Sepsis progression and outcome: a dynamical model

Abstract

Background: Sepsis (bloodstream infection) is the leading cause of death in non-surgical intensive care units. It is diagnosed in 750,000 US patients per annum, and has high mortality. Current understanding of sepsis is predominately observational and correlational, with only a partial and incomplete understanding of the physiological dynamics underlying the syndrome. There exists a need for dynamical models of sepsis progression, based upon basic physiologic principles, which could eventually guide hourly treatment decisions.

Results: We present an initial mathematical model of sepsis, based on metabolic rate theory that links basic vascular and immunological dynamics. The model includes the rate of vascular circulation, a surrogate for the metabolic rate that is mechanistically associated with disease progression. We use the mass-specific rate of blood circulation (SRBC), a correlate of the body mass index, to build a differential equation model of circulation, infection, organ damage, and recovery. This introduces a vascular component into an infectious disease model that describes the interaction between a pathogen and the adaptive immune system.

Conclusion: The model predicts that deviations from normal SRBC correlate with disease progression and adverse outcome. We compare the predictions with population mortality data from cardiovascular disease and cancer and show that deviations from normal SRBC correlate with higher mortality rates.

Figure 1

Correlation between Q and redundant body mass (r%). Solid line is equation (1.8); dots are average values of Q (1.9) with a least squares fit to (1.8) yielding q = 0.233. Each point presents the average value calculated from 15 observations. Error bars represent 95% confidence intervals.

Figure 2

Correlation between observed SRBC (v) and its estimate (v_m) calculated from height. The estimate v_m is calculated from equ. (1.10). Each point presents the average from 12 cases. Dashed line presents v = v_m.

Figure 3

Correlation between two estimates of H: H_g vs. H_v. H_g is calculated from fasting glucose concentration; H_v is calculated from the specific rate of blood circulation. Each point presents the average value calculated from eight observations for q = 0.256 and g= 4.05 mmol/L.

Figure 4

Correlation between two estimates of H: H_g vs. H_w. H_g is calculated from fasting glucose concentration; H_w is calculated from lung capacity. Each point presents the average value calculated from seven observations for g= 3.9 mmol/L.

Figure 5

Correlation between two estimates of H: H_v vs. H_m. H_vis calculated from the specific rate of blood circulation; H_m is calculated from body mass. Each point presents the average value calculated from 15 observations for q = 0.236.

Figure 6

Dynamics of the relative concentration of the pathogen at different values of H. H = 1 – sub clinical form, H = 0.85 – chronic form, H = 0.7 – acute form, H = 0.5 – lethal outcome. Y-axis is the log(X₁(t)).

Figure 7

Dynamics of organ damage during a disease at different values of H. Increase in H leads from acute disease forms to lethal outcome. Y-axis is X₄(t).

Figure 8

Typical age specific dynamic of H. Each dot presents the average from 4 cases; solid line corresponds to equ. (5.2) when a = 2.0021, b = 0.2428, H₀ = 0.8953, λ = 0.0026, X₀ = 65.5076.

Figure 9

Correlation between the total mortality from cardiovascular diseases plus cancer (CVDC; annual number of cases) and the measure of discrepancy (S). S (equ. 5.3) is calculated from female and male mortality rates in Sweden (1951 – 1992). Each point presents the result of averaging (14 cases) for close values of S.

Figure 10

Correlation between the total mortality from cardiac and neoplastic diseases (CND; annual number of cases) and 25 less the age when adult height is first attained. The difference (25 - a*), where a* is the age when height stops increasing, is calculated from female and male mortality rates in Sweden (1951 – 1992). Each point presents the average from 12 observations.