Cardiovascular monitoring of elective aortic aneurysm repair using methods of chaos analysis

Biological signals like arterial blood pressure (ABP) and electrocardiograms are usually displayed in a linear fashion. The often very complex structure may, however, be better described by phase space plots and time-delayed vectors, enabling an advantageous display of the dynamics contained in the signal. The potentials of such a display were investigated during elective aortic aneurysm repair, where profound haemodynamic changes frequently occur.

The peripheral volume pulse was recorded at a digit using noninvasive near infrared photoplethysmography (NIRP). All patients (n = 20, mean age 72.8 years) were invasively monitored using arterial and Swan Ganz catheters. The ABP signal was continuously recorded with a computer (sample rate 128 Hz). Two different phase space plots, [x(t), y(t + 8/128 s) and x(t), d(x(t + 8/128 s) - x(t))/dt] were calculated for the NIRP and the ABP signals and continuously displayed. The stability was subjectively assessed and the fractal dimension calculated using the 'Hausdorff dimension'. The correlation between stability, fractal dimension and frequently used parameters of patient monitoring were investigated.

All patients included in the study had an uncomplicated operation. Cardiac index (CI) and oxygen delivery (DO2) increased, and systemic vascular resistance (SVR) decreased following declamping of the aorta. The ABP signal was generally more stable. After declamping of the aorta, 14 of 16 NIRP signals became unstable, and 9 of 14 ABP signals destabilised. The time required for stabilisation of the signal varied between the individual patients. Thirty minutes after declamping, 11 of 12 ABP signals were stable, whereas 3 out of 9 NIRP signals still revealed an unstable pattern. A fractal dimension was calculated by box counting, which revealed a linear regression over two orders of magnitude in a log-log plot (Hausdorff dimension between 1.19 and 1.71). The mean fractal dimension for NIRP was significantly higher than that of the ABP signal. On clamping and declamping of the aorta, a trend to a higher fractal dimension (p = 0.08) was observed for both signals analysed. No correlation was observed between the fractal dimension and ABP, SVR index, CI, DO2 index and oxygen consumption.

The dynamic changes of the signals were emphasised when they were displayed as phase space plots calculated by time-delayed vectors. The time series of the signal revealed a fractal dimension, and the observed increase at the critical time points of the operation, where the need for cardiovascular regulation is most pronounced, support the contention that a physiological system based on non-linear behaviour may enable a rapid response to haemodynamic challenges. An on-line display of phase space plots calculated by time-delayed vectors may in future provide a valuable method of monitoring for high-risk patients.