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2015 ; 70
(5
): 1119-49
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Spatial pattern formation in the lung
#MMPMID24810407
Donovan GM
; Kritter T
J Math Biol
2015[Apr]; 70
(5
): 1119-49
PMID24810407
show ga
Clustered ventilation defects are a hallmark of asthma, typically seen via
imaging studies during asthma attacks. The mechanisms underlying the formation of
these clusters is of great interest in understanding asthma. Because the clusters
vary from event to event, many researchers believe they occur due to dynamic,
rather than structural, causes. To study the formation of these clusters, we
formulate and analyze a lattice-based model of the lung, considering both the
role of airway bistability and a mechanism for organizing the spatial structure.
Within this model we show how and why the homogeneous ventilation solution
becomes unstable, and under what circumstances the resulting heterogeneous
solution is a clustered solution. The size of the resulting clusters is shown to
arise from structure of the eigenvalues and eigenvectors of the system, admitting
not only clustered solutions but also (aphysical) checkerboard solutions. We also
consider the breathing efficiency of clustered solutions in severely constricted
lungs, showing that stabilizing the homogeneous solution may be advantageous in
some circumstances. Extensions to hexagonal and cubic lattices are also studied.
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