REVIEW ARTICLE
`
`Chn Phormacoklnet 2008 -47 (7) 417-448
`03 l 2-5963/08/0007-04 l 7 /$48 00/0
`
`© 2008 Adis Data Information BV All nghts reserved
`
`Pharmacokinetic/Phannacodynamic Modelling
`in Diabetes Mellitus
`Cornelia B. Landersdorfer and William J. Jusko
`Department of Pharmaceutical Sciences, School of Pharmacy and Pharmaceutical Sciences, University at Buffalo,
`State University of New York, Buffalo, New York, USA
`
`Contents
`
`Abstract, ... , ...................................................................................... , ................... 417
`l . The Glucose-Insulin System ..... , .................................................................................... 418
`2. Mechanisms of Action of Antidiabetic Drugs .......................................................................... 421
`3. Overview of Diabetes Mellitus Models ................................................................................ 422
`4. Models for the Intrinsic Interaction Between Glucose and Insulin ........................................................ 423
`4.1 Models for Diagnostic Tests ..................................................................................... 423
`4.2 Models for the Glucose-Insulin System Not Intended for Diagnostic Tests ............................................. 426
`4.3 Models for Important Components of the Glucose-Insulin System ................................................... 429
`5. Models for the Glucose-Insulin System Incorporating Drug Effects ....................................................... 429
`5.1 Biophase Models .............................................................................................. 430
`5.2 The Minimal Model. .......................................... , .......... , ................................. , , ... 431
`5.3
`Indirect Response Models ...................................................................................... 432
`5.4 Use of Biophase Models versus Indirect Response Models .......................................................... 436
`6. Models that Describe Secondary Drug Effects ........................................................................ 437
`7, Models that Describe Effects on Ancillary Biomarkers ........................... , ...................................... 438
`8, Models for Disease Progression ...................................................................................... 440
`9. Future Needs and Perspectives ........................ , ........ , .. , .. , ....... , ...... , ... , ......................... , . 442
`l 0. Conclusions ........................ , .............................................................................. 443
`
`Abstract
`
`Diabetes mellitus is a major health risk in many countries, and the incidence rates are increasing. Diverse
`therapeutic agents are applied to treat this condition. Since 1960, numerous mathematical models have been
`developed to describe the glucose-insulin system, analyse data from diagnostic tests and quantify drug effects.
`This review summarizes the present state-of-the-art in diabetes modelling, with a focus on models describing
`drug effects, and identifies major strengths and limitations of the published models.
`For diagnostic purposes, the minimal model has remained the most popular choice for several decades, and
`numerous extensions have been developed. Use of the minimal model is limited for applications other than
`diagnostic tests. More mechanistic models that include glucose-insulin feedback in both directions have been
`applied. The use of biophase distribution models for the description of drug effects is not always appropriate.
`More recently, the effects of various antidiabetic agents on glucose and insulin have been modelled with indirect
`response models. Such models provide good curve fits and mechanistic descriptions of the effects of antidiabetic
`drugs on glucose-insulin homeostasis. These and other types of models were used to describe secondary drug
`effects on glucose and insulin, and effects on ancillary biomarkers. Modelling of disease progression in diabetes
`can utilize indirect response models as a disturbance of homeostasis.
`Future needs are to include glucose-insulin feedback more often, develop mechanistic models for new drug
`groups, consider dual drug effects on complementary subsystems, and incorporate elements of disease progres(cid:173)
`sion.
`
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`
`Diabetes mellitus is an increasing health problem in many
`countries. In 2006, the WHO estimated that 180 million people
`worldwide had diabetes, and that this number will likely be more
`than doubled by 2030. The number of deaths attributable to
`diabetes has been estimated at 2.9 million per year.Ill Type 1
`diabetes mellitus (TIDM) is characterized by an inability of the
`body to produce insulin, and has to be treated with exogenous
`insulin. Type 2 diabetes mellitus (T2DM) reflects both insulin
`resistance of liver and peripheral tissues, and deficient insulin
`secretion by pancreatic ~-cells.121 Various oral antidiabetic drugs,
`as well as insulin, are used for treatment. The factors contributing
`to the pathophysiology and disease progression of diabetes are not
`yet fully understood. Long-term complications such as neuro(cid:173)
`pathy, nephropathy and retinopathy are debilitating for patients
`and result in high healthcare costs. In the US, diabetes was the
`leading cause of renal failure and new blindness in 2005,131 and
`total diabetes costs were estimated at $US174 billion in 2007.f41
`For these reasons, early diagnosis and adequate treatment are
`important to decrease the long-term adverse effects of diabetes.
`Mathematical models are needed to better understand the glucose(cid:173)
`insulin system, to evaluate diagnostic tests, to study and predict
`drug effects, and to quantify disease progression. Mechanism(cid:173)
`based models are preferable, as they can be used to study the
`mechanism of action and to predict the effects of new dosage
`regimens. If the number of time- and cost-intensive long-term
`clinical trials that need to be performed can be reduced by simula(cid:173)
`tion studies, the time and costs involved in drug development
`could be considerably decreased, and optimized dosage regimens
`could be prospectively designed and clinically evaluated. Pharma(cid:173)
`cokinetic/pharmacodynamic modelling can also help to design
`better studies, to identify agents with undesirable properties earlier
`and to decrease attrition rates at late stages of drug development.f 51
`Since the l 960s, numerous interesting and useful mathematical
`models have been developed for various applications and with
`different characteristics and employing different methods. With
`this large number of models. it is sometimes difficult to decide
`which one should be used for a specific purpose. A few reviews
`are available on certain aspects of diabetes modelling_l6-10J How(cid:173)
`ever, no extensive overview has been published that includes the
`different types of pharmacodynamic models and assesses the
`mechanisms of drug effects. This review summarizes the state-of(cid:173)
`the-art in diabetes modelling, with a focus on models describing
`drug effects. We sought to identify major strengths and limitations
`of the published models and further needs and perspectives in
`diabetes modelling.
`We performed a literature search of MEDLINE. EMBASE, the
`references of published papers and abstracts from various confer(cid:173)
`ences. The models were subcategorized as models for (i) diagnos(cid:173)
`tic tests; (ii) intrinsic interactions of glucose and insulin; (iii) an(cid:173)
`tidiabetic drug effects: (iv) secondary drug effects; (v) ancillary
`
`biomarkers: and (vi) disease progression. This review focuses on
`models for system and parameter estimation and includes some
`simulation models.
`
`1. The Glucose-Insulin System
`
`Diabetes is a multiorgan disease, which is mainly characterized
`by a disturbance of glucose-insulin homeostasis. A simplified
`diagram of the regulation of the glucose system by insulin and
`other endogenous substances is shown in figure 1. The diagram
`describes the action of relevant biomarkers by stimulation or
`inhibition of production or utilization of other endogenous sub(cid:173)
`stances. The plasma glucose concentration is increased by hepatic
`glucose production and absorption from the gut after food intake.
`It decreases due to utilization by the brain and peripheral tissues
`such as muscle and fat. One of the key characteristics of the
`glucose-insulin system is reciprocal feedback between glucose and
`insulin, i.e. an increase in glucose concentrations stimulates pro(cid:173)
`duction of insulin, and insulin in tum stimulates utilization of
`glucose and inhibits production of glucose.
`In general, the human body aims to maintain blood glucose
`concentrations within a narrow range of about 80--115 mg/dLJ21
`For example. tissues such as the brain and erythrocytes need a
`constant supply of glucose. Therefore, in the fasting state, glucose
`is produced by breakdown of glycogen (glycogenolysis) in the
`liver. After an extended fasting period, hepatic glycogen stores are
`depleted. Then glucose is produced mainly from gluconeogenesis
`in the liver (and to a small extent in the kidneys), utilizing mainly
`amino acids from muscle tissue, lactate or glycerol. Both glycoge(cid:173)
`nolysis and gluconeogenesis are stimulated by glucagon. a peptide
`hormone that is secreted from pancreatic a-cells at low blood
`glucose concentrations (figure 1 ). Only a low basal insulin secre(cid:173)
`41 In
`tion occurs at glucose concentrations below about 80 mg/dL.f 1
`the fasting state. most of the glucose is taken up by insulin(cid:173)
`independent tissues such as the brain. and <20% is taken up by the
`muscle.1 151 During strenuous exercise and anaerobic conditions,
`glycogen in muscle tissue is broken down to lactate, which is
`released into the blood and taken up by the liver, where it can be
`stored as glycogen or converted into glucose by gluconeogenesis.
`The concept of resynthesis of glucose from lactate in the liver was
`formulated by Cori and is known as the Cori cycle or the glucose(cid:173)
`lactate cycle.1 161 The Cori cycle includes the breakdown of glucose
`to lactate in muscle tissue via anaerobic glycolysis, uptake of
`lactate into the liver, conversion of lactate to glucose in the liver,
`and uptake of glucose into muscle tissue again.
`After a meal is ingested, complex carbohydrates from the food
`are split into oligosaccharides which, in tum, are broken down to
`monosaccharides such as glucose by a-glucosidases in the gut
`wall (figure 1 ). Glucose is absorbed into the blood, and glucose
`concentrations increase. Due to increasing glucose concentrations,
`secretion of insulin from pancreatic ~-cells is stimulated (figure 1 ).
`
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`PK/PD Modelling in Diabetes Mellitus
`
`419
`
`, ,
`Insulin
`
`,
`..
`FF/
`....
`'.
`~·. ~ti- .........•••
`
`.
`
`Fig. 1. Simplified diagram of the regulation of glucose metabolism,111-1 31 describing the action of relevant biomarkers by stimulation (open bars) or inhibition
`(solid bars) of production/utilization of other endogenous substances. Many more biomarkers are involved in glucose regulation but have been omitted
`from this diagram for clarity. AG = a-glucosidases; FFA = free fatty acids; GLP-1 = glucagon-like peptide 1.
`
`At increased blood glucose concentrations, more glucose is taken
`up into P-cells and metabolized to adenosine triphosphate, which
`results in closure of potassium channels, membrane depolariza(cid:173)
`tion, opening of calcium channels, an increase in intracellular
`calcium concentrations and, eventually, increased insulin secre(cid:173)
`tion.1111
`
`Insulin is secreted in equimolar amounts with C-peptide (con(cid:173)
`necting peptide) from P-cells. C-peptide is formed due to cleavage
`of insulin from pro-insulin. As a large and vaiiable proportion of
`the secreted insulin is metabolized during the first pass through the
`liver, and C-peptide is not extracted by the liver, peripheral C(cid:173)
`peptide concentrations are often measured to study insulin secre(cid:173)
`tion.l 17l
`In the short-term, insulin secretion is stimulated by high con(cid:173)
`centrations of glucose, free fatty acids (FFA)l 18•191 (figure I) and
`amino acids.1 2o1 However, long-term exposure to elevated concen(cid:173)
`trations of FF A (lipotoxicity )119•21 I (figure l ), glucose (glucotoxici(cid:173)
`ty)l21 l or amino acidsl20l results in P-cell failure and decreased
`insulin secretion. Insulin secretion is also stimulated by incretin
`hormones, such as glucagon-like peptide I (GLP-1) and glucose(cid:173)
`dependent insulinotropic polypeptide (GIP), which are secreted
`
`from the gut wall after food intake (see later in this section and in
`figure I).
`As shown in figure 1, insulin inhibits hepatic glucose produc(cid:173)
`tion and stimulates glucose utilization by peripheral tissues. Insu(cid:173)
`lin promotes uptake of glucose and storage as glycogen in the liver
`and skeletal muscle. It also enhances glucose disposal by stimula(cid:173)
`tion of glycolysis in muscle tissue. Liver glycogen is a readily
`available glucose reservoir for the maintenance of blood glucose
`concentrations in the fasting state, whereas muscle glycogen is
`used to store energy for the muscle itself. Glucose uptake by the
`brain is insulin-independent, as the brain cannot store glucose and
`therefore needs a permanent supply of energy (as shown in figure
`1, where there is no stimulation of brain glucose uptake by
`insulin). At a high carbohydrate intake, insulin also stimulates
`conversion of glucose to fatty acids and their uptake into adipose
`tissue, where they are stored as triglycerides. Insulin also stimu(cid:173)
`lates uptake of amino acids and their storage as protein in skeletal
`muscle, and uptake of FFA and their storage as triglycerides in
`adipose tissue. In addition, insulin inhibits hepatic gluconeogene(cid:173)
`sis by inhibition of key enzymes of this pathway, including
`phosphoenolpyruvate carboxykinase (PEPCK), which catalyses
`the rate-limiting step of gluconeogenesis and also inhibits hepatic
`
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`420
`
`Landersdorfer & Jusko
`
`glycogenolysis (figure 1 ). Insulin also inhibits the release of amino
`acids from skeletal muscle and the release of FF A and tri(cid:173)
`glycerides from adipose tissue.
`These insulin actions lead to a decrease in blood glucose
`concentrations and promote storage of energy in the tissues (ana(cid:173)
`bolic action). Glucagon, conversely, stimulates the release of
`glucose, FFA and amino acids from the liver, fat and muscle
`(catabolic action). At high blood glucose concentrations, secretion
`of insulin is stimulated while glucagon secretion is inhibited, and
`vice versa at low blood glucose concentrations.
`Tl DM patients have an absolute deficiency of insulin, whereas
`T2DM is characterized by impaired insulin secretion and resis(cid:173)
`tance to insulin action in the liver and peripheral tissues. Tl DM
`and T2DM patients who require insulin therapy have elevated
`postprandial glucagon concentrationsP21 whereas Tl DM patients
`also have fasting hyperglycaemia. In addition, it has been pro(cid:173)
`posed that reduced suppression of glucagon secretion by insulin
`contributes to impaired glucose tolerance.f231 Insulin deficiency
`and glucagon excess lead to decreased glucose uptake into cells,
`increased breakdown of protein and lipolysis. In severe uncon(cid:173)
`trolled diabetes, the release of large amounts of FF A that are
`converted to ketone bodies in the liver can result in ketoacidosis.
`Amylin is co-secreted with insulin from ~-cells. It is a hormone
`that has been shown to inhibit postprandial glucagon secretionr24J
`(figure 1 ). Amy Jin also acts by delaying gastric emptying and
`reducing food intake.f22l Therefore, amylin promotes the decrease
`of high postprandial blood glucose concentrations. Amylin secre(cid:173)
`tion is lacking in TIDM patients and impaired in T2DM patients
`because of depletion or dysfunction of ~-cells. r22,251 In rodents,
`especially in the fasting state, injection of amylin resulted in
`increased concentrations of lactate due to enhanced muscle glyco(cid:173)
`gen breakdown. Subsequently, glucose concentrations increased,
`as lactate is a substrate for gluconeogenesis in the liver.l26•27l
`Increased concentrations of lactate in human muscle, adipose
`tissue and plasma, due to lactate release from muscle and adipose
`tissue, have been shown after glucose ingestion.f281
`After enteral nutrition, the incretin hormones GLP-1 and GIP
`are secreted from cells in the gut wall (figure 1 ). The secretion is
`stimulated by endocrine and neural signals and by direct stimula(cid:173)
`tion of the intestinal cells by digested nutrients. Both GLP-1 and
`GIP stimulate glucose-dependent insulin secretion from ~-cells
`(figure I), enhance ~-cell proliferation and increase ~-cell resis(cid:173)
`tance to apoptosis. In addition, GLP-1 inhibits glucagon secretion,
`slows down gastric emptying and food ingestion. and decreases
`food intake.l29•30l Therefore, GLP-1 and GIP both act to decrease
`high blood glucose concentrations after food intake. Both GLP-1
`and GIP are rapidly inactivated by the ubiquitous enzyme dipep(cid:173)
`tidylpeptidase-4 (DPP-4). The half-life of active GLP-1 in plasma
`is <2 minutes.f3°l The active GIP half-life has been reported to
`be 7 minutes in healthy subjects and 5 minutes in T2DM pa-
`
`tients.f3°•31 l Reduced secretion of GLP-1 and decreased action of
`GIP in T2DM patients compared with healthy subjects has been
`reported. r29l
`
`FFA play an important role in glucose metabolism. FFA are
`important for ~-cell function and stimulate insulin secretion.l181
`However, permanently increased FFA concentrations cause 'li(cid:173)
`potoxicity' and decrease insulin secretion from ~-cells (figure 1).
`Obesity, especially an increased mass of visceral fat, leads to
`increased concentrations of FFA, as visceral fat exhibits higher
`lipolytic activity than subcutaneous fat. Increased concentrations
`of FF A stimulate hepatic gluconeogenesisr 321 and decrease glucose
`uptake into skeletal muscle (figure 1 ). Permanently increased FF A
`concentrations promote insulin resistance in both skeletal muscle
`and the liver. As skeletal muscle is responsible for about 75-80%
`of insulin-mediated glucose disposal, decreased glucose uptake by
`the muscle due to peripheral insulin resistance can substantially
`increase plasma glucose concentrations.f33-35l In 1963, Randle
`et al.f361 proposed the glucose-fatty acid cycle, according to which
`fuel selection from FF A is preferred over glucose. Therefore,
`increased availability of FFA results in decreased glucose uptake
`into muscle cells. More recently, it was reported that FFA also
`induce or enhance insulin resistance due to alterations in insulin
`signalling,l37l which leads to decreased muscle glucose transport,
`possibly due to diminished glucose transporter protein isoen(cid:173)
`zyme 4 (GLUT-4) translocation.f38l GLUT-4 is the major insulin(cid:173)
`sensitive glucose transporter in adipose tissue and muscle, and
`facilitates glucose uptake into these tissues.r391 In obese and T2DM
`patients, lipolysis is increased, as the adipose tissue is insulin
`resistant, therefore plasma FF A concentrations are higher which,
`in tum, aggravates insulin resistance in the liver and skeletal
`muscle, and causes deterioration of ~-cell function.
`Recently, it was recognized that adipose tissue is not only a
`storage tissue but has endocrine functions and secretes hormones
`(adipokines) such as adiponectin and leptin (figure l ). Adiponec(cid:173)
`tin, which is specifically secreted from adipose tissue, stimulates
`glucose uptake and utilization in skeletal muscle and inhibits
`gluconeogenesis in the liver (figure I). Therefore it supports
`insulin action, increases insulin sensitivity and decreases plasma
`glucose concentrations. Reduced adiponectin concentrations have
`been related to a higher incidence of diabetes, insulin resistance.
`cardiovascular disease and metabolic syndrome.f40All
`Leptin, which is produced primarily by adipose tissue, acts as a
`central satiety signal (figure 1 ). Leptin decreases food intake,
`stimulates energy expenditure and increases insulin sensitivity.
`Leptin- or leptin receptor-deficient animal models exhibit obesity
`and insulin resistance. Obese subjects have higher leptin concen(cid:173)
`trations because they have a larger fat mass than lean subjects.
`However, obesity appears as a condition of relative leptin resis(cid:173)
`tance. and therefore the effect of leptin is decreased.f41 A21
`
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`PK/PD Modelling in Diabetes Mellitus
`
`421
`
`A simplified diagram, such as in figure I, can be useful for
`model building. Depending on the observed data and the most
`relevant subsystem (e.g. for the action of a drug), part of this
`diagram can be used as the starting point for a model. To date,
`most mathematical models have focused on glucose, insulin or
`both, and have not included other biomarkers.
`
`2. Mechanisms of Action of Antidiabetic Drugs
`
`Tl DM patients cannot produce insulin, and therefore their
`treatment mainly consists of exogenous insulin. Numerous thera(cid:173)
`peutic options are available for T2DM. An overview of the mech(cid:173)
`anisms and sites of action for the different groups of antidiabetic
`drugs is shown in figure 2.
`Hyperglycaemia in T2DM patients can, among other reasons,
`be due to the following : (i) decreased uptake of glucose into
`skeletal muscle due to peripheral insulin resistance; (ii) increased
`hepatic glucose production (mainly gluconeogenesis) due to hep(cid:173)
`atic insulin resistance; and (iii) decreased insulin secretion due to
`exhaustion of P-cells, genetic causes, lipotoxicity or glucotoxici(cid:173)
`ty.l2·43l Therefore, drugs that ameliorate one or more of these
`defects can be used in treating T2DM. It is generally assumed that
`
`insulin resistance precedes P-cell failure in T2DM.12, 15l However,
`there is also evidence for the theory that P-cell dysfunction is
`present before insulin resistance.l44l In general, as long as the P(cid:173)
`cells can increase insulin production enough to compensate for an
`enhanced need due to insulin resistance, the patients do not be(cid:173)
`come hyperglycaemic.f2·44l However, loss of P-cell function , most
`likely due to accelerated apoptosis,1441 leads to overt diabetes.
`Therefore, it has been suggested that approaches that delay the loss
`of P-cell function , e.g. by decreasing glucotoxicity and Iipotoxici(cid:173)
`ty, which are reversible, should be considered.121
`Sulfonylurea drugs stimulate insulin secretion from P-cells.
`Through binding of the drug to receptors on the P-cells, potassium
`channels are closed, which results in stimulation of insulin secre(cid:173)
`tion by a mechanism similar to stimulation of insulin secretion by
`glucose, as described in section l . Examples of sulfonylurea drugs
`for which models have been proposed are glimepiride, gliclazide,
`tolbutamide and glibenclamide (glyburide). Meglitinides such as
`repaglinide and nateglinide stimulate insulin secretion by the same
`mechanism as sulfonylureas but have a faster onset and a shorter
`duration of action.l1 1l
`Metformin is one of the biguanides. It is reported to suppress
`gluconeogenesis and glycogenolysis, increase insulin-mediated
`
`Site
`
`Mechanism of action
`
`Antidiabetic agents
`
`Brain
`
`Regulation of food intake
`
`lncretin mimetics
`
`Delay of gastric emptying
`
`Pramlintide
`
`Intestines
`
`Delay of glucose absorption
`
`Stimulation of GLP-1 release
`
`a-Glucosidase inhibitors
`
`Inhibition of glucagon release
`
`. Sulfonylureas
`
`Pancreas
`
`I
`
`Stimulation of insulin b1osynthes1s
`
`Acute st1mulat1on of insulin releaJe
`
`Meght1nides
`
`Inhibition of ~-cell apoptosIs
`
`- --~
`
`St1mulat1on of ~-cell d1fferent1atIon
`
`lncretIn m1met1cs/DPP-4 InhIbItors
`
`~ Modulation of adIpokIne release
`
`Fig. 2. Sites and mechanisms of action of antidiabetic agents (adapted from Stumvoll et a1.,1151 with permission from Elsevier). DPP-4 = dipeptidylpep(cid:173)
`tidase-4; FFA = free fatty acids; GLP-1 = glucagon-like peptide 1; SC = subcutaneous.
`
`© 2008 Adis Dato Information BV. All rights reserved .
`
`Clin Pharmocokinet 2008; 47 (7)
`
`~
`!
`
`Liver
`
`Muscle
`
`Fat
`
`~ Inhibition of glucose production
`
`Increase in hepatic insulin sensitivity
`
`Metformin
`
`Thiazolidinediones
`
`~ -:=,;
`~ •~•=mm"~'' loo"''"-"""'
`@i ::~:::::"::::::::,:s,-)---~
`
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`

`422
`
`Landersdorfer & Jusko
`
`glucose uptake into muscle and adipose tissue, and stimulate
`anaerobic glucose metabolism in the intestine. Metformin is some(cid:173)
`times called an insulin sensitizer. as it increases hepatic and
`peripheral insulin sensitivity.l 111
`Thiazolidinediones such as rosiglitazone and pioglitazone act
`by stimulation of nuclear peroxisome proliferator-activated recep(cid:173)
`tor y (PP ARy), which affects the transcription of genes that regu(cid:173)
`late glucose and lipid metabolism. Stimulation of PPARyincreases
`glucose uptake by the GLUT-4 transporter in muscle and adipose
`tissue by improving translocation of GLUT-4 to the cell surface.
`Stimulation of PP ARy also decreases concentrations of FF A,
`which results in enhanced glucose utilization, decreased gluconeo(cid:173)
`genesis and increased muscle insulin sensitivity. In addition,
`PPARy agonists stimulate secretion of adiponectin and inhibit
`secretion of tumour necrosis factor (TNF)-a from fat cells, affect
`the secretion of other adipokines, and promote redistribution of fat
`from visceral to subcutaneous fat, which has lower lipolytic ac(cid:173)
`tivity. Thiazolidinediones are also often called insulin sensitizers
`and have been reported to partially reverse insulin resistance_l451 In
`addition, they improve fasting plasma glucose (FPG) levels, main(cid:173)
`ly by inhibition of gluconeogenesis.l461
`Acarbose and miglitol are a-glucosidase inhibitors, which slow
`down the breakdown of poly- and oligosaccharides to monosac(cid:173)
`charides, such as glucose, and delay glucose absorption from the
`intestines. Glucose is absorbed from more distant regions of the
`gut, which results in increased stimulation of GLP-1 produc(cid:173)
`tion. r 151 a-Glucosidase inhibitors are not absorbed into the system(cid:173)
`ic circulation.
`Pramlintide is an amylin analogue and amylin receptor agonist.
`It retains the biological activity of amylin but, in contrast to
`amylin, it does not aggregate into amyloid plaques, which are
`deposited in ~-cells. Amyloid plaques may be linked to ~-cell
`dysfunctionl 151 and development of T2DM.f25l Pramlintide is used
`as an adjunct to mealtime insulin in Tl DM and T2DM patients.
`Like amylin, pramlintide decreases postprandial secretion of glu(cid:173)
`cagon, delays gastric emptying and increases satiety,f 22A71 all lead(cid:173)
`ing to decreased glucose excursions after a meal.
`Incretin mimetics are GLP-1 receptor agonists that are not
`inactivated by DPP-4 and have a longer duration of action than
`GLP-1. Like GLP-1, they stimulate glucose-dependent insulin
`release, stimulate insulin biosynthesis and ~-cell differentiation.
`inhibit ~-cell apoptosis and enhance satiety.1291 Examples are
`exenatide (synthetic exendin-4), which is approved in the US and
`the EU, and liraglutide, which is in the late stages of clinical
`development.
`DPP-4 inhibitors prolong the action of GLP-1 by inhibiting its
`inactivation by DPP-4. They have similar effects to those of the
`incretin mimetics but do not seem to influence food intake.f291
`Sitagliptin is on the market in the US and the EU. Vildagliptin is
`approved in Europe.
`
`Overall, as diabetes is a multiorgan disease, drugs with differ(cid:173)
`ent sites and mechanisms of action are used. Furthermore, one
`drug can have more than one site or mechanism of action. If a
`model includes these different mechanisms for one drug, the
`action of a drug can potentially be better described and predicted.
`However, more data and more complex models are usually
`needed.
`
`3. Overview of Diabetes Mellitus Models
`
`Most of the earlier models focused on description of the glu(cid:173)
`cose-insulin system and evaluation of diagnostic tests (table I). In
`1980, Berman1481 published an overview of models for insulin
`kinetics. Models published during the 1960s and 70s have been
`divided into two categories:1491 (i) 'simple' models with a mini(cid:173)
`mum number of parameters, such as the pioneer model published
`by Bolie in 1961 ;fSOJ and (ii) comprehensive 'library' models,151 -531
`which aim to describe the system as extensively as possible. For
`the latter, not all parameters can be estimated.1491 Two models for
`diagnostic purposes that were originally published in 1979 and are
`still widely used are the minimal modell541 and homeostatic model
`assessment (HOMA).1 55 1
`Overall, a large number of models have been developed. Table
`II lists various purposes for which models have been published.
`Models for estimation tend to have fewer parameters to retain
`parameter estimability. They are most often used to estimate
`pharmacokinetic/pharmacodynamic parameters after diagnostic
`tests or administration of antidiabetic drugs, and to quantify dis(cid:173)
`ease progression. Models for simulation are usually large, too
`complex to allow estimation, and aim to describe the physiological
`situation as closely as possible for certain organs or tissues or even
`the whole body. Whole-body simulation models may be used to
`perform virtual trials, which are difficult to perform in real human
`subjects for ethical or practical reasons.
`
`Table I. Early models of the glucose-insulin system
`
`Year
`1939
`
`References
`56
`
`Development
`First approach to measure insulin sensitivity
`in vivo
`57
`1959
`Steele's equations for glucose (d1s)appearance
`1961
`50
`Solie pioneer model for glucose-insulin system
`1965
`Model similar to Bolie's fitted to data from OGTT 58
`59,60
`1966
`Glucose clamp technique introduced
`51-53
`1970-5 More comprehensive 'library' models
`54
`1979
`Original 'minimal model'
`1979
`55
`Original HOMA model
`HOMA = homeostatic model assessment; OGTT = oral glucose tolerance
`test.
`
`© 2008 Ad1s Dalo lnformat,on BV. All nghts reserved.
`
`Chn Phormocok1net 2008, 47 (7)
`
`MPI EXHIBIT 1051 PAGE 6
`
`Apotex v. Novo - IPR2024-00631
`Petitioner Apotex Exhibit 1051-0006
`
`

`

`PK/PD Modelling in Diabetes Mellitus
`
`423
`
`Table II. Array and purposes of developed models
`
`Model and purpose
`
`Estimation Simulation
`only
`
`✓
`
`✓
`
`✓
`
`✓
`
`✓
`
`✓
`
`Diagnostics: insulin sensitivity and pancreatic
`~-cell function
`Glucose-insulin system after tolerance tests
`Glucose-insulin system in the physiological
`situation
`Important subsystems
`~-cell dynamics
`insulin binding to receptors
`oscillations in insulin secretion
`glycosylation of haemoglobin
`fuel selection in muscle tissue
`insulin signalling
`translocation of GLUT-4
`Effects of antidiabetic drugs
`Secondary drug effects
`Ancillary biomarkers
`Disease progression
`Whole-body simulations (including drug effects)
`GLUT -4 = glucose transporter protein 1soenzyme 4.
`
`✓
`
`✓
`
`✓
`
`✓
`
`✓
`
`✓
`
`✓
`
`✓
`
`✓
`
`✓
`
`✓
`
`✓
`
`✓
`
`✓
`
`for glucose clamp data,164-681 in the majority of studies, no model(cid:173)
`ling was performed for evaluation of the experimental data.
`For the IVGTT, a glucose bolus of 0.3 g/kg of bodyweight is
`administered, and plasma glucose and insulin are measured at
`12-30 timepoints over 3 hours after the dose.1621 The minimal
`model was developed by Bergman et aJ.l49•54•69•70l to estimate
`insulin sensitivity and glucose effectiveness after an IVGTT. The
`intention was to find a model that could capture the most important
`physiological features of the glucose-insulin system and allow
`e