The economists John Kay and Mervyn King assert in their book ‘Radical Uncertainty – decision-making beyond numbers‘ that ‘economic forecasting is necessarily harder than weather forecasting’ because the world of economics is non-stationary whereas the weather is governed by unchanging laws of nature. Kay and King observe that both central banks and meteorological offices have ‘to convey inescapable uncertainty to people who crave unavailable certainty’. In other words, the necessary assumptions and idealisations combined with the inaccuracies of the input data of both economic and meteorological models produce inevitable uncertainty in the predictions. However, people seeking to make decisions based on the predictions want certainty because it is very difficult to make choices when faced with uncertainty – it raises our psychological entropy [see ‘Psychological entropy increased by ineffective leaders‘ on February 10th, 2021]. Engineers face similar difficulties providing systems with inescapable uncertainties to people desiring unavailable certainty in terms of the reliability. The second law of thermodynamics ensures that perfection is unattainable [see ‘Impossible perfection‘ on June 5th, 2013] and there will always be flaws of some description present in a system [see ‘Scattering electrons reveal dislocations in material structure‘ on November 11th, 2020]. Of course, we can expend more resources to eliminate flaws and increase the reliability of a system but the second law will always limit our success. Consequently, to finish where I started with a quote from Kay and King, ‘certainty is unattainable and the price of near-certainty unaffordable’ in both economics and engineering.
During the lock-down in the UK due to the coronavirus pandemic, I have been reading about viruses and the modelling of them. It is a multi-disciplinary and multi-scale problem; so, something that engineers should be well-equipped to tackle. It is a multi-scale because we need to understand the spread of the virus in the human population so that we can control it, we need to understand the process of infection in individuals so that we can protect them, and we need to understand the mechanisms of virus-cell interaction so that we can stop the replication of the virus. At each size scale, models capable of representing the real-world processes will help us explore different approaches to arresting the progress of the virus and will need to be calibrated and validated against measurements. This can be represented in the sort of model-test pyramid shown in the top graphic that has been used in the aerospace industry [1-2] for many years [see ‘Hierarchical modelling in engineering and biology’ on March 14th, 2018] and which we have recently introduced in the nuclear fission  and fusion  industries [see ‘Thought leadership in fusion engineering’ on October 9th, 2019]. At the top of the pyramid, the spread of the virus in the population is being modelled by epidemiologists, such as Professor Neil Ferguson , using statistical models based on infection data. However, I am more interested in the bottom of the pyramid because the particles of the coronavirus are about the same size as the nanoparticles that I have been studying for some years [see ‘Slow moving nanoparticles’ on December 13th, 2017] and their motion appears to be dominated by diffusion processes [see ‘Salt increases nanoparticle diffusion’ on April 22nd, 2020] [6-7]. The first step towards virus infection of a cell is diffusion of the virus towards the cell which is believed to be a relatively slow process and hence a good model of diffusion would assist in designing drugs that could arrest or decelerate infection of cells . Many types of virus on entering the cell make their way to the nucleus where they replicate causing the cell to die, afterwhich the virus progeny are dispersed to repeat the process. You can see part of this sequence for coronavirus (SARS-COV-2) in this sequence of images. The trafficking across the cytoplasm of the cell to the nucleus can occur in a number of ways including the formation of a capsule or endosome that moves across the cell towards the nuclear membrane where the virus particles leave the endosome and travel through microtubules into the nucleus. Holcman & Schuss  provide a good graphic illustrating these transport mechanisms. In 2019, Briane et al  reviewed models of diffusion of intracellular particles inside living eukaryotic cells, i.e. cells with a nuclear enclosed by a membrane as in all animals. Intracellular diffusion is believed to be driven by Brownian motion and by motor-proteins including dynein, kinesin and myosin that enable motion through microtubules. They observed that the density of the structure of cytoplasm, or cytoskeleton, can hinder the free displacement of a particle leading to subdiffusion; while, cytoskeleton elasticity and thermal bending can accelerate it leading to superdiffusion. These molecular and cellular interactions are happening at disparate spatial and temporal scales  which is one of the difficulties encountered in creating predictive simulations of virus-cell interactions. In other words, the bottom layers of the model-test pyramid appear to be constructed from many more strata when you start to look more closely. And, you need to add a time dimension to it. Prior to the coronavirus pandemic, more modelling efforts were perhaps focussed on understanding the process of infection by Human Immunodeficiency Virus (HIV), including by a multi-national group of scientists from Chile, France, Morocco, Russia and Spain [12-14]. However, the current coronavirus pandemic is galvanising researchers who are starting to think about novel ways of building multiscale models that encourage multidisciplinary collaboration by dispersed groups, [e.g. 15].
 Harris GL, Computer models, laboratory simulators, and test ranges: meeting the challenge of estimating tactical force effectiveness in the 1980’s, US Army Command and General Staff College, May 1979.
 Trevisani DA & Sisti AF, Air Force hierarchy of models: a look inside the great pyramid, Proc. SPIE 4026, Enabling Technology for Simulation Science IV, 23 June 2000.
 Patterson EA, Taylor RJ & Bankhead M, A framework for an integrated nuclear digital environment, Progress in Nuclear Energy, 87:97-103, 2016.
 Patterson EA, Purdie S, Taylor RJ & Waldon C, An integrated digital framework for the design, build and operation of fusion power plants, Royal Society Open Science, 6(10):181847, 2019.
 Verity R, Okell LC, Dorigatti I, Winskill P, Whittaker C, Imai N, Cuomo-Dannenburg G, Thompson H, Walker PGT, Fu H, Dighe A, Griffin JT, Baguelin M, Bhatia S, Boonyasiri A, Cori A, Cucunubá Z, FitzJohn R, Gaythorpe K, Green W, Hamlet A, Hinsley W, Laydon D, Nedjati-Gilani G, Riley S, van Elsland S, Volz E, Wang H, Wang Y, Xi X, Donnelly CA, Ghani AC, Ferguson NM, Estimates of the severity of coronavirus disease 2019: a model-based analysis., Lancet Infectious Diseases, 2020.
 Coglitore D, Edwardson SP, Macko P, Patterson EA, Whelan MP, Transition from fractional to classical Stokes-Einstein behaviour in simple fluids, Royal Society Open Science, 4:170507, 2017.
 Giorgi F, Coglitore D, Curran JM, Gilliland D, Macko P, Whelan M, Worth A & Patterson EA, The influence of inter-particle forces on diffusion at the nanoscale, Scientific Reports, 9:12689, 2019.
 Gilbert P-A, Kamen A, Bernier A & Garner A, A simple macroscopic model for the diffusion and adsorption kinetics of r-Adenovirus, Biotechnology & Bioengineering, 98(1):239-251,2007.
 Holcman D & Schuss Z, Modeling the early steps of viral infection in cells, Chapter 9 in Stochastic Narrow Escape in Molecular and Cellular Biology, New York: Springer Science+Business Media, 2015.
 Braine V, Vimond M & Kervrann C, An overview of diffusion models for intracellular dynamics analysis, Briefings in Bioinformatics, Oxford University Press, pp.1-15, 2019.
 Holcman D & Schuss Z, Time scale of diffusion in molecular and cellular biology, J. Physics A: Mathematical and Theoretical, 47:173001, 2014.
 Bocharov G, Chereshnev V, Gainov I, Bazhun S, Bachmetyev B, Argilaguet J, Martinez J & Meyerhans A, Human immunodeficiency virus infection: from biological observations to mechanistic mathematical modelling, Math. Model. Nat. Phenom., 7(5):78-104, 2012.
 Bocharov G, Meyerhans A, Bessonov N, Trofimchuk S & Volpert V, Spatiotemporal dynamics of virus infection spreading in tissues, PLOS One, 11(12):e)168576, 2016.
 Bouchnita A, Bocharov G, Meyerhans A & Volpert V, Towards a multiscale model of acute HIV infection, Computation, 5(6):5010006, 2017.
 Sego TJ, Aponte-Serrano JO, Ferrari-Gianlupi J, Heaps S, Quardokus EM & Glazier JA, A modular framework for multiscale spatial modeling of viral infection and immune respons in epithelial tissue, bioRxiv. 2020.
I need to confess to writing a misleading post some months ago entitled ‘In Einstein’s footprints?‘ on February 27th 2019, in which I promoted our 4th workshop on the ‘Validation of Computational Mechanics Models‘ that we held last month at Guild Hall of Carpenters [Zunfthaus zur Zimmerleuten] in Zurich. I implied that speakers at the workshop would be stepping in Einstein’s footprints when they presented their research at the workshop, because Einstein presented a paper at the same venue in 1910. However, as our host in Zurich revealed in his introductory remarks , the Guild Hall was gutted by fire in 2007 and so we were meeting in a fake, or replica, which was so good that most of us had not realised. This was quite appropriate because a theme of the workshop was enhancing the credibility of computer models that are used to replicate the real-world. We discussed the issues surrounding the trustworthiness of models in a wide range of fields including aerospace engineering, biomechanics, nuclear power and toxicology. Many of the presentations are available on the website of the EU project MOTIVATE which organised and sponsored the workshop as part of its dissemination programme. While we did not solve any problems, we did broaden people’s understanding of the issues associated with trustworthiness of predictions and identified the need to develop common approaches to support regulatory decisions across a range of industrial sectors – that’s probably the theme for our 5th workshop!
The MOTIVATE project has received funding from the Clean Sky 2 Joint Undertaking under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 754660 and the Swiss State Secretariat for Education, Research and Innovation under contract number 17.00064.
The opinions expressed in this blog post reflect only the author’s view and the Clean Sky 2 Joint Undertaking is not responsible for any use that may be made of the information it contains.
I spent a lot of time on trains last week. I left Liverpool on Tuesday evening for Bristol and spent Wednesday at Airbus in Filton discussing the implementation of the technologies being developed in the EU Clean Sky 2 projects MOTIVATE and DIMES. On Wednesday evening I travelled to Bracknell and on Thursday gave a seminar at Syngenta on model credibility in predictive toxicology before heading home to Liverpool. But, on Friday I was on the train again, to Manchester this time, to listen to a group of my PhD students presenting their projects to their peers in our new Centre for Doctoral Training called Growing skills for Reliable Economic Energy from Nuclear, or GREEN. The common thread, besides the train journeys, is the Fidelity And Credibility of Testing and Simulation (FACTS). My research group is working on how we demonstrate the fidelity of predictions from models, how we establish trust in both predictions from computational models and measurements from experiments that are often also ‘models’ of the real world. The issues are similar whether we are considering the structural performance of aircraft [as on Wednesday], the impact of agro-chemicals [as on Thursday], or the performance of fusion energy and the impact of a geological disposal site [as on Friday] (see ‘Hierarchical modelling in engineering and biology‘ on March 14th, 2018) . The scientific and technical communities associated with each application talk a different language, in the sense that they use different technical jargon and acronyms; and they are surprised and interested to discover that similar problems are being tackled by communities that they rarely think about or encounter.