(A-1) A mathematical model to assess obstructive sleep apnea severity

Introduction:: Obstructive sleep apnea (OSA) is a sleep-disorder caused by periodic upper airway collapse, and it impacts a significant portion of the middle-aged population in the US. Patients with OSA experience a pattern of intermittent hypoxia at the tissue level, which is believed to result in several health concerns including cardiovascular disease and cognitive dysfunction. The development and progression of these health consequences has been associated with the severity of OSA. Currently, it is difficult to accurately assess OSA severity due to clinical limitations. For example, pulse oximetry, used to qualitatively represent OSA severity by providing the intermittent hypoxia exposure pattern, may be influenced by inaccuracies in recording and outputs only a generalized measure of systemic arterial oxygen hemoglobin saturation. In addition, the apnea-hypopnea index (AHI), a quantitative measure of OSA severity, has been shown to be a unreliable indicator of disease development in previous clinical studies. Therefore, to better understand the onset and advancement of OSA-related consequences, there is a need to assess OSA severity with a method that avoids the aforementioned clinical limitations. This can be achieved with mathematical modeling, which may provide a more detailed clinical representation of OSA.


Materials and Methods:: Considering the lack of patient-specific approaches in current OSA modeling literature, our model was developed with the ability to use respiratory and heart rate data from polysomnography studies as an input. These time-dependent parameters were linked to tissue-level oxygenation using mass transfer equations to track the movement of oxygen from its inspiration into the lungs to its eventual transport into the tissues. To construct the model, the primary regions in the body associated with mass transfer were treated as separate compartments, which includes the alveoli, pulmonary capillaries, and systemic capillaries. Oxygen transport from the alveoli to the pulmonary capillaries was modeled by incorporating the effects of diffusion across membrane barriers, the reaction between hemoglobin and oxygen, and blood perfusion. Furthermore, mass transfer to the tissues was modeled using an overall metabolic rate for oxygen consumption. The model was implemented with a series of simulated OSA breathing patterns to assess the scoring criteria of the AHI. In addition, patient data was used as an input to demonstrate clinical applicability.


Results, Conclusions, and Discussions:: The model was validated by comparing the results for a simulated normal breathing pattern at rest to expected physiological values of alveolar oxygen partial pressure and hemoglobin oxygen saturation in the systemic vessels. In addition, a case of simulated severe OSA was used to show that the end-pulmonary capillary oxygen partial pressure does not equilibrate with the alveolar oxygen partial pressure after frequent obstructive events. Although this is a common assumption in literature, our results highlight the importance of modeling oxygen transfer in the pulmonary capillaries. Furthermore, results for the oxygen concentration in the systemic vessels were compared for several other OSA simulations, which indicated that the scoring criteria of the AHI does not accurately reflect the severity of hypoxemia at the tissue level. For example, a breathing pattern with longer, less frequent obstructions (lower AHI) was shown to have more drastic oxygen decreases as compared to one with shorter, more frequent obstructions (higher AHI). In addition, a variation in the degree of hypoxemia in the systemic vessels was seen when comparing two breathing patterns with the same AHI but a difference in the duration of obstructive events. Since the AHI is primarily used in the clinic to make decisions regarding patient care, relying on its predetermined criteria may be detrimental to developing treatment plans. In addition to the simulations, patient data from a multi-hour sleep study was used as an input to highlight the flexibility and feasibility of the model for clinical application. Our results showed a greater sensitivity to breathing when compared to pulse oximetry and provided the additional output of systemic venous oxygenation, both of which can be used to demonstrate a fuller clinical picture of OSA. With this developed clinical tool, there are several new avenues that can be explored to improve the evaluation of patient health risks. To name a few, we plan to narrow our analysis to specific target organs and to use the model for creating a link between potential indicators of OSA and comorbidity presentation.


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