The 3D companion simulator treats the whole arterial tree as a single lumped compartment: one compliance, one resistance, one pressure value that changes everywhere at once. That is a good first approximation, but it structurally cannot show one very real phenomenon — pulse wave transit time. A pressure pulse takes a measurable fraction of a heartbeat to travel from the aortic root to the peripheral arterioles.
This 2D model discretizes the arterial tree into 6 elastic segments in series — an RC "ladder" (transmission-line) network. Each segment i has its own compliance and its own peripheral drain, and is linked to its neighbor by a viscous longitudinal resistance RL:
C_i · dP_i/dt = Q_(i-1→i) − Q_(i→i+1) − P_i/R_i
C_i = C/6 (each segment gets an equal share of total compliance)
R_i = 6·R (parallel sum of all 6 segment resistances = R)
Q_(i→i+1) = (P_i − P_(i+1)) / R_L (viscous inter-segment flow)
Q_(-1→0) = Q_in(t) (the same systolic burst as the 3D model)
- Setting RL → 0 collapses every segment to the same pressure instantly, recovering the 3D model's single-chamber behavior exactly (verified numerically: with 1 segment the two models are bit-for-bit identical).
- Vessel-segment resistance RL is the new control this model adds — it sets how "long" and how viscously resistive the path is, and therefore how long the pulse takes to reach the periphery. Larger RL → longer transit time, and a more damped, flattened pressure wave by the time it reaches the last segment.
- Watch the six chambers swell in sequence, left to right, slightly offset in time — that visible lag is the pulse wave, something a single-chamber model has no way to depict.
- Heart rate, stroke volume, total compliance and total resistance play the same physiological role as in the 3D model; only the resistance is now distributed instead of lumped.
This is the same family of model used to reason about arterial stiffening in real physiology: as arteries stiffen with age, the pulse wave speeds up and reflects earlier, arriving back at the heart during systole instead of diastole — a major contributor to isolated systolic hypertension. This simulator isolates the transit-time piece of that story.