Mathematical model for describing cerebral oxygen desaturation in patients undergoing deep hypothermic circulatory arrest

Abstract

Background: Surgical treatment for aortic arch disease requiring periods of circulatory arrest is associated with a spectrum of neurological sequelae. Cerebral oximetry can non-invasively monitor patients for cerebral ischaemia even during periods of circulatory arrest. We hypothesized that cerebral desaturation during circulatory arrest could be described by a mathematical relationship that is time-dependent.

Methods: Cerebral desaturation curves obtained from 36 patients undergoing aortic surgery with deep hypothermic circulatory arrest (DHCA) were used to create a non-linear mixed model. The model assumes that the rate of oxygen decline is greatest at the beginning before steadily transitioning to a constant. Leave-one-out cross-validation and jackknife methods were used to evaluate the validity of the predictive model.

Results: The average rate of cerebral desaturation during DHCA can be described as: Sct(o(2))[t]=81.4-(11.53+0.37 x t) (1-0.88 x exp (-0.17 x t)). Higher starting Sct(o(2)) values and taller patient height were also associated with a greater decline rate of Sct(o(2)). Additionally, a predictive model was derived after the functional form of a x log (b+c x delta), where delta is the degree of Sct(o(2)) decline after 15 min of DHCA. The model enables the estimation of a maximal acceptable arrest time before reaching an ischaemic threshold. Validation tests showed that, for the majority, the prediction error is no more than +/-3 min.

Conclusions: We were able to create two mathematical models, which can accurately describe the rate of cerebral desaturation during circulatory arrest at 12-15 degrees C as a function of time and predict the length of arrest time until a threshold value is reached.

Figures

Fig 1

Physiology model of cerebral tissue oxygen saturation (Scto2) as a function of time superimposed over the individualized subject Scto2 recordings during DHCA.

Fig 2

Observed and predicted values of the physiology model showing the amount of cerebral tissue oxygen saturation (Scto2) decline as a function of time.

Fig 3

Cerebral tissue oxygen saturation (Scto2) and tHb measured by NIRS during the DHCA period to show initial rapid cerebral blood volume depletion under sensor before levelling off. During this period, tHb is proportional to CBV assuming that the blood haemoglobin level is constant.

Fig 4

Residual spaghetti plots demonstrating the magnitude of the individual residuals in our data set. Each line represents a patient. Note that for the majority of patients, the residuals lie within ±3 min.