Quick Scenarios
Live Circuit
IV Line Resistance Network
Series Always Increases Resistance
Every component in series adds its resistance to the total. A 0.2μm inline filter can have 3–10× the resistance of the catheter itself, dramatically reducing flow.
Parallel Lines Are Powerful
Two identical lines in parallel halve the total resistance (double the flow). Three lines reduce resistance to one-third. This is the math behind running two large-bore IVs in trauma.
The Bottleneck Rule
In a series circuit, the component with the highest resistance dominates. A tiny catheter after huge tubing still limits flow to the catheter's capacity. Always identify your bottleneck.
Needleless Connectors
Mechanical valve connectors (e.g., Maximus, Tego) can add significant resistance — some equivalent to a 2–4cm length of narrow tubing. Use split-septum connectors for high-flow needs.
Historical Origin · Ohm → Physiology
An electrical law becomes hemodynamics.
Georg Ohm's 1827 law (V = IR) was adapted directly to blood flow: ΔP = Q × R. Voltage became pressure gradient; current became flow; resistance stayed resistance. The circuit metaphor is not an approximation — it's the same mathematics, rescaled.
Electrical: V = I · R
Hemodynamic: ΔP = Q · R
Hydraulic: R = 8ηL / πr⁴
Hemodynamic: ΔP = Q · R
Hydraulic: R = 8ηL / πr⁴
Intracav Opportunity · Graph-Based Vascular Model
Model the vascular system as a weighted graph.
Every access point, junction, and vessel segment can be represented as a graph where resistance is the edge weight. This enables computation of optimal access points and predicted flow distribution before insertion.
Nodes = junctions & bifurcations
Edges = vessel segments
Weights = resistance (8ηL/πr⁴)
Output = optimal access point + flow distribution
Edges = vessel segments
Weights = resistance (8ηL/πr⁴)
Output = optimal access point + flow distribution