Complex dynamics of human red blood cell flickering: Alterations with in vivo aging

Human red blood cells (RBCs) exhibit vibratory motions, referred to as “flickering.” Their dynamical properties, classically attributed to thermal mechanisms, have not been fully characterized. Using detrended fluctuation analysis and multiscale entropy methods, we show that the short-term flickering motions of RBCs, observed under phase contrast microscopy, have a fractal scaling exponent close to that of $1∕f$ noise and exhibit complex patterns over multiple time scales. Further, these dynamical properties degrade with in vivo aging such that older cells that have been in the circulation longer generate significantly $(p<0.003)$ less complex flickering patterns than newly formed cells. Quantitative assessment of multiscale flickering may provide a way of measuring RBC functionality. Membrane models need to account for the complex properties of these motions and their changes with in vivo senescence.

Figure 1

(Color online) Consecutive pseudocolored phase contrast images (30 seconds apart) of a new (top plots) and an old (bottom plots) red blood cell (RBC). Changes in color (unitless scale) are due to membrane oscillations. White arrows point to a domain with relatively high amplitude flickering. For representational purposes, the background and the “halo” surrounding the cell (a phase contrast imaging artifact) were removed. (The range of values is higher for the old RBC than for the new one because the former is thicker than the latter and therefore appears brighter under positive phase contrast microscopy [15].)

Figure 2

(Color online) Time series of a pixel from the new RBC (a) and the old RBC (b) shown in Fig. 1. The magnitude of the fluctuations is given in arbitrary units. (c),(d) Fourier power spectra for time series in (a) and (b), respectively. A smoothing procedure was applied, which consisted of averaging the spectra for consecutive overlapping segments of 512 data points. Note the absence of a dominant (characteristic) frequency. (e) Detrended fluctuation analyses (DFA) for the two time series shown in (a) and (b). Note that the $\alpha$ (fractal) exponent for the old RBC is higher (closer to 1.5) than for the new cell, indicating that the underlying dynamics of the former membrane is closer to Brownian motion than that of the latter, which shows scaling close to $1∕f$ noise. (f) Multiscale entropy (MSE) analyses for the two time series shown in (a) and (b). The entropy measure (sample entropy [17]) is higher for the new than for the old RBC over time scales ranging from 0.029 (scale factor 1) to $0.174\mathrm{s}$ (scale factor 6). (Since the sampling frequency is $34\mathrm{Hz}$, the scale factor increments by steps of $1∕34=0.029\mathrm{s}$.)

Figure 3

(Color online) Quantitative analysis of the membrane fluctuations of a new (left panels) and an old (right panels) RBC from the same subject. Top plots show the coefficient of variation (standard deviation divided by mean value) maps. Middle plots show the $\alpha$ (fractal) exponent maps calculated using DFA. Bottom plots show the complexity maps calculated using the MSE method. Values of the parameters used to calculate sample entropy were $m=2$ and $r=0.15$ [11]. The complexity index was obtained by integrating the values of entropy between scales 1 and 6, inclusively. Colors code for the amplitude of the measured variable. To construct the maps, we analyzed the time series of individual pixels (such as those presented in Fig. 2). The maps of the coefficient of variation show that the membrane of new RBCs displays different domains of activity. In the online color version, red (blue) regions correspond to areas with relatively high (low) amplitude fluctuations. Old cells appear more homogeneous. The $\alpha$ maps show that toward the end of the RBC circulatory life, the dynamical properties of membrane fluctuations are closer to Brownian motion $(\alpha =1.5)$ than at the beginning. Consistent with these results, multiscale complexity maps show that the membrane dynamics of new RBCs are more complex than those of old RBCs. A blue rim, visible in some of the maps, corresponds to the interface between the thinner central (“drum”) region and the outer (“tire”) area of the cells.

Figure 4

(Color online) Histograms of the $\alpha$ exponent (left panel) and of the complexity index (right panel) for the new and old RBCs used to construct the maps shown in Fig. 3.