Understanding immunology via engineering design: the role of mathematical prototyping

Abstract

A major challenge in immunology is how to translate data into knowledge given the inherent complexity and dynamics of human physiology. Both the physiology and engineering communities have rich histories in applying computational approaches to translate data obtained from complex systems into knowledge of system behavior. However, there are some differences in how disciplines approach problems. By referring to mathematical models as mathematical prototypes, we aim to highlight aspects related to the process (i.e., prototyping) rather than the product (i.e., the model). The objective of this paper is to review how two related engineering concepts, specifically prototyping and "fitness for use," can be applied to overcome the pressing challenge in translating data into improved knowledge of basic immunology that can be used to improve therapies for disease. These concepts are illustrated using two immunology-related examples. The prototypes presented focus on the beta cell mass at the onset of type 1 diabetes and the dynamics of dendritic cells in the lung. This paper is intended to illustrate some of the nuances associated with applying mathematical modeling to improve understanding of the dynamics of disease progression in humans.

Figure 1

Productivity metrics of the United States pharmaceutical industry. Research and development spending by the United States pharmaceutical industry has escalated dramatically during the last several decades (solid line—left axis) [5]. However, the translation of this increased research spending into new therapeutic products, as represented by the number of new medical entities (NMEs) approved by the Food and Drug Administration (circles—right axis), has failed to keep pace [2].

Figure 2

A common example of a prototype. A prototype of a blended wing body aircraft, the X-48B, is shown in a wind tunnel at NASA's research center in Langley Air Force Base, VA. The wind tunnel was used by researchers to evaluate this prototype against structural, aerodynamic, and operational design objectives for an advanced aircraft concept (NASA photo/Jeff Caplan).

Figure 3

Comparison between the predicted and measured excess beta cell mass. Comparison of the excess beta cell mass predicted by the mathematical model (solid curve) compared against the trendline obtained by linear regression (dotted line) for the measured reduction in beta cell mass in 63 patients that died within three weeks of diagnosis of type 1 diabetes mellitus. Figure was originally published in [29].

Figure 4

A schematic process diagram of the interplay between insulin production and glucose homeostasis. The regulation of substrate metabolism is modeled as an open system, where the concentrations of insulin (C _Ins) and glucose (C _Glc) are influenced by flows in (e.g., a glucose input and pancreatic production of insulin (M _Ins)) and out (e.g., the disposal of glucose through cellular metabolism or the disposal of insulin through cellular proteolysis) of the system. Material flows are represented by solid lines while the flow of information is represented as a dotted line. For instance, the production of insulin by the pancreas—a material flow—is regulated by concentration of plasma glucose-a flow of information. The molar production of insulin by the pancreas is the product of the beta cell mass times the insulin production per beta cell. Similarly, the rates of disposal of insulin and glucose within the system (R _Ins and R _Glc) are regulated by the concentration of plasma insulin. The concentration of insulin is a derived intrinsic quantity where the moles of insulin produced by the pancreas are distributed throughout the system volume, which is proportional to body weight.

Figure 5

Dynamic change in residual beta cell mass corresponds to the dynamic change in plasma C-peptide following onset of type 1 diabetes. The residual beta cell mass (x: right axis) and plasma C-peptide (square [31], circle [32], and + [30]: left axis) are shown as a function of time following clinical diagnosis of type 1 diabetes. A 9-point moving average of the residual beta cell mass is shown for comparison (dotted line). The residual beta cell mass is the difference between the observed beta cell mass and predicted beta cell mass. The dynamic change in observed beta cell mass was obtained from pancreata obtained from patients with type 1 diabetes [–27]. The predicted beta cell mass is an estimate of the minimum beta cell mass required to maintain glucose homeostasis. Figure was originally published in [34].

Figure 6

Schematic diagram of mathematical model for dendritic cell trafficking within the lung epithelial microenvironment. An aerosol challenge results in the increase of antigenic proteins and the recruitment of DC precursors from the blood into the lung epithelium. DCs dynamically traffic through the lung epithelium and become programmed by the prevailing epithelial microenvironment. Upon maturation, DCs migrate into the lymph nodes and present antigenic peptides obtained in the lung epithelium to naïve CD4+ T helper cells.