A Data-Driven Approach to Quantifying Immune States in Sepsis

Summary

This study investigates the immune condition in sepsis by analyzing the quantitative relationships among white blood cells, lymphocytes, and neutrophils in sepsis patients and healthy controls using data visualization analysis and three-dimensional numerical fitting to establish a mathematical model.

Abstract

In sepsis, understanding the interplay among white blood cells, lymphocytes, and neutrophils is crucial for assessing the immune condition and optimizing treatment strategies. Blood samples were collected from 512 patients diagnosed with sepsis and 205 healthy controls, totaling 717 samples. Data visualization analysis and three-dimensional numerical fitting were performed to establish a mathematical model describing the relationships among white blood cells, lymphocytes, and neutrophils. Self-organizing feature map (SOFM) was employed to automatically cluster the sepsis sample data in the three-dimensional space represented by the model, yielding different immune states.

Analysis revealed that white blood cell, lymphocyte, and neutrophil counts are constrained within a three-dimensional plane, as described by the equation: WBC = 1.098 × Neutrophils + 1.046 × Lymphocytes + 0.1645, yielding a prediction error (RMSE) of 1%. This equation is universally applicable to all samples despite differences in their spatial distributions. SOFM clustering identified nine distinct immune states within the sepsis patient population, representing different levels of immune status, oscillation periods, and recovery stages.

The proposed mathematical model, represented by the equation above, reveals a basic constraint boundary on the immune cell populations in both sepsis patients and healthy controls. Furthermore, the SOFM clustering approach provides a comprehensive overview of the distinct immune states observed within this constraint boundary in sepsis patients. This study lays the foundation for future work on quantifying and categorizing the immune condition in sepsis, which may ultimately contribute to the development of more objective diagnostic and treatment strategies.

Introduction

Sepsis, a life-threatening organ dysfunction caused by a dysregulated host response to infection, remains a significant challenge in critical care medicine¹. Despite advances in understanding the pathophysiology of sepsis, the complex interplay between the immune system and pathogens continues to pose difficulties in diagnosing and treating this condition effectively². Current clinical approaches often focus on monitoring infection indicators, organ function, cytokines, microbial detection, and gut microbiome³. However, there is a growing recognition of the crucial role played by immune cells, particularly white blood cells, lymphocytes, and neutrophils, in the progression and resolution of sepsis⁴.

During the course of sepsis, the immune system undergoes a complex series of changes, characterized by an initial hyperinflammatory phase followed by a prolonged immunosuppressive phase⁵. The early phase is marked by a surge in neutrophil counts and a concomitant decrease in lymphocyte populations, reflecting the activation of innate immune responses and the suppression of adaptive immunity⁶. As the condition progresses, neutrophil levels may oscillate or become exhausted while lymphocyte counts continue to decline, leading to a state of immunosuppression that renders patients vulnerable to secondary infections⁷. Understanding the dynamic interplay among these immune cell populations is crucial for accurately assessing the immune status of sepsis patients and devising targeted interventions.

Traditional approaches to analyzing immune cell counts in sepsis have relied on univariate or bivariate analyses, which fail to capture the complex relationships among multiple immune parameters⁸. Recent advances in data visualization and machine learning techniques have opened up new possibilities for exploring high-dimensional immunological data⁹. In particular, three-dimensional scatter plot visualization and self-organizing feature maps (SOFM)¹⁰ have shown promise in uncovering hidden patterns and identifying distinct immune states in various disease contexts.

This study aims to investigate the immune condition in sepsis patients by analyzing the quantitative relationships among white blood cells, lymphocytes, and neutrophils using advanced data visualization and clustering techniques. The hypothesis is that these immune cell populations are constrained within a three-dimensional space governed by an underlying mathematical relationship. By uncovering this relationship and identifying distinct immune states using SOFM, the study seeks to provide a framework for understanding the immune dynamic states in sepsis and facilitating clinical decision-making.

The approach involves collecting blood samples from 512 sepsis patients admitted to the intensive care unit (ICU) and 205 healthy individuals, totaling 717 samples. The study population included both male (54.3%) and female (45.7%) participants, with ages ranging from 35 to 100 years (mean age: 73.5 years). Three-dimensional scatter plot visualization and numerical fitting are applied to establish a mathematical model describing the interplay among white blood cells, lymphocytes, and neutrophils in both sepsis patients and healthy controls. SOFM is then employed to automatically cluster the sepsis sample data in the three-dimensional space, yielding different immune states. By comparing the immune profiles and spatial distributions of sepsis patients with those of healthy individuals within the constraint boundary represented by the mathematical model, the study aims to gain insights into the pathophysiological mechanisms underlying sepsis and identify potential targets for immunomodulatory therapies.

By providing a quantitative method for assessing the immune condition of sepsis patients, the approach could enable more precise staging of the disease and guide the selection of appropriate interventions. Furthermore, the identification of distinct immune states using SOFM may lay the foundation for future research on personalized immunotherapy approaches tailored to the specific immune profiles of individual patients.

In summary, this study presents an approach to understanding the immune condition in sepsis by leveraging advanced data visualization and machine learning techniques. By uncovering the mathematical relationship between key immune cell populations in sepsis patients and healthy controls and identifying distinct immune states in sepsis patients, the study provides a new perspective on the complex immune dynamics in sepsis. This approach enables a more precise assessment of the disease state (Different Clusters) and can guide the selection of appropriate interventions, ultimately contributing to developing more effective diagnostic and therapeutic strategies.

Protocol

This study explores the immune condition in sepsis patients by investigating the relationships among white blood cells, lymphocytes, and neutrophils. The patients were enrolled in the intensive care unit (ICU) of Dongzhimen Hospital in Beijing, China, and underwent standard blood tests after providing informed consent. The study was conducted as per the guidelines of the institutional human research ethics committee. Data grouping and detailed data content can be found in Supplementary Table 1. The software tools utilized in this study are enumerated in the Table of Materials.

1. Data collection and preparation

NOTE: White blood cells, neutrophils, and lymphocytes were selected as key indicators of the immune condition in sepsis patients. This choice is based on the well-established clinical observations that lymphocyte counts tend to be suppressed and gradually decrease, while neutrophil counts often oscillate in sepsis patients. These two cell types have been empirically recognized as important markers of the immune status in sepsis patient populations. However, the precise quantitative relationship among these parameters has not been clearly reported in the literature. Therefore, white blood cells, neutrophils, and lymphocytes were chosen as a starting point for quantifying the immune condition in sepsis patients.

1. Installing MATLAB Spreadsheet Link for Excel Add-In.
   1. Open Microsoft Excel and navigate to the Insert tab on the ribbon.
   2. Click on Get Add-ins in the Add-ins section.
   3. In the Office Add-ins dialog box, search for MATLAB Spreadsheet Link in the search bar.
   4. Locate the MATLAB Spreadsheet Link for Excel add-in in the search results and click on the Add button.
   5. Read and accept the terms and conditions, then click Continue to proceed with the installation.
   6. If prompted, log in with a MathWorks account or create a new account to access the add-in.
   7. Once the installation is complete, the MATLAB Spreadsheet Link tab will appear on the Excel ribbon.
   8. Click on the MATLAB Spreadsheet Link tab to verify that the add-in is installed and ready to use.
2. Send data into MATLAB workspace.
   1. Open the spreadsheet containing the sepsis patient data, including white blood cell counts, lymphocyte counts, and neutrophil counts.
   2. Ensure that the data is organized in a structured format, with each variable (white blood cell count, lymphocyte count, and neutrophil count) in a separate column and each patient in a separate row.
   3. Select the range of cells containing the white blood cell counts, lymphocyte counts, and neutrophil counts.
   4. Click on the MATLAB Spreadsheet Link tab in the Excel ribbon.
   5. In the MATLAB Spreadsheet Link tab, click the Send Data to MATLAB button.
   6. In the Send Data to MATLAB dialog box, choose the appropriate MATLAB instance from the dropdown menu if multiple instances are running.
   7. Specify the variable name for the data in the Variable name field. For example, sepsis_immune_data.
   8. Select the desired data type for the imported data in MATLAB (e.g., numeric matrix).
   9. Click OK to send the data to the MATLAB workspace.
   10. Switch to the MATLAB application and verify that the data has been successfully imported by checking the workspace for the specified variable name (e.g., sepsis_immune_data).
3. Checking the data in MATLAB
   1. After sending the sepsis patient data (white blood cell counts, lymphocyte counts, and neutrophil counts) to MATLAB using the MATLAB Spreadsheet Link add-in, switch to the MATLAB application.
   2. To check the contents of the imported data, type the variable name in the MATLAB command window and press Enter.

2. Three-dimensional visualization of white blood cells, lymphocytes, and neutrophils

1. Generating the plot using the Immune_scatter3 function
   1. The variable A stores the immune data of sepsis patients. Call the function Immune_scatter3(A) to obtain a graphical user interface (GUI) displaying the three-dimensional scatter plot of the samples, as shown in Figure 1.
      NOTE: The fitting error between the three-dimensional plane and the sample distribution in the plot is very small. Section 3 will provide the exact formula.
2. The GUI usage
   1. Explore and analyze the three-dimensional scatter plot using the interactive features provided by the generated GUI.
      1. Rotate: Click and drag the plot to rotate it in 3D space, allowing viewing the sample distribution from different angles.
      2. Pan: Right-click and drag the plot to move it horizontally or vertically, adjusting the visible area of the plot.
      3. Zoom: Use the mouse wheel or the zoom controls in the toolbar to zoom in or out of the plot, focusing on specific regions or samples.
      4. Data cursor: Click on individual samples to display their corresponding values for white blood cells, lymphocytes, and neutrophils.
         NOTE: By utilizing these interactive features, clinicians can gain insights into the relationships and patterns among white blood cells, lymphocytes, and neutrophils in sepsis patients, facilitating the exploration and analysis of the immune data.

3. The formula

1. In the MATLAB workspace, assign the neutrophil count, lymphocyte count, and white blood cell count to the variables X, Y, and Z, respectively.
2. To obtain the precise mathematical expression (formula 1; WBC = 1.098 × Neutrophils + 1.046 × Lymphocytes + 0.1645 (RMSE: 1%)) of the three-dimensional plane in Figure 1, invoke the following command:
   [fitresult, gof, output] = fit ([X, Y], Z, 'poly11')
   NOTE: This formula quantitatively describes the relationship among white blood cells, neutrophils, and lymphocytes in sepsis patients, providing a concise and accurate representation of the immune data.
3. To evaluate the goodness of fit, calculate the normalized root mean square error (NRMSE) using the following command:
   gof.rmse / (max(Z) - min(Z))
   NOTE: The resulting NRMSE value of 1% indicates that the fitted plane (formula 1) closely approximates the actual sample distribution in the three-dimensional space. This low error level underscores the reliability and validity of the obtained mathematical expression in capturing the intricate relationships among the immune parameters in sepsis patients.

4. Immune condition in sepsis

NOTE: Self-Organizing Feature Maps (SOFM) were employed for unsupervised clustering to identify immune conditions in sepsis patients.

1. By invoking the Immune_Condition function, generate clusters of sample points on the three-dimensional plane represented by formula 1, as depicted in Figure 2.
2. Use the interactive visualization features for Figure 2 as described in Step 2.2.
   NOTE: Figure 2 showcases nine automated clusters, labeled Cluster1 through Cluster9, derived from SOFM's unsupervised machine learning approach. This clustering technique takes into account both the spatial topology and the density of the samples, enabling the identification of distinct immune conditions within the sepsis patient population.

5. Typical immune oscillation trajectories in sepsis

1. Based on Figure 2, use the hold on command to maintain the figure in an overlayable state, then use the following commands to create a three-dimensional plot of the typical patient's trajectory data.
   hold on
   for i=1: size(p,1)-1
   pause (3); plot3(p (i: i+1,2), p (i: i+1,3), p (i: i+1,1),'k','Linewidth',3);
   end

Results

The progression of sepsis involves a complex interplay between the human immune system and invading pathogens. In clinical diagnosis and treatment, much attention is focused on infection indicators, organ function markers, cytokines, microbial detection, and even the gut microbiome. However, this study emphasizes the importance of three common immune indicators: white blood cells, neutrophils, and lymphocytes, which are not without basis. Research has demonstrated that the pathological pr...

Discussion

This study presents an approach to understanding the immune condition in sepsis by leveraging advanced data visualization and machine learning techniques. By uncovering the mathematical relationship among key immune cell populations and identifying distinct immune states, the study provides a new perspective on the complex immune dynamics in sepsis and contributes to the development of more effective diagnostic and therapeutic strategies^11,12. The key findings in...

Materials

Name	Company	Catalog Number	Comments
MATLAB	MathWorks	2022B	Computing and visualization
Probabilistic Scatter Plots for Immune States	Intelligent  Entropy	Immune States V1.0	Beijing Intelligent Entropy Science & Technology Co Ltd. Modeling for CT/MRI fusion