Psychiatry needs more simulations: the case of serum lithium concentrations
Guest post by the physicist Alex Mendelsohn
Alex Mendelsohn, PhD is a physicist based in the UK and the pseudonymous guest author of this post. He has written about his experience of the mental health system in an article for Physics World, and he wrote the article “Lithium story: eight guidelines, eight recommendations” for the Lancet Psychiatry in which he told the story of how he navigated the confusing and contradictory literature on lithium serum concentrations to figure out a dosing schedule that worked best for him and to persuade his psychiatrist. He blogs at The Anxious Physicist.
In the 1960s, the physicist Richard Feynman gave a series of lectures about the laws of physics.1 In the final lecture, “Seeking new laws” he outlined the philosophy that physicists use to come up with new theories. First, physicists guess what they think might be a new law (in other words, form a hypothesis). Then, physicists compute the consequences of that guess. In most cases, this means coming up with one or more mathematical equations that describe the guess and also produce a prediction (given a set of initial conditions). This is called a “simulation” of the guess. In the final step, the simulation is compared against the experiment. Which, in many cases, informs a new guess.
I used this doctrine extensively throughout my physics doctorate.2 In my case, I actually had a computer do it for me. Due to the advent of personal computers, I found that most of my experimental physics colleagues relied on some sort of combination of simulations and experiments in their papers.
Through deductive reasoning, simulations can improve the analysis of experimental results that would otherwise be difficult. This was one of the philosophies used to capture the first image of a black hole.
In fact, the psychiatrist Amdi Amdisen used this methodology in the 1975 paper 3 that first proposed the 12-hour standardized serum lithium (12h-stSLi) concentration. Firstly, he showed that his two-compartment model simulations of serum concentrations matched well to patient serum concentrations. From the patient experimental data, he then demonstrated that the biological half-life of lithium between patients varied dramatically. To experimentally see how the inter-patient lithium half-lives affected therapeutic monitoring, he would’ve had to put each patient on the same mean steady state concentration of lithium. This would be both unethical (e.g. patients with short half-lives would likely have toxic peak serum concentrations) and difficult to achieve. However, because Amdisen had shown that his two-compartment model simulation matched very well with experimental data, he was able to simulate the pharmacokinetic curves instead. When Amdisen did that, he found that blood draws after 12 hours became increasingly unreliable.
When studying more complicated systems, simulations are often used as a tool alongside observations to dramatically improve empirical judgments. For instance, meteorologists use ensemble simulations alongside observations of known weather patterns (for example, the Madden-Julian Oscillation) to produce a weather forecast. This Met Office YouTube video shows the process rather well.
Given how extensively simulations are used within physics, I was surprised to see the scarcity of computational methods throughout the experimental lithium pharmacokinetic literature. This was despite many occasions when simulated methods would have enhanced a paper.
For example, take a look at the following figure from the 1988 paper by Hunter .
It had been known for almost a decade that lithium serum concentrations abided by a two-compartment model .4 But there is no mention of this model in the paper. When plotted on a semi-log plot (see below), the Hunter data clearly shows the dual half-life characteristic of a two-compartment model.
The above graph showed that Hunter had quality data. So why was the plot not included in the paper? Why was this not spotted in peer review?
However, I was particularly intrigued by the sparse or even absent mentions of Amdisen’s work on the 12h-stSLi concentration in the lithium therapeutic monitoring literature –, given his clear contributions to the subject. After a little bit of exploring, I proposed in a recent Lancet Psychiatry article (which I then explored further in a blog post) that the use of unclear and imprecise language played a significant role in how Amdisen’s research was forgotten. However, I had a niggling feeling that ambiguous language wasn’t the sole reason for the loss of Amdisen’s work. I wondered whether simulation as a tool was not valued as highly in lithium experimental pharmacokinetics as it has been in physics.
I was particularly intrigued by the sparse or even absent mentions of Amdisen’s work on serum lithium concentration in the lithium therapeutic monitoring literature. I wondered whether simulation as a tool was not valued as highly in lithium experimental pharmacokinetics as it has been in physics.
Upon further exploration, I came across a 2013 paper by Sienaert et al. . Titled “How to initiate lithium therapy: a systematic review of dose estimation and level prediction methods”, it provided an extensive analysis of previous simulated methods5 used to predict lithium dose/serum concentration. The authors conclude that none of the simulated methods “provide any relevant advantage” over the current clinical method of a psychiatrist judging therapeutic dose through incremental titration.
While the authors provide a comprehensive analysis of the flaws in current computational methods, the simulation vs. empirical framing is both odd and worrying from my point of view. Odd because simulation has always been thought of as an aid to scientific analysis in physics. A physicist’s framing of the problem would be something like “How can we use simulations with empirical evidence to help the clinician achieve a dose that provides therapeutic benefit without toxicity for a patient?”.
For instance, instead of judging simulations on how accurately and precisely they predict 12h-stSLi concentrations (or therapeutic doses), I’m wondering whether they might be better used as a visualization tool. Given initial parameters such as creatinine clearance and an initial 12h-stSLi level at a very low dose, perhaps many two-compartment pharmacokinetic curves over a range (initial conditions varied to give a long and short half-life interval) could be simulated to give the clinician a rough idea of what the pharmacokinetic curve looks like and the peak concentration. A single number is hard to contextualize. As mentioned previously, lithium elimination half-lives can vary dramatically amongst individuals.
Instead of judging simulations on how accurately and precisely they predict 12-hour standardized serum lithium concentrations (or therapeutic doses), I’m wondering whether they might be better used as a visualization tool. Given initial parameters, perhaps many two-compartment pharmacokinetic curves over a range could be simulated to give the clinician a rough idea of what the pharmacokinetic curve looks like and the peak concentration.
The simulation vs empirical framing by Sineart et al. is worrying because there is ample evidence that empirical judgments by psychiatrists are extremely fallible; Daniel Kahneman and colleagues put it in their book Noise as “the depressing case of psychiatry” . One of the studies the authors reference found that “highly trained specialist psychiatrists under study conditions were only able to agree that a patient [had] depression between 4 and 15 percent at a time” .
This is not to say that I think empirical evidence should be avoided; far from it. An overreliance on simulation and quantitative methods in general can be dangerous too (e.g. overreliance on a 12h-stSLi level in therapeutic range when a patient is exhibiting toxicity symptoms). I am putting forward the idea that perhaps the field of psychiatry does not utilize tools as well as it could. A 2006 study by Aboraya et al.  makes this case: “The reliance on the patient's subjective symptoms, the clinician's interpretation of the symptoms, and the absence of objective measure (such as blood test) implant the seeds of diagnostic unreliability of psychiatric disorders.”
I would like to add the lack of simulation to the list.
In physics, the tool of simulation has proved to be so valuable that it now inhabits the very philosophy physicists use to come up with new laws. I believe it can have a similar value in psychiatry. Having spent a long time as a patient in the psychiatric system, I was surprised at how much overlap there was between physics and psychiatry. For instance, weather forecasters and clinical psychiatrists both use empirical evidence from complex systems to make judgments. Perhaps there would be something to gain if clinical psychiatrists reached out to learn how weather forecasters used simulations to make their judgments more accurate and reliable.
As a final note, I think it is worth mentioning that physics needs help from psychiatry just as much as psychiatry needs help from physics. As the anonymous author of a 2018 Physics World article puts it:
“The history of physics is littered with people affected by mental-health conditions, and too often their stories have sad endings. Isaac Newton, Wolfgang Pauli and David Bohm, to name a few, are all thought to have suffered to some degree, and Ludwig Boltzmann took his own life after struggling with bipolar disorder for years. But mental illness does not just strike the elite. It is something that can affect anyone and you will undoubtedly have friends, family or colleagues facing such problems. Unfortunately, there is very little awareness of mental health in academia and few practical resources or material to draw on.”
I hope it is finally time for the worlds of psychiatry and physics to come together. For both our sakes.
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 A. Amdisen, ‘Monitoring of lithium treatment through determination of lithium concentration’, Dan Med Bull, vol. 22, no. 7, pp. 277–291, Dec. 1975.
 R. Hunter, ‘Steady-state pharmacokinetics of lithium carbonate in healthy subjects.’, British Journal of Clinical Pharmacology, vol. 25, no. 3, pp. 375–380, 1988, doi: 10.1111/j.1365-2125.1988.tb03316.x.
 F. Nielsen-Kudsk and A. Amdisen, ‘Analysis of the pharmacokinetics of lithium in man’, Eur J Clin Pharmacol, vol. 16, no. 4, pp. 271–277, Jul. 1979, doi: 10.1007/BF00608406.
 G. S. Malhi, D. Gessler, and T. Outhred, ‘The use of lithium for the treatment of bipolar disorder: Recommendations from clinical practice guidelines’, Journal of Affective Disorders, vol. 217, pp. 266–280, Aug. 2017, doi: 10.1016/j.jad.2017.03.052.
 W. A. Nolen et al., ‘What is the optimal serum level for lithium in the maintenance treatment of bipolar disorder? A systematic review and recommendations from the ISBD/IGSLI Task Force on treatment with lithium’, Bipolar Disord, vol. 21, no. 5, pp. 394–409, Aug. 2019, doi: 10.1111/bdi.12805.
 L. Tondo et al., ‘Clinical use of lithium salts: guide for users and prescribers’, International Journal of Bipolar Disorders, vol. 7, no. 1, p. 16, Jul. 2019, doi: 10.1186/s40345-019-0151-2.
 L. Carter, M. Zolezzi, and A. Lewczyk, ‘An updated review of the optimal lithium dosage regimen for renal protection’, Can J Psychiatry, vol. 58, no. 10, pp. 595–600, Oct. 2013, doi: 10.1177/070674371305801009.
 E. M. Grandjean and J.-M. Aubry, ‘Lithium: updated human knowledge using an evidence-based approach. Part II: Clinical pharmacology and therapeutic monitoring’, CNS Drugs, vol. 23, no. 4, pp. 331–349, 2009, doi: 10.2165/00023210-200923040-00005.
 P. Sienaert, I. Geeraerts, and S. Wyckaert, ‘How to initiate lithium therapy: a systematic review of dose estimation and level prediction methods’, Journal of Affective Disorders, vol. 146, no. 1, pp. 15–33, Mar. 2013, doi: 10.1016/j.jad.2012.08.013.
 D. Kahneman, O. Sibony, and C. R. Sunstein, ‘Chapter 22: Guidelines in medicine’, in Noise: a flaw in human judgement, HarperCollins UK, 2021.
 S. M. Lieblich, D. J. Castle, C. Pantelis, M. Hopwood, A. H. Young, and I. P. Everall, ‘High heterogeneity and low reliability in the diagnosis of major depression will impair the development of new drugs’, BJPsych Open, vol. 1, no. 2, pp. e5–e7, Oct. 2015, doi: 10.1192/bjpo.bp.115.000786.
 A. Aboraya, E. Rankin, C. France, A. El-Missiry, and C. John, ‘The Reliability of Psychiatric Diagnosis Revisited’, Psychiatry (Edgmont), vol. 3, no. 1, pp. 41–50, Jan. 2006, Accessed: May 08, 2023. [Online]. Available: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2990547/
A hypothesis becomes a law (or “theory”) after its predictions have been compared against experiments many times in many different scenarios without replicable disagreement.
My PhD was about pinpointing the positions of atoms in crystals (Diamond is a crystal for instance). A beam of electrons was fired through the crystal and some electrons would deflect off of atoms within that crystal—all electrons would collect on a screen behind the crystal. This is an electron diffraction pattern. Through something called a refinement algorithm, I would input into a computer program my “best guess” for a crystal structure. The program would then simulate an electron diffraction pattern. I would take data from an experimental diffraction pattern and also input it into the program. The refinement algorithm would see how well the simulated diffraction pattern of my initial guess compared against the experimental one. The computer would come up with a slightly different guess, simulate that pattern, and see whether it was better or worse. If better, it would continue changing the simulated atomic positions in that general direction. If worse, it would change the atomic positions in the opposite direction. The program would finish when the simulated and experimental patterns matched.
The model assumes the body has two compartments: tissues and the bloodstream. After peak serum concentration, lithium enters a distribution phase. This is where lithium is distributed into tissues and is eliminated from the kidneys. After approximately 10 hours, tissue-bloodstream concentration is in pseudo-equilibrium and serum concentration decreases solely through elimination by the kidneys. Given that lithium is leaving the bloodstream via the tissues and kidneys in the distribution phase, it has a shorter half-life than in the elimination phase.
I define a simulated method as one that includes any calculation (whether computational, graphical or analytical)