Red Blood Cells' Area Deformation as the Origin of the Photoplethysmography Signal

Abstract

The origin of the photoplethysmography (PPG) signal is a debatable topic, despite plausible models being addressed. One concern revolves around the correlation between the mechanical waveform's pulsatile nature and the associated biomechanism. The interface between these domains requires a clear mathematical or physical model that can explain physiological behavior. Describing the correct origin of the recorded optical waveform not only benefits the development of the next generation of biosensors but also defines novel health markers. In this study, the assumption of a pulsatile nature is based on the mechanism of blood microcirculation. At this level, two interconnected phenomena occur: variation in blood flow velocity through the capillary network and red blood cell (RBC) shape deformation. The latter effect was qualitatively investigated in synthetic capillaries to assess the experimental data needed for PPG model development. Erythrocytes passed through 10 µm and 6 µm microchannel widths with imposed velocities between 50 µm/s and 2000 µm/s, according to real scenarios. As a result, the length and area deformation of RBCs followed a logarithmic law function of the achieved traveling speeds. Applying radiometric expertise on top, mechanical-optical insights are obtained regarding PPG's pulsatile nature. The mathematical equations derived from experimental data correlate microcirculation physiologic with waveform behavior at a high confidence level. The transfer function between the biomechanics and the optical signal is primarily influenced by the vasomotor state, capillary network orientation, concentration, and deformation performance of erythrocytes.

Keywords: mathematical transfer function; microcirculation; photoplethysmography origin; red blood cell shape deformation; vasomotor activity.

Figure 1

(a) The usual RBC size in healthy individuals in the steady state. (b) Modes of RBC deformation proportional to flow velocities and available space: top—bullet shape; bottom—paraboloid shape.

Figure 2

(a) Design concept of the synthetic capillary network; with the red arrows, the direction of imposed flow is shown within 10–6 µm channel widths; with the red dotted line, the transition region is highlighted. (b) Resulting synthetic capillary network (translucent mid-channel) with attached ports. (c) Resulting 10 µm channel width after the fabrication process; magnification 10× factor. (d) Resulting 6 µm channel width after the fabrication process; magnification 15× factor.

Figure 3

(a) Video frame of the recorded RBC deformation through the synthetic capillary network. The transition zone is also visible. With the red rectangles, ROI were placed across the individual channel. (b) The interface between the 6 µm channel and the free zone space (outlet side).

Figure 4

(a) RBC average length deformation against measured flow velocities. (b) Average area deformation against measured flow velocities.

Figure 5

(a) Interaction between the incident light beam and the biological specimens: tissue and red blood cell. Multiple event possibilities are presented from left to right. (b) Qualitative interaction between the light beam and the erythrocyte element.

Figure 6

(a) Transfer function between mechanical flow rate inside the capillary network and the recorded PPG optical signal. The upper side of the dotted blue line delimits the signal validity boundary. Above this limit, the signal does not exist: reflected light flux cannot be greater than the difference between incident light quantity and losses into the surrounding tissue. (b) PPG waveform interpretation in the context of the obtained mathematical transfer function. The gray area represents the information lost, resulting in the diminution of the initial signal baseline.