**2. Models for therapeutic drug monitoring**

After the administration of a drug, several processes occur leading to the pharmacological effect, so that we can define Pharmacokinetics, PK, as "what the body does to a drug" and pharmacodynamics, PD, as " what the drug does to the body " (Geldof 2007).

PG modelling in drug response, and to investigate the biological mechanisms of action and the efficacy and safety profile of the target drug, being this last point developed along this

The search of a Biomarker begins with the selection of the groups of patients and controls, continous with the selection of the type of sample to use and, finally, the selection of the statistical analysis that allowed us to demonstrate differences between both groups, such as the multivariate analysis of cross-sectional data and multivariate correlation analysis of longitudinal data, so that, there was clear evidence that these Biomarkers are able to distinguish between controls and affected individuals. To complete the validation, we have to check this on a large group of patients following Food and Drugs Administration guidelines (FDA 2008). In the case of Biomarkers used to monitor pharmacological therapies, the choice and validation of these should be supported, in addition, on studies of the etiology of the disease being treated and mechanism of drug action, as well as provide

In the other hand, a Surrogate Marker, defined as a laboratory measurement, physical sign or symptom, is used in therapy as a direct measure of how patient feels, functions, or survives and is expected was able to predict the effect of a treatment, ie, it is a test that is used as measure of the effect of a given specific treatment. It is a candidate Biomarker if it can be validated, taking this atribute when the evidence has proven that the predicted effect induced by drugs or other therapy, on the Surrogate Marker, produces the outcomes desired on the clinical characteristic of interest, such as blood pressure, serum cholesterol, intraocular pressure, etc, while Clinical Surrogate Endpoint refers to the final desirable value that we want to achieve for a specific Surrogate Marker, which is related to the level of disease progression, intensity of a symptom or sign, or a laboratory test, that constitute the

To validate a Surrogate Marker as a Biomarker, we need to understand the biological relationship between the Surrogate Marker that predicts the desired clinical benefit and the clinical outcome achieved. For pharmacological treatments, we have to know, moreover, all therapeutic actions, if we want to conclude that the effect obtained on the Surrogate Marker will result in the beneficial clinical outcomes desired. (Buckley & Schatzberg 2009; Russell

In short, at the present time the biological causality of most psychiatric illnesses and the intimate mechanism of action of most psychotropic drugs are unknown. However, it is possible to modulate pharmacologically a large number of neuroreceptors, using this tool as target of drug therapies and utilizing to control of psychiatric disorders symptoms. We will review in this chapter, the role and potential use of Biomarkers and / or Surrogate Markers to optimize the pharmacological treatments of most common psychiatric illnesses, with emphasis on schizophrenia and depression, in order to use them in the dosage regimen calcualtion and choosing a particular therapeutic drug strategy (Noll 2006; Shaheen 2010).

After the administration of a drug, several processes occur leading to the pharmacological effect, so that we can define Pharmacokinetics, PK, as "what the body does to a drug" and

pharmacodynamics, PD, as " what the drug does to the body " (Geldof 2007).

data on its cost-effectiveness and its side effects (Kemperman 2007).

desired target and that reflect the expected clinical outcome (BDWG 2001).

**2. Models for therapeutic drug monitoring** 

chapter (Riggs 1990).

2004).

There are three unitary models for the therapeutic drug monitoring:


As important part of the construction of these models, a Surrogate Marker or Biomarker is defined as measure that characterizes, in a strictly quantitative manner, the various processes and stages that occur between the administration of a drug and its pharmacological effect, and can be used in clinical practice for the individualization of drug therapy, from the viewpoint of dosage regimen calculation and therapeutic strategy. In fact, there is a growing interest in the use of biomarkers in drug development, as is reflected in the publication of numerous reviews and comments, appeared recently, on this topic. As well as, the recent increase in the number of publications about PK-PD models in journals of Clinical Pharmacology and Clinical Pharmacy, concerning to theoretical models and their implementation. Despite the continued increase in the number of articles, there are still, a large number of publications that contain pharmacokinetic and pharmacodynamic data without PK-PD modeling studies (Francheteau 1993; Geldof 2007; Mandem & Wada 1995; Zuideveld 2001).

Optimization of pharmacologic treatment is usually done by monitoring serum drug concentrations, in PK models, or by the direct or indirect pharmacological response, represented by Biomarkers or Surrogate Markers, in PD models, combined with pharmacogenetic and environmental characteristics, in PG models.

PK models can be non-parametric or compartimental. Non-parametric models provide an empirical description of the temporal evolution of drug concentration in terms of the maximum concentration, Cmax, and time needed to reach it, Tmax, and area under the concentration versus time curve, AUC. While compartmental models provide a description of concentration profile versus time of the drug in a body fluid compartment (Csajka & Vérotte 2006; Geldof 2007; Holford & Sheiner 1982; Perez-Urizar et al 2000).

Binary models PK-PD, PK-PG and PD-PG, as a result of the union of simple models, are aimed to find out the suitable therapeutic dose, body "clearance" and other kinetic parameters related to plasma drug concentration or pharmacological effect, establish an adequate dosage scheme to achieve the desired therapeutic goal, as well as know the time evolution of the pharmacological effect, using the appropiate model and the individual genotype of the different populations to which treatment is targeted, by using the following mathematical tools:

Biomarkers and Therapeutic Drug Monitoring in Psychiatry 159

metabolites to the pharmacological effect, and finally, an aggregate model that takes into consideration other factors that may affect the pharmacological effect, frequently observed in the models of compartmentalized pharmacological effect and in those of indirect

1. Mechanistic-based models, which characterize the time course of drug effect, "in vivo", using expressions that describe the biophase drug distribution, target-drug binding, target-drug activation and feedback homeostatic processes and contain elements corresponding to the distribution in the target site , target-drug binding, and activation and transduction. They are based on the principles of receptor theory, that characterizes the interaction of the receptor with the drug in terms of affinity and intrinsic activity. In these models, PK-PD, when steady-state is reached, drug concentration in the biophase is paralell to the plasma concentration and directly proportional to the dose (BDWG

Under stable conditions, relatively simple models, such as those linear or log-linear, can be used to characterize the dose-response relationship. The most used is the sigmoid model, which is an empirical function to describe the nonlinear relationship between drug concentration and the pharmacological effect; this model is mathematically expressed by the general equation for dose-response curve, equation 1, or also by Hill`s equation, equation 3, a partial solution of the previous, where E is the pharmacological effect observed with a given dose , E0 is the response in the absence of drug, Emax is the maximum effect or intrinsic activity of drug, C is the concentration of drug and/or metabolite in plasma and/or biophase, EC50 is the concentration of drug and / or metabolites that produce 50% of maximal effect, potency, and γ is the Hill factor, that expresses the sigmoidicity of the curve

Under conditions of non steady-state , the basic models PK-PD are unable to describe the time evolution of the pharmacological effect. Factors such as the compartimiental effect, acute tolerance and sensitization, and indirect response modeling, can explain the dissociation, frequently observed, between the temporal evolution of the drug concentration and pharmacological effect, using, in these cases, the previous model but applied to different doses to simulate the change in concentration along the time (Bauer et al 1997; Dayneko et al 1993; Derendorf & Meibohm 1999; Jusko & Ko 1994; Ragueneau et al 1998;

2. Indirect response models, are based on a combination of the inhibitor or stimulant effect, that can produce the drug, and the factors controling the increase or decrease of the pharmacological response, represented by the constants Kin and Kout (Derendorf & Meibohm 1999, Mager et al 2003; Meibohm & Derendorf 1997; Rowland & Tozer 1995). 3. Drug interaction-based models, are used to describe the influence of two or more drugs among them, acting on the same receptor. Their use are limited to situations in which several drugs are administered together, or when a drug becomes an active metabolite. In theoretical terms refer to the prediction of the combined effects of more than one drug. The general approach to the study of these interactions involves the analysis of changes in the velocity of reaction that occur when the drugs are used combined or

pharmacological response (Breimer & Danhof 1997; Geldof 2007).

2001; Geldof 2007; Sheiner et al 1979 Van der Graaf & Danhof 1997).

(Geldof 2007; Hill 1910; Holford & Sheiner 1982; Meibohm & Derendorf, 1997).

separately (Lozano et al 2009a, 2009c, 2010d).

The PK-PD models, can be:

Sheiner et al 1979).

1. General equation of the dose-response relationship, receptor mediated, which relates the intensity of the pharmacological effect, E, with the concentration of the drug, D, and of the receptor, R, presents in the body:

$$\frac{\partial^2 E}{\partial D^2} = \left(\frac{dD}{dR}\right)^2 \frac{\partial^2 E}{\partial R^2} \quad \text{Where} \quad \frac{dD}{dR} = \text{K} \{ \text{cons} \tan t \} \tag{1}$$

Once the steady-state and a pharmacological response, ranging between the 20-80% of maximal effect, is reached we can estimate the optimal dose required to achieve the desired Clinical Surrogate Endpoint, using the following expression, an approximation of the equation 1:

$$\frac{\left[\text{ACSE}\right]\_1}{\left[\text{ACSE}\right]\_2} = 2^{\left[\left(\frac{\text{OD}\right)\_1}{\left(\text{OD}\right)\_2}\right] - 1} \tag{2}$$

Where [ΔCSE]1 is the Clinical Surrogate Endpoint of the drug, equivalent to the average increase (delta, Δ) value obtained for CSE in the patients drug treated, [Δ CSE]2 is the experimental delta value obtained for CSE in a individual, (DD)2 is the dose of drug with which has been obtained a [Δ CSE]2 value equal to 10 and (DD)1 is the drug target dose (Lozano et al 2007,2008a,2008b, 2009b,2010a,2010b,2010c, 2011a).

2. Hill`s equation, equation 3, a partial solution of the above equation 1, from which comes, which relates the intensity of the pharmacological effect, E, on the Biomarker with the concentration of drug in the body, C, (Hill 1910):

$$E = \frac{\mathbf{C}^{\gamma} E\_{\text{max}}}{\mathbf{C}^{\gamma} + E C\_{50}^{\gamma}} \tag{3}$$


$$\frac{d\_{Va}}{d\_{Ca}} = -\frac{d\_{Vb}}{d\_{Cb}}\tag{4}$$

(Lozano et al 2009a, 2009c, 2010d).

#### **2.1 PK-PD models**

Consist of mathematical expressions that describe the quantitative relationships between the response intensity of a Biomarker or Surrogate Marker and drug dose applied. They have three components: a PK model, which characterizes the temporal evolution of the concentration of the drug and/or active metabolites, in blood or plasma, a PD model that characterizes the relationship between a drug concentration and/or possible active metabolites to the pharmacological effect, and finally, an aggregate model that takes into consideration other factors that may affect the pharmacological effect, frequently observed in the models of compartmentalized pharmacological effect and in those of indirect pharmacological response (Breimer & Danhof 1997; Geldof 2007).

The PK-PD models, can be:

158 Biomarker

1. General equation of the dose-response relationship, receptor mediated, which relates the intensity of the pharmacological effect, E, with the concentration of the drug, D, and

*D dR R* Where ( tan ) *dD K cons t*

Once the steady-state and a pharmacological response, ranging between the 20-80% of maximal effect, is reached we can estimate the optimal dose required to achieve the desired Clinical Surrogate Endpoint, using the following expression, an approximation of the

> <sup>1</sup> 2 1

*DD*

*CSE*

1 2

*CSE DD*

Where [ΔCSE]1 is the Clinical Surrogate Endpoint of the drug, equivalent to the average increase (delta, Δ) value obtained for CSE in the patients drug treated, [Δ CSE]2 is the experimental delta value obtained for CSE in a individual, (DD)2 is the dose of drug with which has been obtained a [Δ CSE]2 value equal to 10 and (DD)1 is the drug target dose

2. Hill`s equation, equation 3, a partial solution of the above equation 1, from which comes, which relates the intensity of the pharmacological effect, E, on the Biomarker

> *C E <sup>E</sup> C EC*

3. Kernel density estimation, Kernel`s test, used for poblational analysis, performed in the PK-PG and PD-PG models, which incorporate pharmacogenetic analysis (Wessa 2008). 4. Finally, for interaction-based models, where two or more drugs that interact on the same receptor, the following equation, equation 4, serves to describe the relation between the reaction velocity, dV/dC, of a drug, A, with the receptor, , versus to that of

> *d d Va Vb d d Ca Cb*

Consist of mathematical expressions that describe the quantitative relationships between the response intensity of a Biomarker or Surrogate Marker and drug dose applied. They have three components: a PK model, which characterizes the temporal evolution of the concentration of the drug and/or active metabolites, in blood or plasma, a PD model that characterizes the relationship between a drug concentration and/or possible active

max 50

2

*dR* (1)

(2)

(3)

(4)

of the receptor, R, presents in the body:

another drug, B, on the same receptor:

(Lozano et al 2009a, 2009c, 2010d).

**2.1 PK-PD models** 

equation 1:

 2 2 2 2 2 *E dD E*

(Lozano et al 2007,2008a,2008b, 2009b,2010a,2010b,2010c, 2011a).

with the concentration of drug in the body, C, (Hill 1910):

1. Mechanistic-based models, which characterize the time course of drug effect, "in vivo", using expressions that describe the biophase drug distribution, target-drug binding, target-drug activation and feedback homeostatic processes and contain elements corresponding to the distribution in the target site , target-drug binding, and activation and transduction. They are based on the principles of receptor theory, that characterizes the interaction of the receptor with the drug in terms of affinity and intrinsic activity. In these models, PK-PD, when steady-state is reached, drug concentration in the biophase is paralell to the plasma concentration and directly proportional to the dose (BDWG 2001; Geldof 2007; Sheiner et al 1979 Van der Graaf & Danhof 1997).

Under stable conditions, relatively simple models, such as those linear or log-linear, can be used to characterize the dose-response relationship. The most used is the sigmoid model, which is an empirical function to describe the nonlinear relationship between drug concentration and the pharmacological effect; this model is mathematically expressed by the general equation for dose-response curve, equation 1, or also by Hill`s equation, equation 3, a partial solution of the previous, where E is the pharmacological effect observed with a given dose , E0 is the response in the absence of drug, Emax is the maximum effect or intrinsic activity of drug, C is the concentration of drug and/or metabolite in plasma and/or biophase, EC50 is the concentration of drug and / or metabolites that produce 50% of maximal effect, potency, and γ is the Hill factor, that expresses the sigmoidicity of the curve (Geldof 2007; Hill 1910; Holford & Sheiner 1982; Meibohm & Derendorf, 1997).

Under conditions of non steady-state , the basic models PK-PD are unable to describe the time evolution of the pharmacological effect. Factors such as the compartimiental effect, acute tolerance and sensitization, and indirect response modeling, can explain the dissociation, frequently observed, between the temporal evolution of the drug concentration and pharmacological effect, using, in these cases, the previous model but applied to different doses to simulate the change in concentration along the time (Bauer et al 1997; Dayneko et al 1993; Derendorf & Meibohm 1999; Jusko & Ko 1994; Ragueneau et al 1998; Sheiner et al 1979).


Biomarkers and Therapeutic Drug Monitoring in Psychiatry 161

encoded by the ABCB1 gene, is one of the best known , being its main function the control of the outflow from inside the cells of certain endogenous and / or exogenous substrates, including several drugs and substances such as bilirubin, so the presence of polymorphisms

PD-PG models, consist of mathematical expressions that describe the quantitative relationship between the response intensity of a Biomarker or Surrogate Marker, to a single dose of the drug, and the different genotypes phenotypically actives present in a specific population.

Pharmacogenetic models, PD-PG, are used to adapt the therapeutic use of different drugs to the idiosyncrasy of each patient and their genetic characteristics, increasing its efficiency and minimizing their side effects. Approximately 20-90% of the interindividual variability in drug response is consequence of individual genotype and variants that encode different

Genetic polymorphisms with indirect effects on the response to drugs are those that affect to a genes encoding proteins that often are involved in the mechanisms of the drug disposition,

Therefore, both PK -PG and PD-PG models are used to describe the genotype-phenotype, gene-concentration and gene-dose correlations, necessary to achieve an optimal pharmacotherapy (Brockmöller & Tzvetkov 2008, Tsai & Hoyme 2002; Weinshilboum &

Bipolar disorder, BD, is characterized by the presence of one or more episodes of mania or, in mild cases, hypomania and additional depressive episodes, concomitants or alternants. The cause is unknown, although recent studies suggest the presence of an imbalance between excitatory neurotransmitters, mainly glutamate, and inhibitors, principally GABA, as well as alterations in cation pumps, such as of sodium and of calcium, which would explain the pathogenesis of bipolar disorder and another pathologies as epilepsy (Brown &

To explain the action mechanism of Lithium salts there are several proposals, being the most

1. Inhibition of the enzyme GSK-3B, whose complete mechanism in relation with BD has

2. Blockade of the NMDA/ NO receptor: The Nitric Oxide, NO, plays a crucial role in neuronal plasticity, having shown that the NO system may be involved in the antidepressant effect of lithium amd the increase in antidepressant capacity of lithium by the blockade of NMDA receptor would indicate an involvement of the NMDA/NO receptor in the pharmacological action of lithium (Ghasemi et al. 2008, 2009a, 2009b;

producing alterations in the response to treatment only under certain situations.

**3. Biomarkers for therapeutic drug monitoring in psychiatry** 

not yet been hypothesized (Jonker et al 2003).

3. Inhibition of Inositol monophosphatase enzyme (Einat et al 1998).

in this gene, entails changes in the PK and PD of certain drugs.

**2.3 The PD-PG models** 

Wang 2006).

**3.1 Lithium** 

Sherwood 2006).

Ghasemi & Race 2008).

known:

polymorphs of therapeutic targets.

4. Poblational models, are used to solve the problem of inter and intra-individual variability in the therapeutic response to a drug. In PK and PD models, the kinetic parameters of each individual are modeled in terms of the fixed effect observed, and other of random nature, while PK-PD poblational models, based on nonlinear mixed effects analysis, characterize the pharmacokinetic parameters and concentration-effect relationship, in poblational terms more than individual. Thus, in PK and PK-PD poblational models, we need to know in advance the average behaviour of pharmacokinetic parameters in target population, to identify and assess demographic, pathophysiological and environmental factors, affecting population under study and, finally, evaluate the inter and intraindivual variability through the variation coefficient of the PK parameters and their residual components (Dominguez-Gil & Lanao 1999; Schnider et al 1996).
