Figure 1.
Three-dimensional reconstruction of the human three-quarter alveolus.
Based on a literature survey (parameters are shown in Table 1) we reconstructed the spatial environment of one typical human alveolus, including the spherical shape of the system, the two major AEC types present in alveoli and the pores of Kohn as interalveolar connections (see Video S1).
Table 1.
Model parameters for entities in the human alveolus.
Table 2.
Model parameters for the static case and the two breathing conditions.
Figure 2.
Chemotaxis model for signalling alveolar epithelial cells.
Probability of directed migration by AM towards the AEC associated with the conidium as a function of geodesic distance d between the centroids of the AEC and the AM. See text for details.
Table 3.
Model parameters for human alveolar macrophages.
Figure 3.
Flowchart of the agent-based simulation procedure for first-passage-time measurements.
Integration of the system dynamics over time with timestep by using an asynchronous random order updating scheme [24]. Here, the recording of one first-passage-time sample is shown.
is the total number of cells in the system at time
and
denotes a uniform random permutation of m elements. See text for further details.
Figure 4.
Number of conidia and alveolar macrophages per alveolus.
A Binomial distribution is used to get insight into the number of cells per alveolus. (A) The probability distribution of AM per alveolus derived from their overall number (see Table 3) is shown in blue. The quality of the calibration can be seen by means of two example simulations of the persistent random walk migration mode with breathing being disabled. (B) Probability for the distribution of A. fumigatus in one alveolus is plotted on a logarithmic scale. Different typical doses as used in experiments are plotted for comparison. Daily inhalation refers to a dose of 6300 conidia, which is taken as the upper threshold of the lungs' daily exposure toward A. fumigatus.
Figure 5.
Typical measures of the first-passage-time density distribution used in this study.
Here, we show an example-distribution for a persistent random walk scenario with the parameters and
based on
samples (the corresponding distribution for biased persistent random walk is shown in Fig. S2). One sample of these simulations can be viewed in Video S2.
Figure 6.
Comparison of first-passage-time distribution measures with and without breathing for both migration modes.
Subfigures (A)–(C) show the FPT measures mean, median and probabilities of FPT above six hours for persistent random walk migration mode. Subfigures (D)–(F) show these measures for biased persistent random walk. The two breathing scenarios, resting condition (dashed lines) and heavy exercise (dotted lines) are shown together with the static case (lines) of a constant deflated alveolus. The parameters for the static case and the breathing scenarios are summarized in Table 2.
Figure 7.
Time fractions for successful AM performing biased persistent random walk migration.
The fraction of the biased migration part (, see text for details). (A) Mean and standard deviation of the fraction of biased migration for
, (B) for
. The overall number of samples is 105.
Figure 8.
Geodesic distances and the retention time distribution of successful macrophages for different migration modes in the static case.
(A) and (C) are based on and
, whereas (B) and (D) are based on
and
.