Distance to Healthy Metabolic and Cardiovascular Dynamics From Fetal Heart Rate Scale-Dependent Features in Pregnant Sheep Model of Human Labor Predicts the Evolution of Acidemia and Cardiovascular Decompensation

Figure 1. Typical data recorded in the experiment (here, animal 473726). (A) FHR resampled at 4 Hz. The color indicates the strength of UCO during the experiment: blue and black for no UCO (baseline and recovery), green for mild UCO, magenta for moderate UCO and red for severe UCO. (B) Fetal arterial pH values during the experiment. The pH (as well as the other blood measurements) is obtained at specific time points, indicated by the vertical lines; the open black circles correspond to the actual measurements from blood sampling and the black lines correspond to a linear interpolation.

Figure 2. Illustration of the methodology in the first time-window [0;T] of size T = 20 min, using the fixed time scale τ = 25s. (A): FHR. (B): mt(τ). (C): σt(τ). (D): Rt(τ). The black circles in (B–D) correspond each to a value obtained in a time-interval of size τ = 25 s, according to Equations (1), (3), (5). The horizontal red lines in (B–D) indicate the values mk = 1(τ), σk = 1(τ) and Rk = 1(τ) obtained after averaging all the black circles, i.e., over all available time-intervals of size τ in the time-window, according to Equations (2), (4), (6).

Figure 3. Representation of the time evolutions of mk(τ) (A), σk(τ) (B), Rk(τ) (C), hk(τ) (D), depending on the scale τ for animal 473726. The time in abscissa is kdT + T/2, the location of the kth time-window of size T where the quantity is computed, and the ordinate represents the scale τ. Vertical color lines indicates the times at which blood sampling was performed (same color code as in Figure 1: green in the mild UCO regime, magenta in the moderate UCO regime, and red in the severe UCO regime). In the severe UCO regime and for larger time scales τ, stronger variations are observed.

Figure 4. Quantitative representation of the evolution of m(τ) (A), σ(τ) (B), R(τ) (C), and h(τ) (D) over the time scale τ for a single animal. The data represented here is extracted from Figure 3: each curve corresponds to a time-window of size T for which a fetal arterial blood sample was taken. The color of the curve represents the corresponding UCO level, with the same color code as in Figures 1, 3: blue is the baseline prior to any UCO, green in the mild UCO regime, magenta in the moderate UCO regime, red in the severe UCO regime, and then black in the recovery regime (after UCO). Vertical black dashed lines indicate the time-scales 2.5 and 8 s.

Figure 5. Correlation coefficient between the biochemical measurements (a: lactate, b: pH, c: BE) and the four FHR features: mk(τ) (magenta), σk(τ) (blue), Rk(τ) (red), and entropy rate hk(τ) (black), as function of the scale τ.

Figure 6. Long term AUC of the four FHR features mLT (A), σLT (B), RLT (C), and hLT (D) for all 14 animals. For a given quantity, each line represents an animal (ordered from top to bottom as in Table 1); chronically hypoxic ones are above and normoxic ones are below. Each column represent a time-window of size T and time is increasing from left to right. The region of mild UCO starts at the vertical green line and lasts for four windows, up to the vertical magenta line, followed by 4 windows in the moderate UCO region, and then up to six windows in the severe UCO region, and up to three windows in the recovery region.

Figure 7. Trajectories of the vector u→k-u→0 for all 14 animals in the phase space; the 6 subplots (A–F) correspond to the 6 possible projections onto planes (using 2 coordinates of the vector). Each trajectory corresponds to an animal and is colored to indicate the pH value at the time k: in this way, we observe the joint temporal evolution of u→k and of the pH throughout the experiment. Trajectories have been centered by subtracting u→0, according to Equation (11) to account for the variability between animals: the thick black dot at the origin thus represents the starting point of all trajectories. The gray circle corresponds to D = 1 and the black circle to D = 2.

Figure 8. Two examples of normoxic animals (right: animal 473361, left: animal 461060). (a,e): FHR. (b,f): distance D along time; the horizontal dashed line indicates the value D = 2 and the red vertical line indicates the CVD time (ABP sentinel), i.e., the time point when we visually confirm the onset of CVD. (c,g): projections of the trajectory of the vector u→ on the plane (mLT, hLT) (the two features that individually better correlate with the pH). (d,h): projections of the trajectory on the plane (σLT, RLT) (the other two components of u→). The distance D and the trajectories are color-coded with the pH values in each time-window of size T. For clarity, the last part of the trajectory where D decreases below D = 2 is omitted.

Figure 9. Two examples of hypoxic animals (right: animal 473726, left: animal 473362). See caption of Figure 8.

Figure 10. A representative example of FHR and the corresponding distance D (colored by pH value) for animal 473360. The 4 Hz dataset used in the analysis is reproduced in black, and the original 1,000 Hz dataset is presented in red. (a,b) : complete time trace for all available data. (c,d) : zoom in the problematic region, where D is unexpectedly large. (e,f) : zoom in a region where D is small, as expected. (g,h) : zoom in a region where D is large, as expected. See text.