Combine operations research with molecular biology to stretch pharmacogenomics and personalized medicine—A case study on HIV/AIDS
Introduction
The interaction between chemical (or more generally, process) engineering technologies and biology has a long tradition, from early food fermentation processes based on microorganisms to beyond the ability to design and synthesize deoxyribonucleic acid (DNA)2 sequences and synthetic biologic systems. This interaction – which have made a myriad of products available to promote social development, economic growth and prosperity – will become more intimate as the sustainable, biology-based technologies are applied under whatever name (Hall and Howe, 2010).
In fact, since chemical engineers already possess the skills and occupy the professional role necessary to deliver a sustainable society, they are often also faced to a myriad of opportunities to collaboratively develop innovative, paradigm-breaking technologies which also underpin other front-edge scientific areas. Included here are biologically-oriented research on medical sciences, a prolific field for the development of novel automation solutions such as optimal drug chemotherapy strategies for life-threatening diseases (e.g., cancer (Harrold and Parker, 2009) and acquired immunodeficiency syndrome (AIDS) (Hadjiandreou et al., 2009, Joly and Odloak, 2013a, Joly and Pinto, 2006)), which became a major challenge for modern public health policies in the XXI century (Hanson and Gluckman, 2011).
Data from the World Health Organization (WHO) show that there are more than 34 million people living with the human immunodeficiency virus (HIV) around the world (WHO, 2013). Whereas the scale-up of highly active antiretroviral therapy (HAART) has provided a dramatic reduction in morbidity and mortality in AIDS patients over the last decade, the population of HIV-infected individuals who have received multiple regimens or were infected with highly resistant viruses shows a continuous and perturbing increase worldwide (Aghokeng et al., 2011, Shafer et al., 2007). Included here are pediatric patients, who require treatment during critical phases of growth and development, as well as the lifelong need for therapy (Königs et al., 2012).
In the presence of detectable viral load, the continued administration of antiretroviral drugs (ARVs) dramatically increases the accumulation of drug resistance mutations due to the rapid turnover of HIV in vivo (Ho et al., 1995, Wei et al., 1995). About 60% of HIV patients under therapy develop new mutations after 18 months at a rate of about 1.61 new mutations per year (Napravnik et al., 2005), and one therapeutic option is lost in about 30% of the treated patients after one year of persistent viremia (Hatano et al., 2006).
Although well established treatment guidelines are available for initial therapy in drug naïve individuals harboring wild-type virus (BMH, 2014) (see Appendix A), the optimal management of HAART in heavily treatment-experienced HIV-infected patients remains a challenge (Imaz et al., 2009). Prospective studies have confirmed that patients whose clinicians have access to genotypic drug resistance data respond better to therapy than control patients whose clinicians do not have access to the same data (LANL, 2013, Rhee et al., 2009, Tural et al., 2002). However, difficulties facing anyone, no matter how expert, in the interpretation of genotypic information are considerable. More than 200 individual mutations along the pol gene are known to affect HIV drug resistance (Shafer and Schapiro, 2008). They interact in complex ways; some mutations cause resistance on their own, some in combination; some cause resistance to a number of different ARVs; some cause resistance to one drug and reverse it to another (Shafer and Schapiro, 2008, Van Laethem et al., 2002).
A truly optimized therapeutic strategy can and should be designed to postpone, as much as possible, the condition of irremediable viral resistance in the long term (discussed in Joly and Pinto, 2006). To achieve this unambiguous therapeutic endpoint, the vast knowledge of drug resistance mutations should be cast and joined to different disciplines into a systematic procedure able to properly represent constraints, to assess risks and to improve therapy outcomes in order to produce the best therapeutic plan (instead the best next regimen), that is, the optimal policy for ARV selection and sequencing over time.
In this paper, a novel system engineering approach is developed as an attempt to support HIV/AIDS clinicians when deciding about the best therapeutic strategy for an ARV-experienced patient. The methodology relies on the Stanford University HIV Drug Resistance Database (HIVdb) (Stanford University, 2013), a contemporary and curated public database designed to represent, store, and analyze the divergent forms of data underlying HIV drug resistance. The HIV type 1 (HIV-1) subtype B epidemic, the most frequent HIV variant in Brazil, is focused on in this study and real-world clinical instances are considered to run the computation experiments and estimate the potential benefits of the proposed methodology with respect to standardized recommendations of the Brazilian HIV/AIDS treatment protocol (BMH, 2014).
Section snippets
The HIV-1 mutation model
HIV-1 is a highly mutable pathogen. The rapid turnover of plasma virions and CD4 T-cells in HIV-1 infection (Ho et al., 1995, Wei et al., 1995) contribute in a particular way to viral diversity, and innumerable genetically distinct variants evolve in individuals following infection. The evolution of HIV-1 drug resistance depends on the generation of genetic variation in the virus and on the selection of drug-resistant variants during HAART (LANL, 2013). In order to reduce the problem of
Mathematical modeling
Unlike decision-making problems in which relevant differences in processing time length of the tasks may require the use of a continuous time representation (e.g., Pinto et al., 2000) in order to avoid computational intractability (Garey and Johnson, 1979), this problem can be modeled under a uniform discretization of the planning horizon. Selection of the length of time slot does not impact the number of realistic integer decisions involved, but it should be defined in the light of the
The solution methods
The modeling system GAMS (Rosenthal, 2010) was used in order to implement two MIP models (Table 4) and their solution methods on a Intel Core i5 2520 M 2.50 GHz platform. The mixed-integer non-linear programming (MINLP) model was solved with the augmented penalty version of the outer-approximation with equality relaxation and augmented penalty method implemented in the solver DICOPT++ (Viswanathan and Grossmann, 1990). The generalized reduced gradient method, implemented in the codes CONOPT3 (
Results
Potential benefits of the methodology proposed are theoretically evaluated regarding 11 real-world instances of Brazilian patients infected with HIV-1 subtype B (Table 5, Table 6) under therapeutic failure (Table 7). Most of these patients started treatment in the pre-HAART era with mono- or dual therapies and, sequentially, new drugs were added to a failing regimen as they became available.
Two scenarios related to patient monitoring conditions are considered. Scenario A addresses a typical
Methodological innovations
By presenting a comprehensive yet fine-grained view of HIV-1 drug chemotherapy issues, we tried to show how mathematical programming techniques can be applied to support the complex decision-making process of planning patient-specific HIV-1 (subtype B) treatment strategies for ARV-experienced individuals relying on viral genotyping data. A general MIP-based solution framework that can be parameterized for representing any HIV type/subtype is proposed relying on 13 fundamental assumptions (a1)
Concluding remarks
Our results suggest that, while current practices can generally provide satisfactory management of drug resistance on an individual basis, optimization-based therapy design has a far greater potential to achieve this goal in the long-term due to the advantages of being highly consistent with respect to several intricate trade-offs when predicting the resistance score of multiresistant viruses. The ability of this methodology to produce realistic treatment strategies based on a systematic
Acknowledgements
The authors wish to acknowledge support from FAPESP (grants n. 1999/09897-4 and 2011/21958-2), and Dr. Luana Portes, Dr. Giselle Lopes (Instituto Adolfo Lutz de São Paulo, São Paulo, Brazil), and to Dr. Max Lopes (Hospital das Clínicas, São Paulo, Brazil) for providing experimental data and insightful discussions on HIV therapy. In addition, the authors are grateful to the two anonymous referees for their constructive suggestions which led to an improved version of the paper.
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