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Deep inspirations (DIs) have a dilatory effect on airway smooth muscle (ASM) that helps to prevent or reduce more severe bronchoconstriction in healthy individuals. However, this bronchodilation appears to fail in some asthmatic patients or under certain conditions, and the reason is unclear. Additionally, quantitative effects of the frequency and magnitude of DIs on bronchodilation are not well understood. In the present study, we used a computational model of bronchoconstriction to study the effects of DI volumes, time intervals between intermittent DIs, relative speed of ASM constriction, and ASM activation on bronchoconstriction and the emergence of ventilation defects (VDefs). Our results showed a synergistic effect between the volume of DIs and the time intervals between them on bronchoconstriction and VDefs. There was a domain of conditions with sufficiently large volumes of DIs and short time intervals between them to prevent VDefs. Among conditions without VDefs, larger volumes of DIs resulted in greater airway dilation. Similarly, the time interval between DIs, during which the activated ASM re-constricts, affected the amplitude of periodic changes in airway radii. Both the relative speed of ASM constriction and ASM activation affected what volume of DIs and what time interval between them could prevent the emergence of VDefs. In conclusion, quantitative characteristics of DIs, such as their volume and time interval between them, affect bronchoconstriction and may contribute to difficulties in asthma. Better understanding of the quantitative aspects of DIs may result in novel or improved therapeutic approaches.