Forking network generator is incorrect

[jmpf]

The forking network generator is incorrect. See https://github.com/jmsgrogan/MicrovesselChaste/commit/189d810e5e442f62a1e15866677e95a9ff034d55 for the erroneous line.

Problem

This relates to Bernabeu et al. 2020. As described on page 3 of the supplementary information https://www.pnas.org/doi/suppl/10.1073/pnas.2007770117/suppl_file/pnas.2007770117.sapp.pdf Murray's law says that the vessel diameters scale with cube root. With fixed lambda (length/diameter) this means that the lengths also scale with cube root. In the cube the y-height of each bifurcation is taken to scale by 1/2 and the horizontal position is calculated from knowing the vessel length and vessel height. It's this horizontal position which is wrong. The actual vessel length in our forking networks does not match the description in the SI of the paper.

• vessel lengths are not as advertised so the geometry of all forking networks is wrong
• because vessel diameters are scaled correctly this means that lambda is not fixed to expected value
• because the Pries with memory solver uses a hard-coded parent vessel length (which is the expected length not the actual length) the CFL recovery is wrong
• All panels in Figure 4 of the paper have the potential to be wrong https://www.pnas.org/doi/10.1073/pnas.2007770117#fig04

Todo

• [x] Assess how correcting the parent vessel length (to the actual length in these networks) will affect the Pries with memory solver in these incorrect geometries. See Fig 4b
• [ ] Assess how correcting the geometry will affect Fig 4a and Fig 4b. (How big are these length differences and are they noticeable on Fig4a?)
• [ ] Assess how correcting the geometry will affect Fig 4c and the SI data
• [ ] Potentially issue an erratum

[jmpf]

This what our current code produces for Figure 4b (before clipping and colour adjustments)

[jmpf]

See commit f74f08c This Figure 4b with the same geometry but with the haematocrit solver using the actual vessel lengths (before clipping and colour adjustments)

There is a visible difference. In the original figure the oxygen concentration differences in the central region are more exaggerated. Perhaps this is because the expected vessel lengths are shorter than the actual length (meaning that the CFL recovers more in the new calculation).

[jmpf]

7135cec changes the default behaviour. The haematocrit converges to a slightly different place but, as can be seen here and in ffea809, it's a negligible change to the original plot.