameters. They include age (a), height (h), heart rate (H), systolic arterial pressure (P_sys), diastolic arterial pressure (P_dias), arterial pressure of oxygen (PaO₂), arterial pressure of carbon dioxide blood pressure (PaCO₂), concentration of bound and dissolved oxygen in the mixed venous blood entering in lungs (CvO₂), and concentration of bound and dissolved carbon dioxide in the mixed venous blood entering in lungs (CvCO₂). The parameters are created using the App Designer, which consists of an interactive development environment for designing an app layout and programming its behavior. The medical doctor evaluates the clinical results of the user. The outputs expected are seen by the “Medical Doctor” using the web. They comprised estimated parameters along with their immediate medical scale indicating the customer’s plausible health devices. The parameter estimates include the systemic arterial blood pressure (P_as) and the systemic venous blood pressure (P_vs), respectively, described in equations (1) and (2). Other outputs comprised the estimated values of PaO₂, PaCO₂, CvO₂, and CvCO₂.

Web-Based Graphical User Interface Evaluation and Clinical Tests

In this section, the proposed web-based GUI design integrating MATLAB server is evaluated, and a clinical test is presented for a sample of customers (Figure 8c). This study was conducted using MATLAB R2018b. Numerical simulations were performed with the ode45 solver, which implements an explicit Runge-Kutta (4,5) method for solving non-stiff ordinary differential equations. The simulation covered a 30-minute exercise period, with computation time on the order of minutes. An adaptive timestepping scheme was employed, with convergence controlled through specified relative and absolute tolerance settings to ensure numerical accuracy and stability.

Web-Based Graphical User Interface Design Evaluation

To evaluate the current proposed web-based GUI design that integrates a MATLAB server, 5 tests were conducted successfully, namely “Test environment Setup” to assess its effectiveness and compatibility with different browsers as discussed in Seffah et al²⁰and Puskar²¹, The process is carried out by accomplishing the following tasks: “Functional test” to validate its features and reliability user interactions, which include customer’s registration, medical record access, data entry, and result display (see Kaner et al²²); “Security test” to ensure customer’s data are safeguarded and unauthorized access or breaches are prevented (see Terry²³ and Luxton et al²⁴); “Documentation and reporting test” to ascertain detailed reliable documentation and reports are generated and findings unequivocally communicated to customers including appropriate diagnostics based on the findings;²⁵ and “Test execution” to ensure GUI elements, navigation of the web, medical forms, data entry by the receptionists and nurses, search functions, data retrieval, and result exhibits adhere rigorously to medical standards.²⁵ To reinforce user trust and clinical reliability, the system architecture incorporates secure authentication protocols, encrypted communication between the web interface and MATLAB server, and structured role-based access control for receptionists, nurses, doctors, and administrators. In addition, database isolation mechanisms ensure patient confidentiality. These measures support compliance with recognized medical data governance principles and enhance confidence in subscription-based, cloud-hosted deployment models. The system is designed to complement, not replace, clinical judgment by providing quantitative physiological indicators to assist healthcare professionals in decision-making.

Moreover, the 4 web-based GUI design tests have been validated through a run of a clinical sample results presented in Figure 8c. This sample displays a plausible symptom related to the parameters of the model. The implementation of the current web-based GUI integrating MATLAB server is assumed to be user-friendly. The following steps are followed:

The user (nurses, receptionists, and doctors) signs up into the system or “https://matwebgui.com” with “First name,” “Last name,” “Email,” “Contact,” “Username,” “Password,” “Gender,” and “Position” (see Figure 4) and logs in with “Username,” “Password,” and “Position.”

The receptionist, once in the system, proceeds with the customer’s registration, capturing the following demographic data: “First name,” “Last name,” “Phone,” “Gender,” and “Age” (see Figure 6b) and clicks on the “Register” button to submit the customer information to the database. This is done for every customer requesting the service.

The next step is the nurse who, upon login, accesses customers’ database (see Figure 7a) and retrieves each customer’s data by clicking on the button “Pending.” At this stage, the nurse accesses Figure 7b requesting to input customers’ parameters and submit them into the database (Figure 7c).

At the doctor’s page, he or she logs into the system using personal credentials and accesses the database in Figure 8b, ticks a customer at a time, and proceeds. At this stage, the web-based GUI sends information into the MATLAB server for computation tasks (see Figure 9).

At the completion of all computation tasks requested, the MATLAB server sends results or estimated parameters in the web-based GUI.

Once the estimated parameters are obtained, the doctor interprets them by comparing them with the range for a healthy customer.

At the final stage, the doctor provides the customer’s advice, prints and saves the estimated parameters into the database and can go back to step 4 to tick the next customer and run steps 5 through 7.

Clinical Tests

Let us focus on how the medical doctor obtains the customer’s test results. The process involves selecting the customer in the “Select” column (see Figure 8b) and clicking the “Proceed” button. This action removes the customer from the list of those awaiting the cardiovascular-respiratory system test, so that he or she is added to the list of consulted customers, as shown in Figure 8c. For example, if the medical doctor selects Peter’s name, clicks the “Proceed” button, returns to the main window, and then clicks the “Consulted” button followed by the “result” button, the customer’s outputs will be displayed on the web page, as shown in Figure 10a. The same process is used to obtain the results for Jennifer, as shown in Figure 10b.

Figure 10.

A web page to display the results computed for the customer using a web design that integrates a MATLAB GUI, comparing them to the range for a healthy customers, where all parameters fall within the required range (a) and beyond this range (b).

The results are computed similarly for Jane and Joel. They are depicted in Figure 11a and b, respectively.

Figure 11.

A web page to display the results computed for the customer using a web design that integrates a MATLAB GUI, comparing them to the range for a healthy customers, where some parameters fall within the required range and others are beyond it.

Discussion of Findings

The current estimates from tests conducted on 4 sampled units/customers of diverse medical physiological conditions demonstrate that the web-based GUI design integrating the MATLAB server is running indeed, delivering realistic medical results from which doctor(s) can now formulate any medical diagnostic. Taking the reference parameters into consideration, Figure 10a shows that Peter presents the healthy medical conditions, while Jennifer is in abnormal conditions, as shown in Figure 10b. Figure 11a illustrates that all parameters of the cardiovascular-respiratory system for Jane are outside the normal range, except for the concentration of bound and dissolved oxygen in the mixed venous blood entering the lungs (CvO₂). The same behavior occurs for Joel, except that only the concentration of bound and dissolved oxygen in the mixed venous blood entering the lungs (CvO₂) and the arterial pressure of oxygen (PaO₂) are within the required range (Figure 11b). Two customers of different genders may have different estimated values, even if their input values are identical. Although the proposed web-based GUI integrating MATLAB server demonstrates effective functionality within a single institutional deployment, its current configuration supports one medical institution at a time. For global scalability, future development will focus on multi-tenant architecture, allowing multiple healthcare institutions to operate independently within the same cloud-hosted infrastructure. This enhancement will include institution-specific data isolation, configurable licensing mechanisms, scalable server orchestration, and secure distributed deployment to enable broader adoption across hospitals and research centers worldwide.

Conclusion and Recommendations

Conclusion

In this work, it has been observed that either MATLAB GUI or some web-based GUI designs have been used as IT tools to model the human cardiovascular-respiratory systems. However, the accessibility for users was quite limited. The cost of MATLAB software being expensive, individual users faced huge difficulties to use the proposed tools in their medical profession. To circumvent the problem, this article proposes a web-based GUI design integrating MATLAB server to be used to model the human cardiovascular-respiratory system in Rwanda, thus widening accessibility of the needed tool, given that it requires only access to the Internet, no need to have a pre-installed MATLAB software. While the model under application remains unchanged, including the estimation of its parameters, the novelty of this article is to have made it a web-based design, thus opening accessibility to users worldwide. Standard efficiency web-based GUI tests, including “environment setup,” “Functional,” “Security,” “Documentation and reporting,” and “Execution” were conducted successfully. Moreover, to evaluate its functionality, a sample of size 10 of customers with plausible symptoms of cardiovascular-respiratory problem has been tested using data captured from customers of different medical attributes, including age, height, heart rate, systolic and diastolic blood pressure, arterial oxygen partial pressure, and an arterial pressure of carbon dioxide blood pressure, a concentration of bound and dissolved oxygen in the mixed venous blood entering in lungs, and a concentration of bound and dissolved carbon dioxide in the mixed venous blood entering in lungs. Tested at normal and off-normality health measure, the proposed web-based GUI integrating a MATLAB server for internal computation exhibited consistently customer results that are medically realistic. The implementation of the proposed web-based GUI design entails the receptionists and the nurses, once they access the web, performing their respective duties sequentially: capturing the customers’ identity and the customers’ physiological measurements and then submitting data to a database hosted by the server for further processing. Likewise, the medical doctor accesses the web through login, retrieves the customers’ data from database and proceeds by estimating the customers’ physiological parameters through the MATLAB server that performs the computations and delivers results through the web-based GUI design for the doctor to proceed with diagnostics for each customer. As a medical website, it is therefore proposed to be used by professional to examine the human cardiovascular-respiratory disease.

Limitations

The first limitation of the proposed web-based GUI design is its current lack of universal integration; the system is customized to function for a single medical institution at a time. While it successfully integrates a MATLAB server to eliminate the need for users to have expensive, pre-installed software, it does not yet support multiple institutions by default. As a consequence, its broader application across various health centers is restricted until further robust customization is completed. The second limitation is that the evaluation of the system presented was conducted on a relatively small sample of customers in Rwanda, which restricts the generalizability of findings to broader populations. The third limitation is that the system requires accurate input of physiological parameters by nurses and doctors; thus, any measurement errors or data entry mistakes could propagate through the model, leading to misleading outputs. All these have been identified as a key area for future work, aiming to make the platform (https://matwebgui.com) clinically robust to support any medical institution upon licensing.

Recommendations

Having tested successfully the proposed web-based GUI design that integrates MATLAB server for the developed mathematical model of human cardiovascular-respiratory system in Rwanda, we would recommend its use:

To be adopted by international and all national health centers, including mostly referral hospitals and district hospitals, through licensing.

To be integrated into the medical school’s curriculum.

Footnotes

Acknowledgements

The authors are deeply indebted and sincerely grateful to the University of Rwanda (UR) for supporting this work through its Directorate of Research and Innovation (research grant under the UR-Sweden collaboration for the 2020/2021 cycle).

Authors’ Note

In accordance with Sage’s Artificial Intelligence policy, the authors disclose that generative AI tools (ChatGPT-4 and Google Gemini) were used exclusively for language refinement, grammar correction, and stylistic enhancement of the manuscript. These tools were applied strictly to improve clarity and readability. No scientific data, mathematical modeling, computational results, analyses, figures, or interpretations were generated, modified, or influenced by artificial intelligence systems. All research design, modeling, simulations, validation processes, and conclusions remain entirely the intellectual work and responsibility of the authors.

ORCID iDs

Jean Marie Ntaganda

Dominique Harelimana

Ethical Considerations

Ethical clearance was unnecessary because the research involved no human participants, confidential data, or interventions.

Consent to Participate

Participation consent declarations were not applicable because the study involved no human subjects or personal data.

Author Contributions

Jean Marie Ntaganda: Conceptualization; Investigation; Funding acquisition; Writing—original draft; Methodology; Validation; Visualization; Writing—review & editing; Software; Formal analysis; Project administration; Data curation; Supervision; Resources.

Solange Mukeshimana: Writing—original draft; Methodology; Writing—review & editing; Formal analysis; Resources; Data curation.

Marcel Ndengo: Conceptualization; Writing—original draft; Methodology; Validation; Visualization; Writing—review & editing; Formal analysis; Data curation.

Theogene Bizimungu: Conceptualization; Methodology; Software; Data curation; Formal analysis; Validation; Investigation; Writing—original draft; Writing—review & editing; Visualization.

Dominique Harelimana: Conceptualization; Methodology; Software; Data curation; Formal analysis; Validation; Investigation; Writing—original draft; Writing—review & editing; Visualization.

Celestin Kurujyibwami: Conceptualization; Investigation; Writing—original draft; Methodology; Validation; Visualization; Writing—review & editing; Formal analysis; Data curation.

Marie Aimee Uwineza: Conceptualization; Investigation; Writing—original draft; Writing—review & editing; Visualization; Data curation.

Jean de Dieu Maniraguha: Writing—original draft; Visualization; Writing—review & editing; Data curation.

Lydie Mpinganzima: Writing—original draft; Writing—review & editing; Visualization; Formal analysis; Data curation; Methodology.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was funded by the University of Rwanda under the Sweden collaboration under grant number 2020/2021 cycle.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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