Question

Observing under the microscope the movement of red blood cells in the capillary, one can measure the velocity of blood flow (V= 0.5 mm/s). The average velocity of blood flow in the aorta is = 40 cm/s. Based on these data, determine how many times the sum of the cross sections of all functioning capillaries is greater than the aortic section. (S1V1 =S2V2).

Answer 1

Ответ:

As capillaries exhibit heterogeneous and fluctuating dynamics even during baseline, a technique measuring red blood cell (RBC) speed and flux over many capillaries at the same time is needed. Here, we report that optical coherence tomography can capture individual RBC passage simultaneously over many capillaries located at different depths. Further, we demonstrate the ability to quantify RBC speed, flux, and linear density. This technique will provide a means to monitor microvascular flow dynamics over many capillaries at different depths at the same time.

Keywords: capillaries, cerebral blood flow measurement, cranial windows, microscopy, optical imaging

Answer 2

To solve this problem, we can use the principle of continuity of flow, which states that the product of the cross-sectional area and the velocity of fluid flow is constant along a continuous tube, assuming no branching or merging of vessels.

Let's denote the cross-sectional area of the capillaries as S1 and the velocity of blood flow in the capillaries as V1. Similarly, let's denote the cross-sectional area of the aorta as S2 and the velocity of blood flow in the aorta as V2.

According to the principle of continuity, we have:

S1V1 = S2V2

We are given the following values: V1 = 0.5 mm/s (0.5 mm per second) V2 = 40 cm/s (40 cm per second)

To ensure that the units are consistent, let's convert the units of V1 from mm/s to cm/s: V1 = 0.5 mm/s = 0.05 cm/s

Now we can rearrange the equation to solve for the ratio of the cross-sectional areas:

S1/S2 = V2/V1

Substituting the given values: S1/S2 = 40 cm/s / 0.05 cm/s

Simplifying: S1/S2 = 800

Therefore, the sum of the cross-sectional areas of all functioning capillaries is 800 times greater than the cross-sectional area of the aorta.