Edited nearly a year later to clarify: dry ice cryonics probably won't work, for reasons hinted at in the post, and stated by Gav in the comments, regarding nanoscale ice crystals. It seems like there may be less of a tradeoff between fracturing and having ice crystals now than there used to be, especially if newer approaches involving e.g. cryonics with persufflation end up working well in humans.
This post is a spot-check of Alcor's claim that cryonics can't be carried out at dry ice temperatures, and a follow-up to this comment. This article isn't up to my standards, yet I'm posting it now, rather than polishing it more first, because I strongly fear that I might never get around to doing so later if I put it off. Despite my expertise in chemistry, I don't like chemistry, so writing this took a lot of willpower. Thanks to Hugh Hixon from Alcor for writing "How Cold is Cold Enough?".
More research (such as potentially hiring someone to find the energies of activation for lots of different degradative reactions which happen after death) is needed to determine if long-term cryopreservation at the temperature of dry ice is reasonable, or even preferable to storage in liquid nitrogen.
On the outside view, I'm not very confident that dry ice cryonics will end up being superior to liquid nitrogen cryonics. Still, it's very hard to say one way or the other a priori. There are certain factors that I can't easily quantify that suggest that cryopreservation with dry ice might be preferable to cryopreservation with liquid nitrogen (specifically, fracturing, as well as the fact that the Arrhenius equation doesn't account for poor stirring), and other such factors that suggest preservation in liquid nitrogen to be preferable (specifically, that being below the glass transition temperature prevents movement/chemical reactions, and that nanoscale ice crystals, which can grow during rewarming, can form around the glass transition temperature).
(I wonder if cryoprotectant solutions with different glass transition temperatures might avoid either of the two problems mentioned in the last sentence for dry ice cryonics? I just heard about the issue of nanoscale ice crystals earlier today, so my discussion of them is an afterthought.)
Using dry ice to cryopreserve people for future revival could be cheaper than using liquid nitrogen for the same purpose (how much would using dry ice cost?). Additionally, lowering the cost of cryonics could increase the number of people who sign up for cryonics-- which would, in turn, give us a better chance at e.g. legalizing the initiation of the first phases of cryonics for terminal patients just before legal death.
This document by Alcor suggests that, for neuro and whole-body patients, an initial deposit of 6,600 or 85,438 USD into the patient's trust fund is, respectively, more than enough to generate enough interest to safely cover a patient's annual storage cost indefinitely. Since around 36% of this amount is spent on liquid nitrogen, this means that completely eliminating the cost of replenishing the liquid nitrogen in the dewars would reduce the up-front cost that neuro and whole-body patients with Alcor would pay by around 2,350 or 31,850 USD, respectively. This puts a firm upper bound on the amount that could be saved by Alcor patients by switching to cryopreservation with dry ice, since some amount would need to be spent each year on purchasing additional dry ice to maintain the temperature at which patients are stored. (A small amount could probably be saved on the cost which comes from cooling patients down immediately after death, as well).
This LW discussion is also relevant to storage costs in cryonics. I'm not sure how much CI spends on storage.
Relevant Equations and Their Limitations
Alcor's "How Cold is Cold Enough?" is the only article which I've found that takes an in-depth look at whether storage of cryonics patients at temperatures above the boiling point of liquid nitrogen would be feasible. It's a generally well-written article, though it makes an assumption regarding activation energy that I'll be forced to examine later on.
The article starts off by introducing the Arrhenius equation, which is used to determine the rate constant of a chemical reaction at a given temperature. The equation is written:
k = A * e^(-Ea/RT) (1)
- k is the rate constant you solve for (the units vary between reactions)
- A is a constant you know (same units as k)
- Ea is the activation energy (kJ/mol)
- R is the ideal gas constant (kJ/K*mol)
- T is the temperature (K)
As somewhat of an aside, this is the same k that you would plug into rate law equation, which you have probably seen before:
v = k * [A]m[B]n (2)
- v is the rate of the reaction (mol/(L*s))
- k is the rate constant, from the Arrhenius equation above
- [A] and [B] are the concentrations of reactants-- there might be more or less than two (mol/L)
- m and n are constants that you know
The Arrhenius equation-- equation 1, here-- does make some assumptions which don't always hold. Firstly, the activation energy of some reactions changes with temperature, and secondly, it is sometimes necessary to use the modified Arrhenius equation (not shown here) to fit rate constant v. temperature data, as noted just before equation 5 in this paper
. This is worth mentioning because, while the Arrhenius equation is quite robust, the data doesn't always fit our best models in chemistry.
Lastly, and most importantly, the Arrhenius equation assumes that all reactants are always being mixed perfectly, which is definitely not the case in cryopreserved patients. I have no idea how to quantify this effect, though after taking this effect into consideration, we should expect degradation reactions in cryopreserved individuals to happen much more slowly than the Arrhenius equation would explicitly predict.
Alcor on "How Cold is Cold Enough?"
The Alcor article goes on to calculate the ratio of the value of k, the rate constant, at 77.36 Kelvin (liquid nitrogen), to the value of k at other temperatures for the enzyme Catalase. This ratio is equal to the factor by which a reaction would be slowed down when cooled from a given temperature down to 77 K. While the calculations are correct, Catalase is not the ideal choice of enzyme here. Ideally, we'd want to calculate this ratio for whatever degradative enzyme/reaction had the lowest activation energy, because then, if the ratio of k at 37 Celsius (body temperature) to k at the temperature of dry ice was big enough, we could be rather confident that all other degradative reactions would be slowed down at dry ice temperatures by a greater factor than the degradative reaction with the lowest activation energy would be. Of course, as shown in equation 2 of this post, the concentrations of reactants of degradative reactions do matter to the speed of those reactions at dry ice temperatures, though differences in the ratio of k at 37 C to k at dry ice temperatures between different degradative reactions will matter much, much more strongly in determining v, the rate of the reaction, than differences in concentrations of reactants will.
I'm also quite confused by the actual value given for the Ea
of catalase in the Alcor article-- a quick google search suggests the Ea
to be around 8 kJ/mol
or 11 kJ/mol
, though the Alcor article uses a value of 7,000 cal/(mol*K), i.e. 29.3 kJ/(mol*K), which can only be assumed to have been a typo in terms of the units used.
Of course, as the author mentions, Ea values aren't normally tabulated. The Ea for a reaction can be calculated with just two experimentally determined (Temperature, k (rate constant)) pairs, so it wouldn't take too long to experimentally determine a bunch of Eas for degradative reactions which normally take place in the human body after death, especially if we could find a biologist who had a good a priori idea of which degradative reactions would be the fastest.
Using the modified form of the Arrhenius equation from Alcor's "How Cold is Cold Enough", we could quickly estimate what the smallest Ea for a degradative biological reaction would be that would result in some particular and sufficiently small number of reactions taking place at dry ice temperatures over a certain duration of time. For example, when neglecting stirring effects, it turns out that 100 years at dry ice temperature (-78.5 C) ought to be about equal to 3 minutes at body temperature for a reaction with an Ea of 72.5 kJ/mol. Reactions with higher Eas would be slowed down relatively more by an identical drop in temperature.
So, if we were unable to find any degradative biological reactions with Eas less than (say) 72.5 kJ/mol, that would be decent evidence in favor of dry ice cryonics working reasonably well (given that the 100 years and three minutes figures are numbers that I just made up-- 100 years being a possible duration of storage, and three minutes being an approximation of how long one can live without oxygen being supplied to the brain).
Damage from Causes Other Than Chemical Reactions in Dry Ice Cryonics
The most important instability for cryopreservation purposes is a tendency toward ice nucleation. At temperatures down to 20 degrees below the glass transition temperature, water molecules are capable of small translations and rotations to form nanoscale ice-crystals, and there is strong thermodynamic incentive to do so [5, 6]. These nanoscale crystals (called "nuclei") remain small and biologically insignificant below the glass transition, but grow quickly into damaging ice crystals as the temperature rises past -90°C during rewarming. Accumulating ice nuclei are therefore a growing liability that makes future ice-free rewarming efforts progressively more difficult the longer vitrified tissue is stored near the glass transition temperature. For example, storing a vitrification solution 10 degrees below the glass transition for six months was found to double the warming rate necessary to avoid ice growth during rewarming . The vitrification solution that Alcor uses is far more stable than the solution used (VS41A) in this particular experiment, but Alcor must store its patients far longer than six months.
The same article also discusses fracturing, which can damage tissues stored more than 20 C below the glass transition temperature. If nanoscale ice crystals form in patients stored in dry ice (I expect they would), and grew during rewarming from dry ice temperatures (I have no idea if they would), that could be very problematic.
Implications of this Research for Liquid Nitrogen Cryonics
If someone has a graph of how body temperature varies with time during the process of cryopreservation, it would be trivial to compute the time-at-body-temperature equivalent of the time that freezing takes. My bet is that getting people frozen too slowly hurts folks's chances of revival far more than they intuit.