Question

Given the formula Q = Vt for flow rate and a normal velocity in the carotid artery of 35cm/s, calculate the flow rate from each artery into the next with given diameters. Aortic Arch (2.1cm/m2) -> Right common carotid (7.7mm) -> Right Internal Carotid (4.24mm) -> Anterior Communicating artery/Anterior Cerebellar Artery ( 2.09mm) -> Posterior Communicating Artery (1.32mm) -> Posterior Cerebellar Artery ( 1.94mm) -> Basilar Artery (3.22mm).

Answer 1

Flow rate can be calculated by the formula

Q = vA, where v = velocity and A = area of cross section.

A = πr^2, if diametre is then r = d÷2.

Given, v = 35 cm2/sec.

1. Aortic (2.1cm) :

Q = vA

    => Q = 35 × 3.14 × 2.1 × 2.1 ÷ 2 ÷2 **(r= 2.1/2)

   => Q = 121.17 cm3/s

2. Right common carotid (7.7mm) :

   Q = vA

     =>Q = 35 × 3.14 × 7.7mm × 7.7 mm ÷2÷2

=> Q = 35 × 3.14 × 7.7cm × 7.7cm ÷2÷2÷10÷10

(mm must be converted to cm because to have same unit with velocity)

=> Q = 16.29 cm3/s

3. Right Internal Carotid (4.24mm) : similarly calculation as 2

Q = 4.94 cm3/s

4. Anterior Communicating artery/Anterior Cerebellar Artery ( 2.09mm):

Q = 1.2 cm3/s

5 . Posterior Communicating Artery (1.32mm) :

Q = 0.48 cm3/s

6. Posterior Cerebellar Artery ( 1.94mm):

Q = 1.03 cm3/s

7. Basilar Artery (3.22mm):

Q = 2.85 cm3/s