First off, I love that you're actively pursuing alternative methods of human preservation. That's awesome, and I hope you manage to find some useful ideas in your search. However, I fear that this approach in particular doesn't really solve the problem that cryoprotectants successfully do (toxicity briefly aside).
without cryoprotectants the water will expand upon freezing, and break the cells.
This line in particular is my biggest point of contention. I am by no means an expert in this field, and my understanding may be moot in this context, but the expansion of water-ice crystals isn't the central concern for frozen biological cells. A quickly found source claims that:
Since ice is essentially pure H2O, ice formation can increase the concentration of minerals in the remaining cytosol to a toxic level. The increased mineral concentration in the cytosol will cause water to be drawn in from the surrounding cells by osmosis, which can cause the cell to swell and burst.
Alcor's official FAQ also says that:
When tissue is slowly cooled, ice first forms between cells. The growing ice crystals increase the concentration of solutes in the remaining liquid around them, causing osmotic dehydration of cells.
Your method doesn't prevent the formation of ice crystals, it merely changes the structure of the crystals, and at what temperature they form, so I suspect harmful cell osmosis can still occur. Of course, I could be insufficiently understanding why ice crystals effect the mineral concentration of cytosol, or the order in which certain biological areas freeze under variable conditions, and your smaller ice/lower freezing temperature would successfully prevent this issue. I don't believe this is necessarily the case, given your explanation, but if anyone who's more studied in these fields could speak up, I'd be happy to defer to their expertise.
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It seems like the approach of cooling the organism to -30C at 350MPa, and then raising pressure further to ~600Mps to freeze it could actually solve that. As far as I understand, the speed of diffusion in water it far slower that the speed of sound (speed of sound at 25C is 1497 m/s, while diffusion coefficient for protons at 25C is 9.31e-5 cm^2/s, which corresponds to 1.4e-4 m/s - 8 orders of magnitude less), which is the speed of pressure gradient propagation. So if we use raising pressure as a way to initiate phase transition, it will occur nearly simultaneously everywhere, and the solutes won't have time to diffuse anywhere.
ETA: I just realized that since diffusion propagates according to inverse square law, while sound is linear, they should be compared to each other at the shortest distance possible. So I checked the time it takes for a proton to cover 0.1nm (hydrogen atom diameter) in water - 5.37e-13s, which gives us 186 m/s. It's far greater than the original number, but still an order of magnitude smaller than the speed of sound. And if we take 4nm (the thickness of a cell membrane) we have 8.59e-10s - only 4 m/s, so it decreases very quickly, and we're pretty much safe.
That's a very sound (pun partially intended) insight, and I don't immediately see a significant reason for why that shouldn't be the case.
However, humans aren't perfectly uniform spheres of water (to borrow from a common physics joke), so some concerns do still exist. Namely: Pressure might propagate through them less predictably/quickly than just water, and different areas of the body might begin freezing at different pressures/in different orders (which can, however, be countered by raising pressures quickly).
I have updated significantly in the direction of "This idea might actually be very valuable to cryonics proponents," for sure.