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Process Systems Engineering has tackled a wide range of problems including manufacturing, the environment, and advanced materials design. Here we discuss how tools can be deployed to tackle medical problems which involve complex chemical transformations and spatial phenomena looking in particular at the liver system, the body's chemical factory. We show how an existing model has been developed to model distributed behavior necessary to predict the behavior of drugs for treating liver disease. The model has been used to predict the effects of suppression of de novo lipogenesis, stimulation of b-oxidation and a combination of the two. A reduced model has also been used to explore the prediction of behavior of hormones in the blood stream controlling glucose levels to ensure that levels are kept within safe bounds using interval methods. The predictions are made resulting from uncertainty in two key parameters with oscillating input resulting from regular feeding. V C 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 62: 3285-3297, 2016 Keywords: mathematical modeling, biomedical engineering, systems biology, medical, controlThe liver, its regulation, and its diseases Why systems engineering of the liver?Systems Engineering is the discipline of the management of complex engineering systems over their whole life cycle. Process Systems Engineering is the study of complex process engineering systems involving chemical and physical change. Prof Roger Sargent was a pioneer from the 1950s in seeing the potential that computers could have to revolutionize the way that we tackled these problems.1 He also saw the way Chemical Engineering was broadening its base into molecular and biological systems to improve manufacturing. 1,2The liver is one part of a very complex processing system which ensures that all parts of the body receive the energy and nutrients that they need, that waste products are removed efficiently from the various streams, and that short and long term well being are maintained. It is the body's central chemical processing organ. Considering the liver system as one which controls chemical and physical change within the body, particularly of nutrition, makes it a legitimate area of study for Process Systems Engineers. A number of Chemical Engineers have also contributed to the use for Process Systems Engineering to a range of medical applications. Bogle 3 reviews recent

Engineers seek optimal solutions when designing dynamic systems but a crucial element is to ensure bounded performance over time. Finding a globally optimal bounded trajectory requires the solution of the ordinary differential equation (ODE) systems in a verified way. To date these methods are only able to address low dimensional problems and for larger systems are unable to prevent gross overestimation of the bounds. In this paper we show how interval contractors can be used to obtain tightly bounded optima. A verified solver constructs tight upper and lower bounds on the dynamic variables using contractors for initial value problems (IVP) for ODEs within a global optimisation method. The solver provides guaranteed bound on the objective function and on the first order sensitivity equations in a branch and bound framework. The method is compared with three previously published methods on three examples from process engineering.

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Table S1. Properties and abbreviations of compounds used in the RD model 1. Component Abbreviation Formula MW CAS Tb/K Cyclohexanone CX-ONE C6H10O 98 108-94-1 428 2-Cyclohexen-1-one CX-ENONE C6H8O 96 930-68-7 443 2-(1-cyclohexen-1-yl)cyclohexanone D2 a C12H18O 178 1502-22-3 538.15 2-cyclohexylidencyclohexanone D3 a C12H18O 178 1011-12-7 538.15 [1,1'-bicyclohexyl]-2,2'-dione C1 b C12H18O2 194 32673-76-0 601±25.0 [1,1'-bicyclohexyl]-2,3'-dione C2 b C12H18O2 194 88974-62-3 601±25.0 Cyclohexanol CX-OL C6H12O 100 108-93-0 434 a Lumped as DIMER with the properties of 2-(1-cyclohexen-1-yl)cyclohexanone. b Lumped as DIONE with the properties of [1,1'-bicyclohexyl]-2,2'-dione.