# The Science Behind the Mattress

**Comparison of Additional Capillary Blood/Fluid Flow **

### The Zero Pressure Mattress vs.

### Negative Pressure Therapy and Alternating Pressure Mattress

### Based on Poiseuille’s Law

**Given Data:**

- Poiseuille’s Law states Q = (3.14 r
^{4}P)/Ln

Q= capillary blood/fluid flow

R = capillary radius

P = Pressure drop across capillary length (L)

N= blood/fluid viscosities

- Average pressure applied using an Alternating Pressure Mattress (APM) in the buttock/sacrum region = 27 mmHg
- Average pressure applied using the Zero Pressure Mattress in the buttock/sacrum region = 0 mmHg
- Capillary gradually closes as applied pressure gradually increases and becomes 100% closed at 32 mmHg.
- At 27 mmHg, the capillary is 75% closed, or 25% open
- At 0 mmHg, the capillary is 100% open
- Average pressure drop across capillary is 40 mmHg -15mmHg = 25 mmHg
- Pressure drop across capillary provided by Negative Pressure Therapy = 40 mmHg – (-130 mmHg) = 170 mmHg

**Comments:**

Note the variable in the equation: Q = (3.14 r^{4} P)/Ln that applies to the Zero Pressure Mattress is the capillary radius (r). Also note the variable in the equation that applies to the Negative Pressure Therapy is the pressure drop (P) across the capillary length (L). Significantly, (P) is linear and has far less influence on blood/fluid flow compared to changing the capillary radius (r), which is raised to the 4th power in accordance to the equation.

**Calculations:**

- Capillary blood/fluid flow using an Alternating Pressure Mattress
**= x** - Capillary blood/fluid flow using the Zero Pressure Mattress = ( 100%/25%)
^{4}(x) =**256x** - Capillary blood/fluid flow using Negative Pressure Therapy = (170/25) (x) =
**6.8x**

**Final Comments:**

Thus, Poiseuille’s Law explains why Negative Pressure Therapy works. Poiseuille’s Law also explains why the Zero Pressure Mattress is far more effective than any product in the market with respect to treating and preventing pressure injuries.