With Institutional Review Board (IRB) approval and informed consent, 36 patients undergoing elective thoracic aortic surgery with DHCA were monitored intraoperatively using the FORE-SIGHT® cerebral oximeter (CAS Medical Systems, Branford, CT, USA) at our institution from 2005 to 2008. Cerebral tissue oxygen saturation (Scto2) and cerebral tissue haemoglobin (tHB) concentration were continuously recorded.
After the induction of general anaesthesia, two sensors were placed on the subjects' foreheads bilaterally for continuous monitoring of Scto2. Subjects remained in the supine position during surgery, allowing for only positional changes to facilitate surgical exposure. There was no alteration in surgical technique or routine clinical monitoring.
General anaesthesia was induced in all patients with etomidate, fentanyl, and midazolam. Neuromuscular block was achieved with vecuronium or cisatracurium before tracheal intubation. A balanced anaesthetic technique was used for maintenance consisting of isoflurane (0.6–1.5% end-tidal concentration), fentanyl, vecuronium or cisatracurium, and midazolam. All patients were mechanically ventilated with Fio2 100% in a pressure-regulated volume-controlled mode so as to maintain the Paco2 at 4.6–6.0 kPa.
The following monitoring devices were placed: a left radial arterial catheter, a pulmonary artery catheter inserted via the right internal jugular vein, a 20 G jugular bulb catheter for intermittent sampling of jugular venous blood, and a urinary bladder catheter with an integrated temperature thermistor (to measure core temperature). Additionally, nasopharyngeal temperature was measured in all patients.
The jugular bulb catheter was inserted into the internal jugular vein under ultrasonic vessel guidance. The catheter was advanced using the Seldinger technique to a maximal length of 10–12 cm. A baseline measurement was obtained to confirm proper placement (oxyhaemoglobin saturation <70%). Saturations higher than 70% were believed to represent a malpositioned catheter (e.g. facial vein), requiring an additional attempt at proper placement. Once a bladder temperature of 20°C was reached, serial Sjvo2 measurements were performed every 5 min. After obtaining at least one Sjvo2 measurement >94%, with a total cooling time of at least 45 min, DHCA commenced. Nasopharyngeal arrest temperatures ranged between 12°C and 15°C.
The technique of DHCA used at our institution was consistent throughout the study and has been described in detail previously.8,9
Two subsets of patients presenting for elective thoracic aortic arch surgery were included in this study. The first population required replacement of the entire aortic arch. The technique utilized is described in detail by Spielvogel and colleagues.8
Briefly, CPB is achieved by cannulation of the right axillary artery and venous drainage through a two-stage cannula placed into the right atrium. After CPB is commenced, patients are cooled down to a nasopharyngeal temperature of 12–15°C utilizing α-stat management. Ischaemic DHCA is commenced once the abovementioned criteria are fulfilled. During circulatory arrest, a trifurcated graft is sewn to the head vessels. Once all three anastomoses are completed, the graft is deaired and the proximal end clamped. Via the right axillary artery, selective antegrade cerebral perfusion (SCP) is started (10 ml kg−1
ideal body weight min−1
) after 15–45 min of ischaemic DHCA. During SCP, a tube graft is used to connect the non-diseased portion of the ascending aorta with the proximal end of the descending aorta. Subsequently, the trifurcated graft is sewn to the aortic tube graft. After meticulous deairing, total body perfusion is commenced and the patient rewarmed.
The other group consisted of patients presenting for repair of the ascending aorta with a beveled suture line at the arch (hemiarch procedure). This technique is described by Etz and colleagues9
in detail. Briefly, CPB technique and temperature management on bypass are identical as described for total aortic arch replacement. The proximal anastomosis is performed with the aorta cross-clamped. Once completed and all arrest criteria fulfilled (temperature 12–15°C, S
>94%, and a minimal cooling time of 45 min), circulatory arrest is commenced for suturing of the distal anastomosis. Once completed, total body circulation is resumed and the patient rewarmed. No SCP is required for this technique.
Hence, it is important to note that all patients received ischaemic DHCA without supplemental cerebral perfusion enabling us to model the decline of Scto2 during the time of arrest.
Modelling and statistical analysis
Scto2 and total haemoglobin concentration in tissue (tHB) data were recorded every 2 s, along with subject characteristic information from our institution's Anesthesia Information Management System (AIMS) (Compurecord, Philips Medical Systems, Andover, MA, USA). Each subject's left and right sensor Scto2 data were averaged together for each event. For analysis, the median Scto2 from each minute, rounded by 0.25, was used, and the first data point of the same Scto2 value was used.
To determine the rate of S
decline during DHCA, a non-linear mixed model was fit for the S
physiological model based on the individual appearance of the S
decline during DHCA. The model assumes that the rate of oxygen decline is greatest at the beginning before steadily converging to a constant (so the trend of S
becomes linear after a certain time point). For each subject i
, the S
at time t
 is the initial S
, and (β0
)) is the model describing the degree of S
decline over time. As time t
increases, the term 1−λ×exp (−(κ+γi
) converges to 1, leaving the model to be affected only by the linear component (β0
). In other words, 1−λ×exp (−(κ+γi
) modulates when the S
decline changes from the exponential trend to the linear trend. The coefficient β1
is the decline rate thereafter.
Note that in the non-linear mixed model in equation (1), β0
, λ, and κ are the population parameters that characterize the overall trajectory of S
, whereas bi
are the random components which allow each individual to have his/her own intercept (bi
) and scale parameter (γi
) deviated from the population averages β0
and κ. The two random variables bi
were assumed to have a bivariate normal distribution with mean zeros and a covariance structure with unspecified mathematical form. Compared with the population average, a positive bi
or both correspond to a greater decline rate before reaching to the linear phase, and a positive bi
also corresponds to a more significant total reduction of S
at the end. The data, however, did not suggest random slopes among individuals based on the Akaike information criterion, a statistic used for choosing among models.10
This implies that the final decline rate is similar across all subjects. The residual errors at time t
, that is, e
, were assumed to be independent and identically normally distributed.
Additionally, a predictive model was derived enabling clinicians to estimate the maximal acceptable DHCA time that can pass before reaching an ischaemic threshold. Since the aforementioned physiological model has an exponential component, it is natural to use a logarithmic function to predict the DHCA time given a pre-specified S
value. Specifically, the DHCA time will be predicted using the following functional form:
where LN is the natural logarithm function, and δ is the difference between the S
at 15 min and the pre-specified S
threshold (i.e. δ=S
]). Because the coefficient of δ tended to be small, to increase the stability of the modelling process, and to ensure that a larger decline is associated with a longer time, an exponential function for the coefficient of δ was used.
Similar to the physiological model, we allowed individual baseline characteristics to influence a, b, and c in equation (2) of the predictive model. The potential predictors for each of a, b, and c included age (yr), height (cm), gender, pre-arrest haematocrit (%), core temperature (°C), pH, Paco2 (mm Hg), Pao2 (mm Hg), the Scto2 value at 10 min after the onset of DHCA (Scto2), and the rate of Scto2 decline between 5 and 10 min (i.e. r[5,10]=(Scto2−Scto2)/5).
As a first step, we fitted a full model including all of the potential predictors. Because gender, core temperature (°C), pH, Paco2(kPa), and Pao2 (kPa) were not close to reaching statistical significance (P>0.5), the list was further reduced by omitting them altogether. The final model was obtained based on manual elimination of the least significant predictor one at a time (akin to the backward selection method) until all of the remaining predictors had P<0.05.
Leave-one-out cross-validation and jackknife resampling were performed to assess the prediction error and bias of the parameter estimates of the predictive model.11
Both methods involve omitting one subject at a time and remodelling on the remaining subset using the same set of predictors. In leave-one-out cross-validation, we computed the predicted values across various time points of the left-out subject based on the model without that subject, and then calculated the mean square error and the mean absolute error for that subject. The mean square (absolute) error is the average squared (absolute) difference between the observed and the predicted values. Since there were only 30 subjects with more than one observation in the time period after 15 min of DHCA onset, this was repeated 30 times leaving out one subject at a time. The final prediction error was defined as the average (or median) of these 30 individual prediction errors. In jackknife, the medians (because of the small sample size, we chose to use the median) of the parameter estimates were compared with those estimated from the predictive model. The jackknife bias is the (number of validations−1) times the differences of these two estimates.
All statistical analysis was carried out using SAS v9.1 (SAS Institute, Inc., Cary, NC, USA), and PROC NLMIXED was used to develop the physiology and time predictive models. The level of statistical significance for hypothesis testing was set to be 0.05. The authors had full access to the data and take responsibility for its integrity. All authors have read and agree to the manuscript as written.