Medical Device Design Formulas and Calculators

As pushability is related to tube longitudinal stiffness, it is calculated to be:

k_long = EA/L

Where

• k_long is the longitudinal spring constant,
• E is the modulus of elasticity,
• A is the cross-sectional area
• L is the length of the catheter shaft.

To maximize pushability k_long must be maximised.
This can be achieved in various ways:

• By maximizing the cross-sectional area of the tubing.
• By maximizing the modulus of elasticity by using a stiffer material.
• By decreasing the overall part length.

Torqueability is a measure of the tubes torsional stiffness and can be modelled using:

k_torq = GJ/L

Where

• k_torq is the torsional spring constant
• G is the shear modulus
• J is the polar moment of inertia
• L is the length of the catheter shaft

Maximizing torqueability is achieved by maximizing the torsional stiffness value, k_torq, through actions that include:

• Maximizing the polar moment of inertia. For a tube, the governing equation for J is:

J= PIE/32 (d⁴_o- d⁴_i)

In order to maximize J, the outside diameter and the wall thickness should be maximised.

• By maximizing the shear modulus using a stiffer material.
• By decreasing the overall part length.

The flexibility or flexural stiffness of a tube is determined by:

k_flexural = 3EI/L³

Where

• k_flexural is the flexural spring constant
• E is the modulus of elasticity
• I is the moment of inertia
• L is the length of the catheter shaft.

To improve the flexibility of the tube the flexural stiffness value, kflexural, the must be minimized through actions that include:
Minimizing the moment of inertia. For a tube, the governing equation for I:

I = PIE/64 (d⁴_o- d⁴_i)

In order to minimize I, the wall thickness must be at a minimum:

• By minimizing the modulus of elasticity by using a soft material.
• By increasing the overall part length.

Flexibility is not however a measurement of kink resistance. Experimental Data has shown that tubes with a small ID/OD ratio perform better than those with higher ID/OD ratios. That is those with thick walls have better kink performance than those with thinner walls.