Mathematical models are increasingly being used in medicine to study physiological, pathophysiological and therapeutic pathways [1–3]. In hepatology, mathematical abstractions have been beneficial to predict the viral load of hepatitis C following treatment [4], outcome after acetaminophen overdose [5], or to quantify porto-systemic shunting and inter-organ ammonia metabolism at different stages of cirrhosis [6]. However, in many medical fields (including hepatology), there is much resistance to include theoretical models in their traditional tool set and furthermore a lack of confidence in the generated theoretical results

Noiret, Lorette

Rose, Christopher

Journal of Hepatology

English

Papyrus Université de Montréal

Mathematical models and hepatology; oil and vinegar?

Lorette Noiret

Christopher F. Rose

Crossref

Université de Montréal

                             Elsevier Editorial System(tm) for Journal of 
Hepatology 
                                  Manuscript Draft 
 
 
Manuscript Number:  
 
Title: Mathematical models and hepatology; oil and vinegar?  
 
Article Type: Invited Editorial 
 
Section/Category: Basic liver failure 
 
Corresponding Author: Dr. Christopher Rose, PhD 
 
Corresponding Author's Institution: CRCHUM 
 
First Author: Lorette Noiret, PhD 
 
Order of Authors: Lorette Noiret, PhD; Christopher Rose, PhD 
 
 
 
 
 
 
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Title: Mathematical models and hepatology; oil and vinegar? 
 
Mathematical models are increasingly being used in medicine to study physiological, 
pathophysiological and therapeutic pathways[1–3]. In hepatology, mathematical abstractions 
have been beneficial to predict the viral load of hepatitis C following treatment [4], outcome 
after acetaminophen overdose[5], or to quantify porto-systemic shunting and inter-organ 
ammonia metabolism at different stages of cirrhosis[6]. However, in many medical fields 
(including hepatology), there is much resistance to include theoretical models in their traditional 
tool set and furthermore a lack of confidence in the generated theoretical results. One obvious 
hindrance that prevents the expansion of mathematics in medicine is the difficulty to 
comprehend the methods and results, especially when described with technical terminology. 
However, even when results are presented in a clear comprehensible way, a suspicion remains 
regarding the validity of the model, and therefore the simulation-generated results and 
conclusions are mistrusted. This uncertainty may be further aggravated by the fact that although 
it is possible to appreciate the limitations of an experimental biological setting, understanding the 
limitations of a mathematical model is extremely difficult, even for mathematicians. Validating 
model assumptions and results is not straightforward [3]. In many cases, different assumptions 
(eg. number of transporters, concentration of enzymes, etc) could produce similar outcomes, and 
so attempting to validate a model by simply displaying concurrence between simulations and 
experimental data is not adequate. A more convincing way would be to use the model to 
formulate correct and surprising predictions. However, this is not always truly possible. So, with 
all this in mind, how can we increase the confidence in mathematical approaches? The key is to 
better understand what type of answer can be extracted from models and to recognize that a good 
fit between model simulations and experimental data is not necessarily the ultimate goal. Misfits 
can equally lead to noteworthy results, helping to discard competing scenarios or point to a 
missing component.  
In this issue, Ghallab et al. provide an excellent example of how a misfit can provide new 
and exciting insights regarding the underlying mechanisms of hyperammonemia in acute liver 
failure. Here, the authors reinvestigated the results of their previous published mathematical 
Manuscript
Click here to view linked References
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model of hepatic ammonia metabolism in mice following CCl4 injection, and tried to understand 
why some of the predictions were significantly higher than experimental values [7]. At first, the 
authors believed the discrepancy was due to the calibration of the model. However, refining the 
estimation of parameters by including changes in the concentration of enzymes over time did not 
eliminate the discrepancy. Subsequently, the authors developed a hypothesis stating their initial 
model lacked a component; in other words, that a novel and unidentified mechanism should 
detoxify ammonia in addition to urea production and glutamine synthesis. After careful analysis 
of plasma components, the missing element was proposed to be glutamate dehydrogenase 
(GDH), a reversible enzyme that converts glutamate to α-ketoglutarate and ammonia. The 
rational was that in acute liver failure, GDH is released from necrotic hepatocytes in the 
extracellular fluid where high ammonia concentrations would favor the synthesis of glutamate 
from α-ketoglutarate. And indeed injecting GDH, α-ketoglutarate and NADPH in mice 24h after 
injection of CCl4 rapidly decreased the blood concentration of ammonia. This hypothesis was 
further tested theoretically by inserting GDH into the mathematical model (one of the great 
advantages of mathematical models is that a new hypothesis can be tested rapidly). In turn, 
including GDH improved the fit with the data, which supported the hypothesis. This paper 
represents therefore a successful example of hypothesis driven by a mathematical model (model 
guided experimentation). The model helped identify and test a quantitatively important 
mechanism. The future lies ahead on whether GDH, α-ketoglutarate and NADPH can be used as 
a therapeutic strategy for the treatment of hyperammonemia in acute liver failure or if this 
cocktail is pertinent to patients with chronic liver disease where intra- and extra-hepatic shunting 
play a critical role. Unfortunately, the current model may not be able to answer these questions.  
A dangerous temptation when employing mathematical models is attempting to answer 
questions that are beyond its limitations. A mathematical model is designed to answer a specific 
set of questions, and can rarely be extended. In the study by Ghallab et al., predicting the long 
lasting systemic effect of GDH (including α-ketoglutarate and NADPH) on blood ammonia 
levels would be unreliable without including the complex dynamics of glutamine, glutamate, 
ammonia (and α-ketoglutarate) in various organs.  
With such potential, the question remains; how to promote the development of 
mathematical modeling in medicine?  The strength of Ghallab’s paper is the multiple (back and 
forth) exchanges between modeling and experimental results, which is probably not due to 
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chance. It is vital to expand mathematics in medicine and to develop close interdisciplinary 
collaborations. Medical researchers need to integrate mathematicians at the beginning of a study 
in order to measure the necessary parameters to calibrate a model. In turn, it is essential for 
mathematicians to closely discuss with researchers in order to identify the key components of the 
biological process, resolve which questions/model structures would help to discard the 
hypothesis, and discuss what model predictions would be clinically useful. One way to promote 
such interaction would be to physically incorporate mathematicians in laboratories and hospitals. 
Fruitful long term collaborations can help to understand the constraints and limitations involved 
in both mathematical modeling and experimental/clinical measurements. Such a simple change 
may lead the better insights in health and disease, and could play a powerful role in personalized 
medicine.  
 
Lorette Noiret, PhD 
Center for Systems Biology, Massachusetts General Hospital 
Systems Biology, Harvard Medical School 
Boston, USA 
 
 
Christopher F. Rose, PhD 
Hepato-Neuro Laboratory 
CRCHUM, Université de Montréal 
Montréal, Canada 
 
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organisation can inform liver disease pathogenesis. J Hepatol 2014;61:951–6. 
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dynamics in vivo and the antiviral efficacy of interferon-alpha therapy. Science 
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injury and dysfunction after acetaminophen overdose: early discrimination between survival 
and death. Hepatology 2012;56:727–34. doi:10.1002/hep.25656. 
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[6] Noiret L, Baigent S, Jalan R. Arterial ammonia levels in cirrhosis are determined by 
systemic and hepatic hemodynamics, and by organ function: a quantitative modelling study. 
Liver Int 2014;34:e45–55. doi:10.1111/liv.12361. 
[7] Schliess F, Hoehme S, Henkel SG, Ghallab A, Driesch D, Böttger J, et al. Integrated 
metabolic spatial-temporal model for the prediction of ammonia detoxification during liver 
damage and regeneration. Hepatology 2014;60:2040–51. doi:10.1002/hep.27136. 
 
 
Model of hepatic ammonia metabolism in 
mice after CCl4 injection 
 (based on current knowledge) 
Discrepancy between the model simulations 
and experimental data 
Explanation 1 : 
Issue with model calibration  
New  
experiments 
Inclusion of time-dependent enzyme 
concentrations in the model does not 
eliminate the discrepancy 
Explanation 2 : 
The model misses an 
unrecognized but yet important 
mechanism of hepatic ammonia 
detoxification 
New  
experiments 
Addition of this 
hypothesis to the model 
Validation of hypothesis  
New treatment for 
hyperammonemia in ALF? 
Hypothesis: 
GDH 
released 
from 
necrotic 
hepatocytes 
detoxify 
ammonia 
Figure


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Mathematical models and hepatology; oil and vinegar?

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