Weight and Power Requirements for an Implantable Total Artificial Heart

Summary.

Daily volume requirement: 2000 gallon daily as base. Safety factor of 2 → 4000 gallons per day
Stroke Volume: 70 mL = 70×10⁻⁶ m³ per beat
Work per “beat” or stroke volume displacement: 1.3 J per beat
Energy Rating: deliver ≥1.53 Watts for at least 8 hours ~ 12.2 Watt-hours. Safety factor of two → ~25Wh
Power density: (batteries should be ≤ average weight of the heart)→ 25Wh/0.35kg ……or 71Wh/kg.
Pump requirements: assuming a diaphragm/piston design performing a pumping stroke of 2cm displacement. → F = 65N per stroke

Volume to pump

When at rest, the adult heart pumps ~5 litres of blood per minute[1]. That comes out to ~2000 gallons per day.

Assuming a safety factor of 2, one would require an artificial heart that can pump ~4000 gallons of blood per day.

Work done against pressure

Work is the energy transferred to an object via the application of force along a displacement.

The energy(W) required to pump blood mostly comes down to the work done against pressure in the ventricular cavities( $W_{p}$ ) From Work = Force x Displacement,

W_{p} = Δ P (V)

Where: ΔP is the pressure difference across the ventricle(Pa) V is the stroke volume(m³) per beat

$W_{p}$ left ventricle:

For the left ventricle, systolic pressure (ΔP) is ~90–140 mmHg. For this case study, we’ll assume; ΔP ~ 100 mmHg ≈ 13,300 Pa.

Stroke volume (V) is the volume of blood pumped from one ventricle of the heart with each beat, averaging approximately 60–100 mL in a healthy resting adult. Here, we’ll assume V ≈ 70 mL = 70×10⁻⁶ m³ That brings us to: $13, 300 x 70 \times 10 ⁻ ⁶ \approx 0.93 J p e r b e a t$

$W_{p}$ right ventricle:

For the right, normal right ventricular systolic pressure is <40 mmHg[2]-> ΔP ~ 40 mmHg = 5300 Pa

V ≈ 70 mL (same as left) = 70×10⁻⁶ m³

5300 x 70×10⁻⁶ ≈0.371 J per beat

So the combined $W_{p}$ ≈ 1.3 J per beat

Power (Rate of cardiac work)

Power(watts) = W/T

The typical resting heart rate for adults is 60 to 100 beats per minute[3]. Let’s assume 70 bpm.

The energy of heart expended over a minute(60 seconds) would then be ~91J.

91J/60s = 1.52 W.

So we need a battery that can deliver >1.52 Joules per second. And do this for multiple hours. Say ~8 hours under moderate load.

1.52W x 8 hours ≈12.2 Watt-hours(Wh).

So we need a battery and mechanical device rated >12.2Wh.

Battery requirements

Energy: Assume a safety factor of 2 on the Wh. Say ~25Wh.

Power density: And try to get the density right. Such that 25Wh are packed in a weight below 0.35kg which is the average weight of an adult heart as a benchmark. So the device doesn’t crush your chest cavity.

That is 25Wh/0.35kg or 71 Wh/kg

Current batteries meet this comfortably:

Photo Credit: NASA - National Aeronautics and Space Administration

Source: https://www.epectec.com/batteries/cell-comparison.html

Battery tech seems solved. Just beef it up with nanomanufactured high performance, high energy density and low weight materials

Pump requirements.

force capacity (F = W/D)

Work = 1.3J

Distance (displacement) → assume ~2cm(0.02m) for a diaphragm/piston design performing a pumping stroke.

That is F= 65N at a 2cm stroke.

References

What Is Cardiac Output?, Matt Smith, Web MD, https://www.webmd.com/heart/heart-cardiac-output
Kotrri G, Youngson E, Fine NM, Howlett JG, Lyons K, Paterson DI, Ezekowitz J, McAlister FA, Miller RJH. Right Ventricular Systolic Pressure Trajectory as a Predictor of Hospitalization and Mortality in Patients With Chronic Heart Failure. CJC Open. 2023 Jun 3;5(9):671-679. doi: 10.1016/j.cjco.2023.05.011. PMID: 37744660; PMCID: PMC10516718.
Mayo Clinic, What's a normal resting heart rate?, https://www.mayoclinic.org/healthy-lifestyle/fitness/expert-answers/heart-rate/faq-20057979#:~:text=What's a normal resting heart rate%3F