Distinguish arterial storage from mean perfusion

1. Trace the anatomical pathway

Elastic arteries store some ejected volume as their walls expand and return it during the interval between ventricular ejections. Resistance and compliance are distinct properties: resistance links pressure drop to flow, while compliance links stored volume change to pressure change. A reservoir description can explain smoothing of pulsatile input without resolving every traveling wave in the arterial tree.

2. Define the mechanism and boundary

The original linear reservoir has downstream pressure zero, resistance 2 and compliance C. Each instantaneous input adds volume 6, so pressure jumps by 6/C. Between pulses, outflow P/2 removes stored volume and pressure decays exponentially with time constant 2C. Pulses recur every T time units. All quantities are arbitrary and are not a blood-pressure reference range.

At a periodic steady state, pressure just before the next pulse equals the prior peak times exp(−T/(2C)), and the next volume input restores the same peak. Solving gives Pmax=(6/C)/[1−exp(−T/(2C))]. Mean flow is input per period, 6/T; mean pressure is resistance times that flow, 12/T. Compliance changes peak/trough and pulse size but does not change this mean under fixed input and resistance.

The graph displays one between-pulse segment, not a continuous ventricular ejection waveform. Actual arteries exhibit nonlinear elasticity, reflected waves, changing resistance and active regulation. The model supplies no safe pressure threshold, heart-rate advice or interpretation of an individual pulse. Conservation over a full period is the useful test: integrated outflow must equal the input volume.

3. Reconstruct the original evidence

At C=2 and T=1, pressure jump is 3 and time constant 4. Peak is 3/[1−e^(−1/4)]≈13.5624, trough≈10.5624, mean pressure 12 and mean flow 6. Stored-volume decrease C(Pmax−Pmin)=6 closes the period.

4. Predict and investigate

Predict first: Can greater compliance reduce pulsatility without reducing the specified mean flow?

Compare all compliances at period 1, then change period at fixed compliance. Retain peak, trough, mean and integrated outflow, distinguishing the instantaneous pulse from the displayed runoff segment.

5. Defend a changed transport case

Apply the mechanism to a changed boundary

At C=1 and T=2, find pulse difference, mean flow, mean pressure and runoff time constant.

Retain the first response, units, uncertainty and any prior feedback exposure in the notebook before comparing this public explanation.

Compare a worked response

Pressure jump is 6, mean flow 3, mean pressure 6 and time constant2. Peak is 6/(1−e^(−1))≈9.49186 and trough≈3.49186, still losing exactly volume 6 per cycle.

6. Preserve a bounded explanation

Retain your first prediction, full units and conservation checks, an alternative mechanism and a discriminating observation in the Anatomy course workspace. These invented data are not individual physiological values. Do not perform breath-holding, forced breathing, exercise challenges, blood sampling or personal measurements. Public answer exposure does not establish independent learner or practical competence.

Supporting anatomical mechanism, checked 30 October 2026. Original models, diagrams and exercises; no clinical interpretation or treatment guidance.