What is modeling and simulation (M&S) for in biology and medicine?

A model is a representation of natural phenomena by means of physical or computer processes, logical relations or mathematical formulas. The representation can be essentially graphic or only discursive like most current pathophysiological models (general reviews). It can also be a laboratory animal that has undergone a preparation that makes the whole, including the experimental conditions, resemble a human pathological situation (this is called an “animal model”); or physical, mechanical and electronic construction such as flight simulators for learning to fly aircraft.

The mathematical representation of a set of pieces of knowledge, when possible, allows formalization in a condensed and portable form, and lends itself to quantitative deductions. The translation of the physical (or chemical) processes to which the phenomenon under study is assimilated by analytical functions makes it possible to calculate the outputs when the inputs are artificially varied. It is simulation, which can be carried out on purely logical or computer models. Mathematical representation has enough advantages to be favoured because, according to G.G. Granger’s remark : “… Mathematics is not a solitary game but a means of advancing knowledge of the objects of the world, and of man in particular.”

We can see the construction of biology and medicine, and more widely the natural sciences, which, as their name suggests, are interested in the description and explanation of nature and in its midst of living systems, as a succession in time of increasingly sophisticated models that are for us the

representation and imitation of reality. This approach to reality without ever really penetrating it has been expressed by several authors, writers and scientists, as seen above for a few of them. Further, cognition scientists claim that creating is one of our brain’s steps toward action (see below).

Reality is elusive and the construction of knowledge can only be achieved through the development of models. 

The observation of an inaccessible and perhaps even non-existent reality has long preoccupied philosophers and scientists. Indeed, if we cannot assure that our image of reality is reality, one of two things. Either reality doesn’t exist as Xenophanes of Colophon though; or everything we think of it is false. It is therefore useless to try to know it. This is the position of the philosophers of the skeptical school. Either it exists, but we cannot, at best, anything but approach it. To approach it, we need a method that excludes opinion in favor of science because one opinion cannot be refuted in favor of another with arguments of knowledge. Science is then defined as a progression, probably infinite, towards reality, by means of convincing evidence serving as a demonstration. 

According to the Robert dictionary, a model is “that which serves or must serve as an object of imitation to make or reproduce something”; it can also be “a simplified representation of a process, a system”. The dictionary adds: “mathematical model [of a process]: a model formed by mathematical expressions and intended to simulate such a process”. Let’s complete with computer simulation, which, from a logical and/or mathematical model of the process studied, seeks to predict output functions by modifying the inputs (example: the effect of the angle of list on the speed and drift of a 12 meter JI).

The above definitions give the model, and modelling, which is the act of creating a model, a voluntarist (but what for?) aspect that is characteristic: a model of the process under study is constructed. The model is therefore the result of an elaboration of the human mind confronted with a natural phenomenon. By extension, a model of this natural phenomenon can be described as any coherent construction based on a defined collection of observations and experimental facts, in short of knowledge, concerning this phenomenon. The coherence is both internal (the model “stands”) and external (it is not in contradiction with other elements of knowledge, not taken into account, i.e. external to the defined collection). Often the model bases its internal coherence on a theory intended to explain the phenomenon. But it is often (always?) more than the theory itself, because it integrates, explicitly or implicitly, the consequences (or at least some of) the consequences of the theory.

Even if the boundaries are never very clearly identifiable, it is important to distinguish between theory and model. The theory pre-exists the model, which feeds on it. Theory is born through intuition and imagination. Its genesis from the known is difficult, if not impossible, to follow. Once formulated, it will make it possible to build a model of reality. To do this, a greater or lesser number of more or less simplifying hypotheses, more or less strong are added (a hypothesis is said to be “strong” when its likelihood is weak). Since these hypotheses, for a given natural process and theory, do not constitute a single whole, it is conceivable that several models derived from the theory can compete with each other or complement each other. In the latter case, they have different objectives !again, a model, what for?). Here we see an element of the initial definition of the word model reappear: its usefulness. The relationship between theory and model is in fact more complex because the use of the model may lead to a new theory, or, more often, affect the one that led to it.

(model and cognition here?)

Two characteristics of the word model applied to the natural and human sciences must be mentioned, because their consequences, particularly in the field of medicine and therapeutics, which concerns us here, are crucial. A model is always a reduction of the phenomenon studied, a simplification that puts it within the reach of its designer and its user. Here we find the meaning of the “reduced model”. Being a simplification, being built on a body of knowledge that is necessarily limited in relation to the complexity of reality and, moreover, evolving, a model is fragile and ephemeral. The accumulation of knowledge, including that generated by the confrontation of the consequences (outputs) of the model with the perceptible reality (experience) and with the knowledge external to that which served as its basis, i.e. the evaluation of its external coherence (always through experience or at the very least observation), will render the model obsolete, allowing it to be replaced by a more adequate one,  or at the very least impose its modification so that it better fits in with observations and new facts (adequacy of the model). But it is rare that the new one does not retain some of the constituent elements of the obsolete model. Despite its inherent fragility, and paradoxically, a model can be robust if the knowledge it is based on is robust (i.e. of high strength of evidence) and if its path of change is slow and limited, which is often the cas in biology and physiology.

In each of the quotes in the ‘History hallmarks” section, we find the notion of model under various labels: the “worlds” that we draw to explain the world, the general theory which is certainly false, the organizing discourse (modeling) and the levels of organization (levels of complexity and granularity of the model). We find the points that seem important to us: the fragility of the model, its ephemeral nature, its necessary questioning by a constant confrontation with observations and facts, its foreseeable partial or total obsolescence after this confrontation, its distance from reality that is otherwise inaccessible. Henri Atlan’s quote also suggests the normative role of discourse. It is necessary to denounce the pitfalls of this obligatory pre-eminence of discourse below and beyond logic and mathematical formulation (another form of discourse): the risks of intoxication of thought by the word and the dangers of this deviation for the adequacy of the model to the real problem. Ernest Renan states the impossibility of knowing reality. The image he offers of the topographical plan is an appropriate illustration, because there are plans of varying granularity depending on the use made of them, from the street plan of a city with metro stations to the topographical surveys of the military or the maps of sailors. Popper uses the word truth where we would put reality. He was then interested in the concept of truth, as a correspondence between statements and facts. He adds that the theories are more or less false.

In biology and medicine, as in any other scientific domains, the models can be explanatory, and then they are supposed to reflect the intimate mechanisms that lead to what is observed. They may be purely descriptive, seeking only to represent the visible part of phenomena. Many of the models are both explanatory and descriptive. However, a careful distinction must be made between these two aspects to avoid misinterpretations of the modelling results. Predictive models represent a particular class of “utilitarian” models. 

A model can be defined by its use, i.e. its purpose, at least partially and sometimes independently of the conditions that led to its design. As mentioned above, we will then see the coexistence of several models of the same phenomenon, which will be used in turn according to the goals pursued. These “utilitarian” models can persist even when the evolution of knowledge has shown their imperfection and their inadequacy to the state of knowledge considered as a whole. This durability is justified by their usefulness. An extreme type of utility model is the flight simulator used for learning (there are many other real-life simulators used for learning). There is no solution of continuity between purely explanatory models and learning models. Explanatory when invented, then used for the description of the phenomenon, it will be used for prediction, then for teaching: this is the case of compartmental models applied to the pharmacokinetics  of drug substances. 

Let’s make a special case for MIDD, model informed drug development

Innovation and the development of new therapeutics for humans are particularly suitable for the use of mathematical models. Indeed, this process is made up of a series of decision-making steps that are based on the knowledge available at the time of their execution. Traditionally, this knowledge is modeled by the minds of developers who, like any human mind, are limited in their ability to integrate multiple pieces of knowledge, most of which are quantitative. In addition, some of this knowledge, in particular that which the previous stage decided to acquire, is the result of animal or human trials. Thanks to mathematical models of the disease and of the therapeutic of interest  these trials are better designed, usefully completed and more finely interpreted (for instance exploring why a trial has failed). Thanks to this virtuous circle where experiments and simulations complement and enrich each other, decisions are easier and safer.

The case for mathematical models and personalized medicine will be the subject of a forthcoming blog.

Finally, it is important to understand that the model cannot be a perfect representation of reality, whether it is explanatory or even merely descriptive. It is a construction of the mind that cannot faithfully translate the reality that we do not know. The discrepancy, which is unknown, depends on the degree of sophistication of the model, which in turn depends on the use that is to be made of the model, and on the knowledge available on the phenomenon modelled. A model is therefore only an approximate and provisional construction, since knowledge progresses, in part thanks to the modeling itself, and whose level of complexity is related to the use for which it is intended.