In September 2026, Stage B replaced an image-space sketch with k-Wave through an analytic three-layer skull plate — outer cortical bone, diploe, inner cortical bone — at pediatric-scale thicknesses of 1.0, 1.5, and 1.0 mm, with a smooth change in thickness from side to side. A 64-element array at 0.3 mm pitch transmits into the model. k-Wave solves the acoustic wave equations; it is the method most published transcranial work uses. This plate is not the measured infant geometry in the October research update.
How the distortion was measured
A point source sits at the target inside the simulated brain. Arrival time is recorded at each of 64 elements, once with no skull and once through the skull. The difference is the delay the bone adds — a number the earlier image-space model could not produce. In water, arrival time must equal distance divided by the speed of sound. That control matched to within 0.17 percent. Through the skull, peak pressure fell to 54 percent of the water value. The aim shifted 4.1 mm off target. Energy landing within 3 mm of the target fell from 12.4 percent to 1.6 percent.
What delay correction did
Timing each element to cancel its measured delay restored aim from 4.1 mm off target to 0.4 mm, and raised energy inside the 3 mm box from 1.6 percent to 6.8 percent — just over half the no-skull value of 12.4 percent. It did not narrow the focal spot. One delay per element cannot cancel a wave that bounces inside the thin bone and arrives more than once. A control with the delay sign reversed scored 2.1 percent against 6.8 percent, which confirms the sign by experiment.
How much room is left
Time reversal — recording the field at each element and playing it backwards — recovered 9.9 percent of energy on target, about 80 percent of the ideal, and a focal spot narrower than the water beam. It is a simulation benchmark, not a method for a child: it needs a sound source at the target, which a child does not provide. Its value is that the remaining gap is physics, not a coding error. The next stage is to close that gap without a source inside the head.
What this is not
A two-dimensional, lossless simulation through an analytic skull plate. No patient data. No phantom data. No hardware. No trained model — corrections in the current code are estimated or blind, not learned. No clinical claim and no regulatory clearance.