Drug structure–transport relationships
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Malcolm Rowland has greatly facilitated an understanding of drug structure–pharmacokinetic relationships using a physiological perspective. His view points, covering a wide range of activities, have impacted on my own work and on my appreciation and understanding of our science. This overview summarises some of our parallel activities, beginning with Malcolm’s work on the pH control of amphetamine excretion, his work on the disposition of aspirin and on the application of clearance concepts in describing the disposition of lidocaine. Malcolm also spent a considerable amount of time developing principles that define solute structure and transport/pharmacokinetic relationships using in situ organ studies, which he then extended to involve the whole body. Together, we developed a physiological approach to studying hepatic clearance, introducing the convection–dispersion model in which there was a spread in blood transit times through the liver accompanied by permeation into hepatocytes and removal by metabolism or excretion into the bile. With a range of colleagues, we then further developed the model and applied it to various organs in the body. One of Malcolm’s special interests was in being able to apply this knowledge, together with an understanding of physiological differences in scaling up pharmacokinetics from animals to man. The description of his many other activities, such as the development of clearance concepts, application of pharmacokinetics to the clinical situation and using pharmacokinetics to develop new compounds and delivery systems, has been left to others.
KeywordsMalcolm Rowland Physiological pharmacokinetics Structure–transport relationships
“Write for the reader – not for oneself” Malcolm Rowland, personal communication, 1983
I would like to acknowledge from the outset that I have been privileged to be an invited speaker at the 70th birthday of one of my mentors, Malcolm Rowland, who has greatly assisted in the development of my views about science and life. There are a number of other Australians, including Felix Bochner, Garry Graham, Andrew McLachlan, Allan Evans and Lloyd Sansom, who have also worked with Malcolm and would like to have been here. There are many others who have been influenced by your many sojourns “Down Under”. Malcolm was successful in attracting one of us, Leon Aarons, to work with him at Manchester from postdoctoral studies to today, a collaboration that has resulted in many pivotal papers in our discipline. In this paper, I highlight the influence Malcolm has had on my own research, especially the role of solute structure on pharmacokinetics. I begin with the physiological perspective Malcolm brought to pharmacokinetics and how he used that knowledge to define solute structure pharmacokinetic relationships. My perspective is an intensely personal one in that I started in membrane transport and was influenced by Malcolm’s thinking early on, I had the pleasure to work with Malcolm whilst on my only sabbatical leave, to watch Malcolm’s continuing journey but, at the same time, working independently to reach where I think we are now.
The second “stand-out” drug that Malcolm studied during his postdoctoral studies at the University of San Francisco with Sid Riegelman was aspirin , a compound that I also did a number of studies on, including defining its disposition in elderly and alcoholic subjects , extrahepatic metabolism , its effects on platelets  and in describing the apparent autoinduction of the salicyluric acid pathway on chronic ingestion of high doses [9, 10]. We also followed up on Tom Tozer and colleagues’ steady state work on salicylate clearance being determined by saturable protein binding and metabolism  to model these effects during a single dose . Perhaps, one of the most fulfilling aspects of our work on aspirin is that a dose form we helped to develop  as a prophylaxis for heart attacks and stroke, Cartia® (Glaxo-Smith-Kline) is still on the market today. Malcolm, Leon Aarons and others also showed that aspirin absorption was faster in women after oral administration but slower after intramuscular administration . They also defined the kinetics of aspirin hydrolysis by albumin . These early studies, many of which we conducted on ourselves naive in terms of today’s ethics requirements, have not all been without problems. One of my colleagues suffered from a most profound, long and sustained Arthus reaction (i.e. a rare but rather severe and immediate nonatopic hypersensitivity reaction) when we each injected each other with diluted wasp venom to see if topical aspirin and other products lessened the resulting inflammatory response . Another Australian colleague, Felix Bochner, obtained his tinnitus in taking high doses of salicylate whilst on sabbatical with Malcolm .
Figure 1c and d shows two illustrations of Malcolm’s work with aspirin. Figure 1c shows the importance of blood flow in oral absorption. Here, blood sampling continued to be undertaken in one of their subjects who felt faint. It is clear that there is impairment of aspirin absorption in this situation . The second example shows that there may be a delay in reaching a target site of action is distant from the plasma, contributing to a delay in response. Here, the peaking of aspirin in synovial fluid occurs some time after that in plasma (Fig. 1d) . One of the “follow-up” questions that I studied was how did posture and sleep affect pharmacokinetics and, if the changes observed meant a need to change dosing regimens? The first drug we studied, amoxicillin, showed the most pronounced postural effect with the plasma AUC being significantly greater in the upright position than in the lying down position or during sleep . I feel certain that exercise (subjects were allowed to walk whilst in the upright position) possibly added to the postural effect of an increase in real blood flow and higher active renal secretion of amoxicillin. We did not find differences when we examined benzyl penicillin given intramuscularly  or intravenously . Lying down and sleeping had the effect of delaying the absorption of paracetamol .
The third “stand out” compound is lidocaine. Here, Malcolm and colleagues showed that an altered clearance can lead to enhanced plasma levels and, in heart failure, disposition effects further compounds lidocaine pharmacokinetics. Figure 1e and f shows the altered disposition of lidocaine in heart failure after intravenous bolus and infusion administration, examples I have often used in my teaching. Here, the reduced body perfusion in cardiac failure leads to reduction in the apparent distribution volume by about one third. Lidocaine clearance in heart failure is also reduced by about one third. An important finding is that the dependent variable half life (= 0.693 × apparent distribution volume/clearance) is effectively unchanged in heart failure [23, 24]. A reduced dosing is indicated with both a reduced clearance (target steady state plasma concentration = infusion rate/clearance) and a reduced volume of distribution (initial plasma concentration = dose/apparent distribution volume), whereas the lack of change in half life would predict that no change in lidocaine dosing was necessary. It is noted that physiological pharmacokinetic principles does not predict a reduced volume of distribution at steady state in heart failure for all drugs. For example, cardiac failure leads to a reduction in the clearance of midazolam but not in its steady state distribution volume . In contrast to the significant changes in lidocaine pharmacokinetics in cardiac failure, no significant changes in lidocaine pharmacokinetics are observed in renal failure; whereas, in liver disease, only lidocaine clearance is impaired, leading in turn to an increased half life (Fig. 1g).
Structure transport relationships in absorption and distribution
Most target tissues contain vasculature, interstitium, and cells, and representing them as a single compartment is physiologically naive. .
An elegant part of Malcolm and Rene’s subcutaneous absorption kinetics studies was to show that blood flow and ionisation were components in the subcutaneous absorption kinetics. As shown in Fig. 2d, there was negligible absorption for lidocaine from subcutaneous solutions with no blood flow (post-mortem studies) and when the lidocaine was in an ionised form (pH 5.42). On the other hand, initial uptake an unionised lidocaine (pH 7.95) was faster than the partially ionised lidocaine in vivo and the later disappearance from a pH 7.95 solution in vivo was greater than for post-mortem studies showing the importance of subcutaneous blood flow in determining clearance from the site into the systemic circulation. We used a similar approach to show that vasoconstrictors modified the salicylate concentrations in deeper tissues after dermal application to be intermediate between in vivo and post-mortem tissues (Fig. 2e). We also used the lack of blood flow induced changes in interferon disappearance from dermal sites to show that the dermal absorption of larger molecules, like interferon, was most likely absorbed via the lymphatics . The role of lymphatics in solute disposition has been extensively studied by my Australian colleagues [33, 34]. Finally, in contrast to the absorption findings shown for subcutaneous and dermal administration of aqueous solutions, the uptake of compounds from synovial fluid in man decreases with increasing lipophilicity. Here, binding to synovial fluid protein dominates and, indeed, for diclofenac about half its clearance occurs as diclofenac bound to albumin (Fig. 2f) . A similar finding was reported by Malcolm’s group but this time using an air pouch in the rat . They concluded that a perfusion rate limitation probably applied to the uptake of NSAIDs into the pouch during the first 2 h when albumin flux into the pouch is not enough to affect the permeability of the NSAIDs. The effective flux of the NSAIDs is lowered when the albumin concentration in the pouch increases after 5 h. In a later paper, they suggested that drug transport into the site cannot be based on unbound drug only and must also include the simultaneous flux of drug bound to albumin, which enters the target site due to increased vascular permeability associated with the inflammatory response .
Malcolm and a then young postdoc Andrew MacLachlan, also ventured into the area of using regional administration to more effectively target drugs by applying pharmacokinetic principles . Earlier studies had initially used a well-stirred pharmacokinetic models and transport by blood flow. Later studies included a permeability barrier as well as a tissue partition coefficient. Together, they showed that a positive Drug Targeting Index (DTI), or Selective Advantage could be achieved using intra-arterial administration. They showed that DTI depended on the relative permeability of unbound drug across the vascular and cellular membranes in the target tissue relative to the tissue blood flow rate and that the flux of bound drug between the vascular and interstitial spaces of the target could also affect the DTI .
Whole body physiological pharmacokinetics
“An overall objective of physiological modelling is to simulate the complete system through a fundamental study of its component parts.” 
Pharmacokinetics in the perfused rat liver
The manner in which alterations in physiological states, such as organ blood flow, degree of drug binding within blood, and hepatocellular enzymatic activity, influence the hepatic handling of drugs and hence their oral availability is poorly understood 
Malcolm also saw the wisdom of studying solute disposition in isolated organs so as to excluding varying blood flow, systemic feedback and recirculation effects. His work on lidocaine in isolated perfused livers with Sandy Pang is in some ways an extension of his work at the subcutaneous site, if both are seen as isolated organs. Malcolm and Sandy had shown the disposition of lidocaine and its metabolite MEGX was better described by a “well-stirred” than by a “tube” model [67, 68, 69].
The question of what was the most appropriate physiological clearance model for the liver was also a topic that I embarked on during my time at Manchester with Malcolm. This occurred during the years 1983 to 1984 and were an eventful time for my family and I as it was our first time out of Australia and I was taking my first (and as it has proved to be so far, only) sabbatical leave. I had organised to spend most of my time with Malcolm but had also organised to spend some time in Clinical Pharmacology at Guy’s Hospital in London and to also visit various institutions in Europe. It was during my time with Malcolm that I met and spent time with Dawn and a fellow Australian Leon Aarons and his family as well as others in Malcolm’s team. During my family’s sojourn to Europe in the middle of this leave, we ventured behind the then Iron Curtin to meet Michael Weiss and his family (a separate ‘mystical’ story), and one also leading to a long term collaboration.
The dispersion number derived from Goresky’s data was 0.12 (Fig. 7a), intermediate between the well stirred model value of infinity and tube model value of zero . Thus, the dispersion model was an intermediate model and the work to date had been on comparing the extremes of this model. Importantly, when one fits steady state data and allows the dispersion number to vary, one obtains an intermediate, if not a precise a value. For instance, the dependence of chromic phosphate hepatic availability on liver flow rate has a dispersion number of 0.35 ± 0.24 (Fig. 7b) whereas the hepatic availability for diazepam varies with fraction unbound in plasma with a dispersion number of 0.29 ± 0.23 (Fig. 7c) . In addition, the formation of metabolites  (Fig. 7d) and the correspondence of perfused liver availability and in vitro microsomal enzyme activity  (Fig. 7e) are consistent with intermediate dispersion numbers. The importance of the latter is in scaling up human microsomal and hepatocyte data to predict hepatic extraction in vivo as exemplified by Sugiyama’s group [86, 87] and others . It should also be noted that the well stirred and parallel-tube models are the asymptotic solutions for the dispersion model and that, when the availability in the liver is high (F > 0.6), one can show that the predicted availability for all models is similar .
It would be remiss of me not to acknowledge also the extensive and continuing work on modelling of drug disposition in the liver undertaken by Sandy Pang, Carl Goresky, Yuichi Sugiyama, Frank Burzynski, Andreas Schwab, Ludvik Bass, Tony Bracken, Yuri Anissimov, Peter Robinson, Bruce Luxon, Leigh Forker, Denis Morgan and colleagues using a physiological ‘segregated” transit time approach that contrasts with the micromixing that is assumed for the convection–dispersion model in the liver and the “tank-in-series” model described by Dick Weisiger, Gray and Tam and by us. As Malcolm, John Donaldson (great applied mathematician and, incidentially, father of Princess Mary of Denmark) and I showed, the choice of an overall micromixing or segregated transit time does not affect outflow predictions for linear kinetics . It does however, matter for non-linear kinetics as can be seen by comparing inflow into a tank in series with a tube with inflow into a tube in series with a tank. Notably, also, the morphological organisation of the liver is characterised by high intervascular mixing in the periportal (zone 1) region but mainly segregated vascular flow in the central (zone 3 region). One possible pharmacokinetic hypothesis for the arrangement is that an efficient “flattening” of plasma concentrations brought about by well-stirred conditions (Fig. 6) is needed in the periportal region to limit exposure of the cells to drug and metabolite, especially as much drug metabolism occurs in zone 3 . The segregated “tube” arrangement would allow more efficient extraction in zone 3.
Our work on heterogeneity in liver kinetics  as well as nonlinear models  is an area developed greatly and contributed to by Sugiyama’s group [86, 87] and others . There has been some controversy on what boundary conditions are the most appropriate for use with the dispersion model [91, 92]. Malcolm and his colleagues have made the last comment on this issue and, in noting the pros and cons of the closed conditions (favoured in providing mass conservation at the boundary) and mixed conditions (ease of its analytical form), suggest that the two models give essentially equivalent fits and dispersion numbers . My group has moved, influenced by Michael Weiss, to using an empirical dual inverse Gaussian function that best describes the outflow profiles after bolus injections into the liver  combined with a two compartment model that enables the relative importance of permeability, diffusion and binding in the cells to be dissected out . With Yuri Anissimov, we have also developed a compartmental model for hepatic elimination that accurately describes the observed vascular dispersion , but our application of this model has, to this stage been limited .
Let us return to the original question that led to the development of the dispersion model, the ability to predict the extraction of highly extracted drugs. Currently, two approaches are being taken. One is to ignore that a substantial difference exists between the predicted and observed values using the well stirred model . In the end, it is about changing paradigms as Malcolm has most recently pointed out .
Pharmacokinetics in other perfused organs
Physiologically-based pharmacokinetics: academic curiosity or the holy grail to prediction? Why do we get the profiles we see? Can we predict quantitatively events in humans from in vitro, animal and other information? Can we explain differences across compounds? Can we predict likely variability in target patient population under clinically realistic conditions?
Malcolm Rowland 2009
Three different models described in 1968 set the scene for seeking to better understand physiological pharmacokinetics at a more basic level.
Malcolm along with Sid Riegelman started questioning the one compartment pharmacokinetic model . Ken Bischoff and Bob Dedrick suggested that the pharmacokinetics for thiopental could be described by an a priori mathematical pharmacokinetic model that included blood flows, tissue volumes, lipid solubility, protein binding and metabolism . Perl and Chinard described a convection–diffusion model to describe solute disposition in the kidney in 1968 . This model is identical to the convection–dispersion model we described for the liver, except that the terminology is different. The need to apply a convection dispersion model in describing renal clearance of drugs has yet to be established. It could be argued that, for most drugs, the well stirred model is adequate in describing renal clearance. Indeed, Malcolm’s group used a simple physiologically based model of tubular reabsorption to relate the renal clearances of a homologous series of six 5-substituted barbituric acids, of varying lipophilicity, in a recirculating isolated perfused rat kidney preparation . In addition, Malcolm, with Stephen Hall, has also conducted a number of studies in the perfused kidney, emphasising the role of protein binding [128, 129].
We also investigated the importance of dispersion in the human placenta . The perfused head proved to be a more challenging organ as we were unable to distinguish uptake between the brain and other parts of the head [141, 142]. Recently, we have described disposition in the pancreas . Most recently, we have described the disposition of solutes in the perfused rat lung . The eventual outcome of bringing these various organs together is a whole-body physiologically based pharmacokinetic model based on dispersion concepts and to scale it to man in vivo . The human venous outflow profiles were characterised by the oscillation in venous and arterial blood flow at early times as reported in the anaesthesiology literature, as illustrated in Fig. 9c. At longer times there was a build up of drugs in the skeletal muscle, skin, and fat and was better able to accurately predict the distribution of drugs in the body than the conventional well-stirred organ whole-body PBPK model. In our experience, similar profiles, with much less computation, can be achieved by representing each organ with a three compartment in series model and interlinking the organs as in the classical physiological PBPK model. It is possible, however, that the dispersion generated by the varying flows to individual organs will prove to be the major determinant of whole body dispersion  rather than the vascular dispersion in individual organs. Indeed, Michael Weiss has generated a similar profile to that in Fig. 9c for the whole body based on cardiac output and systemic transit time dispersion .
Sampling body organs
The alternative to trying to understand what happens in the individual organs of the body and resynthesising them back into the body is to study drug disposition in organs directly in vivo. This latter approach was reported by Malcolm’s group in 1998 as basis for evaluating the contribution of structural and physicochemical properties to pharmacokinetics. They studied the distribution kinetics of nine 5-alkyl-5-ethyl barbituric acids in arterial blood and 14 tissues (lung, liver, kidney, stomach, pancreas, spleen, gut, muscle, adipose, skin, bone, heart, brain, testes) after i.v. bolus administration in rats using well-stirred organ compartments and assuming that either permeability rate limitation or perfusion rate limitation may be involved in the distribution processes . Muscle accounted for ~ 50% of the total unbound volume of distribution for all compounds. This data was then analysed using tissue-to-unbound plasma distribution coefficients for each of the 14 rat tissues in terms of their octanol to water partition ratio, P, binding capacity of each tissue and its water content . Confounders include albumin diffusion  and lipophilic solutes . Later work included the benzodiazepines . This work was then extended to the predictability of tissue-to-plasma water partition coefficients for 7 very weak bases, 20 acids, 4 neutral drugs and 8 zwitterions in rat adipose, bone, brain, gut, heart, kidney, liver, lung, muscle, pancreas, skin, spleen and thymus [153, 154]. Expressions were developed that recognise solubility in tissue water, partitioning into neutral lipids, neutral phospholipids and other sites as well as drug ionisation). Interestingly, in their latest paper in the series, Trudy Rodgers and Malcolm found a prediction for binding restricted to muscle was similar to that using individual tissues and was high in rats and humans . Figure 9d shows that their modelling has provided an excellent description of unbound partitioning coefficients for a series of heterogeneous compounds.
The dilemma remains—what is the best way forward. My group is adopting three key approaches. One is to image events as they occur in individual organs in space and time in vivo  (Fig. 9e). The second is to sample those organs with time. Our group has used blood and destructive tissue sampling (Fig. 9b) as well as cutaneous microdialysis [134, 135] to define the time course of drugs in organs. Data analysis involves using either a mechanistic physiological pharmacokinetic model [64, 65, 137] or to use simulation spatiotemporal processing of solutes in individual organs . Interestingly, the convection–dispersion developed with Malcolm underpins each approach. For instance, the dispersion process is seen on the direct imaging of the liver. Unpublished work on the transport of solutes into deeper tissues of human skin after topical application in vivo measured by microdialysis suggests that a convection dispersion process is partly responsible for the carriage of highly albumin bound drugs to deeper tissues. Finally, all of our in vivo simulations include an empirical gamma function that mimics the dispersion process.
Comments made by Malcolm in 2009 at the American Society of Clinical Pharmacology and Therapeutics contextualises our work in the way that drugs may be developed in the future. In brief, the physiological pharmacokinetic model structure is common to all mammals and includes both physiological parameters, such as blood flow, tissue size, composition etc. that are independent of drug (system properties) and compound specific parameters that must be overlaid onto this system such as clearance, tissue affinity, membrane permeability etc. Much is now known about pharmacokinetic variability with intrinsic factors such as age, genetics, gender, and extrinsic factors such as formulation, disease, co-medication, environment, diet and nutrition) affecting tissue weight, composition, blood flow, enzyme and transporter activity as well as hepatic metabolism, biliary, renal, gastrointestinal and lung function. Building mechanistic physiological pharmacokinetic models by this approach, as emphasised by this overview, is essentially a bottom up synthetic approach in which parameter variability is defined by determinants such as enzyme activity, organ size, age etc. I would suggest that a futuristic opportunity is a combination of the synthetic in silico approach that Tony Hunt has led [119, 120, 121, 157] and The Simcyp Population-based ADME Simulator  led by Geoff Tucker and Amin Rostami to predict drug-drug interactions and pharmacokinetics in clinical populations. Simcyp integrates existing human physiological, genetic and epidemiological data base information with supplied in vitro data to predict ‘real-world’ pharmacokinetics.
Pharmacokinetics and pharmacodynamics
The idea of applying the concept of clearance, well established in renal physiology, to drug kinetics was of singular importance and one to which Malcolm Rowland and Grant Wilkinson made the major contribution. .
The story I have presented to date represents only a small fraction of the total impact Malcolm has had on our discipline and on me, in particular. There are many other stories to tell about Malcolm’s contribution to the broader discipline of pharmacokinetics and pharmacodynamics, including the development of clearance concepts , the application of pharmacokinetics to the clinical situation [162, 163], understanding toxicokinetic principles  and using pharmacokinetics in drug development [165, 166, 167] and making pharmacokinetics easier to understand . I will leave it to others to tell those stories!
I would like to thank Dr Simon Gunn for his assistance in preparing the diagrams for this manuscript and Professor Leon Aarons for reviewing the manuscript. This work has been supported by the Australian National Health and Medical Research Council (NHMRC).
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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