STUDY NOTES: Mathematical Applications in Blood Pressure & Circulation

1. Blood Pressure (BP)

• BP = Blood Pressure

• CO = Cardiac Output (amount of blood pumped per minute)

• SVR = Systemic Vascular Resistance (resistance of blood vessels to flow)

 2. Cardiac Output (CO)

• HR = Heart Rate (beats per minute)

• SV = Stroke Volume (mL of blood ejected per beat)

Example:

If HR = 70 bpm and SV = 70 mL
→ CO = 70 × 70 = 4900 mL/min (≈ 5 L/min)

This shows that an adult heart pumps about 5 liters of blood per minute.

3. Mean Arterial Pressure (MAP)

• SBP = Systolic BP

• DBP = Diastolic BP

Example:
If BP = 120/80 mmHg
→ MAP = 80 + ⅓ (40) = 93 mmHg
MAP represents average arterial pressure during one cardiac cycle — the key to perfusion.

4. Poiseuille’s Law (Flow in Circulation)

• Q = Blood flow

• r = Vessel radius

• ΔP = Pressure difference

• η = Blood viscosity

• L = Length of the vessel

Meaning:
Flow is proportional to the fourth power of radius — small changes in vessel diameter cause large changes in blood flow.
→ Vasoconstriction = huge ↓ in flow
→ Vasodilation = huge ↑ in flow

 5. Ohm’s Law in Circulation

Analogous to electricity:

 6. Height and Circulatory Dynamics

• Taller individuals have longer blood vessels → greater resistance (R ∝ length of vessel).

• The heart must generate slightly higher pressure to maintain perfusion to the brain in taller people (gravity effect).

• Hydrostatic pressure difference increases with height:
  

  • ρ = blood density

  • g = gravity

  • h = height difference (heart to head)

Clinical example:
When standing suddenly, blood pools in the legs due to gravity -causing a drop in cerebral perfusion (orthostatic hypotension).

7. Velocity and Cross-sectional Area

• v = Velocity of blood flow

• Q = Flow rate

• A = Cross-sectional area

Meaning:

• In capillaries (huge total area) → velocity ↓ → allows gas/nutrient exchange.

• In aorta (small total area) → velocity ↑.

8. Pulse Pressure (PP)

Wider pulse pressure can indicate arterial stiffness or increased stroke volume (e.g., in aging or aortic regurgitation).

9. Ejection Fraction (EF)

• SV = Stroke Volume

• EDV = End-Diastolic Volume

Normal EF = 55–70%
Represents how effectively the heart pumps blood with each beat.

10. Body Surface Area (BSA) and Height

Used to normalize cardiac measures (e.g., cardiac index):

Normal CI = 2.8–3.6 L/min/m²

Table

Concept	Formula	Physiological Meaning
BP	CO × SVR	Blood pressure depends on flow and resistance
CO	HR × SV	Heart pumping efficiency
MAP	DBP + ⅓(SBP − DBP)	Average perfusion pressure
Flow (Poiseuille)	(πr⁴ΔP)/(8ηL)	Flow depends heavily on vessel radius
Flow (Ohm’s Law)	ΔP / R	Flow is pressure over resistance
Velocity	Q / A	Inverse relationship with area
PP	SBP − DBP	Arterial elasticity
EF	SV / EDV × 100	Ventricular performance
CI	CO / BSA	Flow adjusted to body size