Journal ofPharmacokinetics and Biopttarmuccutics. Vol. 27. No. 6, J99?
`
`Modeling Interactions between Adrenal Suppression
`and T-Helper Lymphocyte Trafficking during Multiple
`Dosing of Methylprednisolone
`
`Fung-Sing Chow,"2 Amaranth Shanna,L2 and William J. Juskom
`
`Received September [4, 1999—F‘inal March 22, 2000
`
`A physioiogic pharmacodynamic model was developed to jointly characterize the effects ofcortico-
`steroid treatment on adrenai suppression and T-heiper ceii traffictting during single and muitipie
`dosing in asthmatic patients. clothyiprcdnisoione (MP). cortisoi. and T-iteiper ceii concentrations
`obtained from a previousiy pubiisited study during singie day and 6 days of muitipie dosing MP
`treatment were examined. Tire formation and disposition kinetics of MP were described wttk a
`compartmentai model. The bioritytiimic profiie of basal cortisol secretion rate was analyzed using
`a recent Fourier approach based on circadian harmonics. A three—compartment toop model was
`proposed to represent titres major T-netfirer ceii poois: Mood, extravascuiar site. and iyrnpit nodes.
`T—iteiper ceii synthesis and degradation rate constants were obtained from the literature. The
`Suppressive effects ofcortisoi andr MP on T—iteiper ceii concentrations were described with a joint
`additive inhibition function aitcrt'ng the cell migration rate from iymph nodes to blood. The model
`adequately described both plasma cortisol profiles and T-iteiper cells in Moon" after single and
`muitipie doses of MP. The potency of MP for suppression of'eortisoi secretion was estimated as
`ICm = 0.8 rig/rat. Tire biorhytitmic nature of the basai T—iteiper ceiis in blood was well described
`as under the influence of basal circadian cortisol concentrations with [C,9 = 79 rig/mi. Tire model
`fitted potency of MPfor suppression of T-iteiper ceiis was lCm = 4.6 rig/mi. Tire observed rebound
`of T-iteiper ceiis in Mood can also be described by the proposed modei. The rhythm and suppression
`ofptastna cortisol and T—itetjoer ceiis before and during singie and rnuitipie dose MP treatment
`were adequately described ity these extended indirect response models.
`
`KEY WORDS: T-helper cells; trafficking; rebound; corticosteroids; circadian rhythm; methyl-
`prednisolone; drug interactions; pharmacokinetics; pharmacodynamics.
`
`Supported by Grant GM 24211 from the National Institute of General Medical Sciences,
`National Institutes of Health.
`
`‘Department of Pharmaceutics. School of Pharmacy. State University of New York at Buffalo.
`New York 1426!).
`2Present address: Drug Metabolism and Phannacokinctics, SmithKlinc Beecham Pharmaceut-
`icals, King of Prussia, Pennsylvania 19406.
`’To whom correspondence should be addressed at 565 Hochatctter Hall, Department of Phar-
`maceatics, School of Pharmacy, State University ofNew York at Buffalo, New York 14260;
`e-mail: wjjusko@acsu.buffalo.edu
`
`559
`
`lltflfl-dfibXNWI20ll-lliS'35lfiflU/{l © 199') Plenum Publishing Corporation
`
`Apotex v. Novartis
`lPR2017-00854
`
`NOVARTIS 2059
`
`Apotex v. Novartis
`IPR2017-00854
`NOVARTIS 2059
`
`

`

`560
`
`Chow, Shanna, and Jusko
`
`INTRODUCTION
`
`The trafficking of lymphocytes between blood and extravascular pools
`occurs throughout their life-span. Newly formed lymphocytes migrate from
`bone marow via the thymus to lymph nodes during which they undergo
`maturation. This migration process may take a period of weeks prior to
`their full differentiation into T lymphocytes. The trafficking of mature non-
`dividing lymphocytes involves migration from blood into lymphoid tissue
`and back to the blood. This trafficking process is relatively fast and can be
`measured in hours (1). The T lymphocytes in tissues move via the lymphatic
`system to blood. Therefore, the drainage of lymphocytes into blood from
`the thoracic duct lymph is the predominant process. The extent of lympho-
`cyte trafficking through the blood is significant; in a 24—hr period the total
`mass of lymphocytes in blood can be replenished several times (2,3). The
`ability of lymphocytes to exchange between the blood and tissues is essential
`to enable the immune system to react to antigens virtually anywhere in the
`body. This allows lymphocytes to be concentrated at sites where they can
`most effectively respond to and eliminate foreign antigens (4).
`Corticosteroids trigger multiple effects in the body. In addition to inhi-
`bition of cortisol secretion, one of the rapid effects of synthetic cortico-
`steroids is producing lymphocytopenia (5). Lymphocytes in blood exhibit a
`circadian rhythm (6). This rhythm is partly caused and regulated by cortisol
`concentrations, which has a similar but opposite circadian profile (7).
`Among the lymphocytes, the T-helper cells are the most sensitive subset to
`corticosteroid treatment (8) and reside in the heart of the immune cross-
`talking network. Therefore, characterizing the T-helper lymphocyte tem-
`poral profile in response to corticosteroids is of importance for understand—
`ing the action of this important class of drugs.
`The effort to model cortisol concentrations and lymphocyte trafficking
`under the influence of corticosteroids has been an evolutionary process.
`Dunn er of. (9) used a cosine function to quantitate the circadian rhythm of
`cortisol concentratious and the trafficking of T-helper cells from extra-
`vascular sites to blood. These two sets of pharrnacodynamic (PD) data were
`modeled separately with the assumption that trafficking of T-helper cells to
`blood followed a zero-order process. Explicit equations were employed to
`describe the change in T-helper cells as affected by the corticosteroid. Fisher
`er of. (10) applied the concepts of indirect response modeling (11) on T-
`helper cell dynamics. Corticosteroids were assumed to inhibit the circadian
`input of cells into blood. The combined action of dexamethasone and
`hydrocortisone effects on lymphocyte distribution in blood was suggested
`by Braat at at. (12) based on a competitive interaction model of Ariens
`and Simonis (13). A multiple-dosing study of methylprednisolone (MP) was
`
`

`

`Dynamics of T-Helper Cell Trafficking
`
`561
`
`Dose
`Harmonic
`
`
`Function
`
`
`
`Fig. 1. Schematic diagram of the joint cortisol and T-helper cell trafficking
`models.
`
`published by Milad et ai. (14) in which the T-helper lymphocyte time profile
`was described with a model similar to Fisher er a1. (10) and included the
`joint competitive effects of exogenous and endogenous corticosteroids.
`However, some important features of these data had not been explored.
`First, a higher degree of T-cell suppression occurred after multiple dosing.
`After seven doses of MP, the predose T—helper cell concentration showed a
`higher value than baseline with a pronounced rebound after the last dose.
`Moreover, differences in estimated [C50 values were found when separately
`fitting the single and multiple-dose data. In this paper, data from Milad e:
`at. (14) were reexamined to develop a physiological explanation and model
`for characterizing the effects of MP on cortisol suppression and their dual
`role in T-helper cell dynamics.
`
`THEORETICAL
`
`The proposed model is shown in Fig. 1. Blood (THBL), extravascular
`{THEV ), and lymph node (THLN) pools as well as natural production (1:5,...)
`and loss (kdcg) of T-cells along with the joint effects of exogenous and
`
`

`

`562
`
`Chow, Sharma, and Jusko
`
`endogenous corticosteroids are utilized to explain the natural baseline cir-
`cadian rhythms, acute suppression, and rebound phenomena of the time
`profiles
`of
`blood T-helper
`cells
`during multiple
`dosing with
`methylprednisolone.
`
`Pharmacokinefics
`
`The kinetics of MP after doses of its prodrug have been well charac-
`terized (14,15). The soluble prodrug, methylprednisolone sodium succinate
`(MP5) was rapidly metabolized with a first-order rate (lg) to its active form.
`The elimination of methylprednisolone was best described by a monoexpon—
`ential decline. The equations used were
`
`dMPs
`a: : «ram:
`
`dM—P2 k, - MP3 —9- MP
`
`a:
`
`V
`
`(1)
`
`(2)
`
`where CL and V are the systemic clearance and volume of distribution of
`MP. Model-estimated parameters were kr, CL, and V.
`
`Circadian Rhythmic Secretion Rate of Cortisol
`
`Over the past 5 years, various extensions of indirect response models
`have been proposed to describe the circadian nature of cortisol time profiles
`(15—19). Each of these models has its unique features, advantages, and dis—
`advantages in regard to characterizing the nature of cortisol secretion. A
`review and comparison of these models was done by Chakraborty er al.
`(20). Among these models, the multicomponent harmonic function with a
`24-hr rhythm was the most accurate model for the cortisol secretion rate. A
`new Fourier analysis method with a circadian (Le, 24 hr) constraint was
`used to describe the secretion rate of’cortisol (19). Briefly, the baseline eor~
`tisol concentrations (Cc‘mw) are represented as the Fourier series
`
`Comm : no + E [aI cos(2:tnt/24) + b,1 smarter/24)]
`n = I
`
`(3}
`
`where an, a“ and b;- are Fourier coefficients which can be obtained by fitting
`Eq. (3) to baseline or placebo data. The value of n represents the frequency
`of the harmonic function. For example, when n = 0, the harmonic function
`describes a steady baseline value of .520, when n = 1, the harmonic function
`has a period of 24 hr; when n = 2, the period is 12 hr; and so on. The L2-
`norm approximation method was used to derive the secretion rate function.
`Rama). The selection of the numbers of harmonics which are best to
`
`

`

`Dynamics of T-Helper Cell Trafficking
`
`563
`
`describe the baseline cortisol concentrations was determined by the percent-
`age contribution of each harmonic to the overall data fitting. To generate
`the cortisol secretion rate, the following equation was applied:
`
`
`
`RCort( I) =
`
`+ kC I CCort
`
`(4)
`
`where kc is the cortisol disposition rate constant. Endogenous cortisol syn-
`thesis and loss is then described by
`
`
`(16' on:
`C : RCorlU) I 1(3) _kC' CCorL
`
`.
`(5)
`
`where the inhibition function (1(1)) is added when MP is present. The phar-
`macodynarnics is related to MP and cortisol via
`
`If:
`
`I )1“? C t
`
`CM?
`_ o, =——
`
`{GIMP-Cort + CMp
`
`6
`
`(
`
`)
`
`Equation (6) depicts the effect of MP on the suppression of cortisol
`secretion rate. The circadian secretion rate of cortisol is inhibited decreasing
`hyperbolic function (I(I)MP.CM) with methylprednisolone concentration
`from Eq. (2) as the driving fierce.
`
`Circadian Rhythmic Trafficking of T-Helper Cells
`
`Movement of TH cells between the three pools is given by
`
`
`
`dig“ : km _ km", - THEV — kEL . THEV + kEE - THBL
`
`
`
`dTZLN = km. - THEV — I‘m; ‘ 1(0Cort-TH ‘ THLN
`
`
`
`‘17:”: km . Itasca-m - mm — knE - THBL
`
`The inhibition function related to cortisol concentrations is
`
`mam” = 1—#
`ICSO Cort-TH + CCort
`
`(7)
`
`(3)
`
`(9)
`
`“0)
`
`where ICsu Comm reflects the cortisol concentration producing a 50% change
`in the rate constant, km.
`The synthesis rate of T-helper cells follows a zero-order rate constant
`(ksyn) while the elimination of these cells from blood is by a first—order rate
`
`

`

`564
`
`Chow. Sharma, and Josh:
`
`constant (kdc31-»HJ. Intercompartmental rate constants are km; , It“, and kg.
`to describe the trafficking process. The circadian rhythm of T-helper cells
`in blood observed under basal conditions is controlled by the inhibitory
`effect of cortisol
`(ICSUCMTH), which is secreted in a circadian rhythm.
`Hence, T-helper cells in blood have a rhythmic profile similar but opposite
`to cortisol.
`
`The total recirculating lymphocyte pool in extravascular sites has been
`estimated to contain 30 to 45 times as many cells as found in blood (21,22).
`The lymphocyte subset composition is similar in these pools (23). In this
`model, we separated the lymph from the extravascular site. The T-helper
`cell pool sizes of the compartments in this model were assigned (initial con-
`ditions) based on estimates from Trepel (22). The T-helper cell pool
`in
`lymph was [9 times larger than the pool size in blood (TH3L)- The T-helper
`cell pool size in the rest of the lymphoid tissues (EV) was 26 times larger
`than that in the circulation. The T-helper cell production (km) and degra-
`dation (meg-rt.) rates were calculated based on the life-span estimated by
`Hellerstein et a1. (24). With an estimated km.“ : 0.00033 hr“, we related
`kg,“ to the initial condition of the EV site (THEV) by kwfl = THEY x kdcgm.
`Therefore,
`the production rate was specified for each subject.
`It was
`assumed that these parameters apply to asthmatic patients.
`The joint effects of cortisol and MP on T—helper cells arises from
`
`[UlcertaMP-TH '= 1 —
`
`CMP ' §+ CCorl
`— (1 la)
`Ing Cort-TH + CH? ' §+ CCort
`
`fixes—mm
`ICSD MF—TH
`
`(11b)
`
`which is inserted into Eq. (9). Equation (1 l) was adapted from Milad et at.
`(14), and has a similar structure as Eq. (10) with the inclusion of the additive
`effects from both corticosteroids. The g is an index of the potency ratio of
`cortisol and MP for inhibition of T—helper cells input from lymph to blood
`(km), It is assumed that short-term corticosteroid treatment will not affect
`
`the production rate of T-helper cells in bone marrow. Parameters estimated
`in modeling the dynamics were kc and ICE Mag,“ for adrenal suppression
`and kLE, kBE, kEt, [Quests-m, and a for T—helper cell trafficking.
`
`METHOD
`
`Data from Milad e: a]. (14) were used to test the applicability of this
`model. Six asthmatic male volunteers were studied. Five data sets were used
`
`for this modeling as the sixth subject had irregular responses. Analytical
`and other study details can be found in the original report. The study design
`
`

`

`Dynamics of T-Helper Cell Trellicking
`
`565
`
`consisted of three sessions. In Session I, the basal cortisol and T-helper cell
`concentrations were monitored for 24 hr. [11 Session 2, a single dose of 20 mg
`MP was administered as MP5. The MP, cortisol, and T—helper cell concen-
`trations were monitored for 32 hr, In Session 3, beginning 48 hr after the
`initiation of Session 2, a daily dose of 20 mg of MP was given for 6 days.
`On the last dosing day, monitoring the same scheme as in Session 2 was
`carried out for 32 hr.
`
`Data were analyzed using a piecewise approach. The pharmacokinetie
`(PK) parameters were first estimated and then were fixed as constants when
`fitting the cortisol suppression data. Then, parameter estimates from PK
`and cortisol fittings were subsequently fixed as constants when the T-helper
`cell data were fitted. The estimated potency factor (5) for each individual
`was fixed during the final fittings to obtain the precision of the remaining
`parameter estimates for the T-helper cell PD.
`All fittings were done with subroutines written for Adapt II release 4
`(27). Assuming that the additive error is normally distributed, the Maximum
`Likelihood Estimator along with a general variance model was used to
`obtain the system and variance parameter estimates. This error model
`described a nonconstant relationship of variance and predicted values with
`a slope and a power function based on predicted values: Variance of Y:
`(slope of 3m2 x (predicted WW
`
`RESULTS
`
`Pharmacokinetics of MP
`
`Equations (1') and (2), which describe the pharmacokinetics of MP,
`were fitted simultaneously to the first and multiple—dose MP concentrations
`for each subject. The profiles for one of the subjects is shown in Fig. 2. The
`estimated parameters are summarized in Table 1. These estimated param-
`eters were then fixed to generate the forcing functions for the later fitting of
`cortisol and T-helper cell concentrations. The kinetics of MP is well
`described with a first-order formation rate and monoexponential decay of
`MP. The formation rate (kr) of MP from MP3 was rapid with a mean value
`of 6.2 hr“. The mean half-life of MP was 2.6 hr, with an average V of 841
`and CL of 231/hr. These parameter estimates were similar to those pre-
`viously reported (9,10,25,26). With a half-life of 2.6 hr and a daily dosing
`scheme, there was no accumulation during 6 days of once-daily treatment.
`Therefore, differences in response to single and multiple doses were not
`caused by any changes in the pharmacokinetics of MP.
`
`

`

`566
`
`Chow, Shanna, and Jusko
`
`100
`
`
`
`
`
`MethylprednlcaohneConcentration(ngi'I'nL)
`
`i—_|—|—|—I—I—t—l
`0
`20
`4D
`30
`ED
`10!)
`mo
`ND
`
`Time (hr)
`
`time profile of one
`Fig. 2. Metltylprednisolone concentration vs.
`subject during multiple dosing. Symbols are the observed data with
`line fitted using Eqs. [1) and (2).
`
`Table 1. Summary of Methylprednisolme Phannacokinetic Parameters"
`
`Subject
`
`1
`2
`3
`4
`5
`
`M
`SD
`
`kr
`(hr' ')
`
`7.7 (39.4)
`3.2 (27.1)
`4.9 {12.6)
`4.0 (9.6)
`6.1 {24.3)
`
`6.2
`1.3
`
`V
`(L)
`
`100.7 (6.9}
`75.7 (5.0)
`79.5 (3.3)
`73.7 (2.4)
`34.3 (4.5)
`
`83.3
`9.9
`
`CL
`[L/hr)
`
`23.6 (8.1)
`21501.2)
`24.3 (3.5)
`19.4 (1.1)
`20.2 (2.9)
`
`22.3
`3.7
`
`[”2
`(hr)
`
`2.4 (12.3)
`2.4 (6.3)
`2.3
`(5.3)
`2.3 (2.5)
`2.9 (3.3]
`
`2.6
`0.3
`
`”Data presented as parameter estimate {% C V).
`
`Baseline Cortisol
`
`A baseline profile of cortisol for one subject is shown in Fig. 3. The
`insert of Fig. 3 further illustrates its circadian nature. The harmonic func—
`tions that contributed more than 1% to the overall function of cortisol
`
`secretion rate were selected. The baseline cortisol concentrations of these
`
`subjects from the first study session were well described with three to four
`harmonic functions plus an average cortisol secretion rate. (it 2 0). The har-
`monics selected for each subject are summarized in Table II. The contri-
`bution of each harmonic to the total function is listed in rank order. This
`
`cortisol function was stable and reproducible over the whole study period.
`Hence, the effect of MP on suppression of cortisol secretion can be assessed.
`
`

`

`567
`
`o
`
`Dynamics of T-Helper Cell Trafficking
`
`0
`
`m
`
`’
`
`‘
`
`120
`
`(nglmL} S8
`CortisolConcentration
`
`
`
`
`Time (hr)
`
`Fig. 3. The basal cirCadian profile of cortisol concentration versus time for one
`subject. Symbols are the observed data with the line fitted using the Fourier
`approach.
`
`Table ll. Summary of Cortisol Pharmacodynamic Parameters”
`
`Subject
`
`Harmonic functions
`(it)
`
`Initial CCall
`(mg/ml)
`
`0. l. 3, 2, 4
`0. l, 2, 4
`0. 1. 3. 2
`01 1.2.3
`0. 1.3, 4
`
`107.6
`26.2
`47.5
`104.?
`61.4
`
`l
`2
`3
`4
`5
`
`M
`SD
`
`kc
`[hr")
`
`(12)
`0.2]
`0.36 [20.2)
`0.30 {15.3)
`0.22 (10.4)
`0.16 (10.5)
`
`0.25
`0.03
`
`[C50 MP—Corl
`(Hg/ml)
`
`0.25 (21.3)
`0.36 (44.”
`1-62 (42.9)
`(17491.3)
`0.37 (“5.5)
`
`0.77
`0.54
`
`“Data presented as parameter estimate (%C V).
`
`Cortisol after MP “Treatment
`
`Cortisol concentrations of each subject from baseline, single dose, and
`multiple doses were arranged according to their sample collection times
`based on the study design. Therefore, a single differential equation [Eq. (5)]
`with a single initial condition of cortisol (at r= 0) was used. This avoided
`the need to assume initial conditions for each treatment session. The pharm-
`acokinetics of MP was used as a fixed function for suppression of the circad-
`ian cortisol secretion rate. Figure 4 shows the fitting of this model to the
`
`

`

`568
`
`Chow, Slant-me, and Jusko
`
`
`
`
`
`CortisolConcentration(nymL')
`
`120
`
`asD
`
`ha
`
`7
`
`ti 1
`
`1 W
`
`Time (hr)
`
`300
`
`Fig. 4. The cortisol concentration vs. time profile for one subject in all
`sessions. Symbols are the observed data with the line fitted using Eqs. (5)
`and (6}.
`
`cortisol data of one subject. The fitting well described all cortisol concen-
`trations From the study. Table II summarizes the cortisol initial condition,
`disposition rate constant (kc), and MP potency (ICSG MPCM) for each sub-
`ject. The mean kc is 0.25 hr‘I and {(350 Mpg,” is 0.77 ng/ml. These parameter
`estimates are similar to those previously reported using a single cosine cir-
`cadian cortisol secretion rate (26,28). The mean kc value obtained using the
`Fourier approach is similar to that (0.38 hr'l) reported by Lima 6! a]. (28)
`following short-term infusions of cortisol.
`
`Dynamics of T-Helper Cells
`
`The T-helper cell concentrations were also arranged in the same
`sequential manner as the cortisol data for each subject. The parameters for
`MP pharmacokinetics and cortisol pharmacodynamics were used according
`to the model as fixed joint effects on the suppression of the kw rate process.
`Figure 5 shows fitting of the model to T—helper cell concentrations for one
`subject. The T-helper cell concentrations of Session 1 (baseline) were placed
`on Day 22 to demonstrate the stability of model. The fitting was able to
`simultaneously describe data from all sessions. The nature of T-helper cell
`rebound after multiple doses was well captured. The rhythm of T—helper
`cells in blood was predicted to be restored about 5 days after the last treat-
`ment. The parameter estimates are summarized in Table III. The mean
`
`

`

`Dynamics of T-Helper Cell Trafficking
`
`569
`
`1600
`
`1200
`
`800
`
`400
`
`
`
`
`
`T-halperCells(cellsluL)
`
`
`0|
`I
`r
`T
`0
`
`300
`
`350
`
`400
`
`50l
`
`1““1 it fit
`
`2i”
`
`Time {hr}
`
`Fig. 5. The T-helper cell concentration in blood vs. time profile for one
`subject in all sessions. Symbols are the observed data with line fitted using
`Eqs. m—(n).
`
`1C5.) Comm and 15:35.3,“qu were 79.3 and 4.6 ng/ml with potency ratio (.5) of
`17.1. The mean blood T-helper cell trafficking rate constants were kw =
`0.0291hr" and kBE=0.379 hr". The EV to LN rate constant (km) was
`0.018hr“. The cell dynamic parameter estimates were similar among the
`subjects except for Subject 2. The mean basal cell level of Subject 2 was
`higher at about 1200 cells/n1. His degree of rebound was more pronounced
`(maximum of 2000 cells/p1) after multiple doses. Although the estimated
`parameters suggested Subject 2 was insensitive to cortisol-induced T-hclper
`cell suppression (high ICSOCD,,_CD4), the high basal T-helper cell
`level
`in
`blood indicated a higher production rate.
`Figure 6 shows the simulated profiles of cells in LN and EV of the
`indicator subject. The LN and EV pools in this model show an opposite
`profile to each other. The magnitude of change in these pools is similar.
`During MP treatment, the LN pool increased from about 15,500 to 20,000
`cells/m1 (—30% increase) and the EV pool decreased from about 20,000 to
`16,000 cells/ml (~20% decrease). With the assumption that MP does not
`affect the trafficking of T-helper cells from EV to LN, this simulation shows
`that T-helper cells were retained in the LN while the EV pool continuously
`depletes over the treatment period. Upon the cessation of MP treatment,
`both pools rapidly return to the steady-state cell counts. This swift equili-
`bration of these circulation pools agrees with indications that lymphocyte
`trafficking through the blood compartment occurs at a high rate (2).
`
`

`

`570
`
`Chow, Sharma, and Jusko
`
`
`
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`Dynamics of T-Helper Cell Trafficking
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`571
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`20000
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`18005
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`16000
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`T-helperCells[CellaiuLl
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`14000
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`...°..
`
`t
`
`
`I
`I
`I
`I
`I
`I
`I
`50
`10
`150
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`r ”H 1 1h 25"
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`400
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`Fig. 6. The simulated 'T—helper cell concentrations in the extravascular (solid
`line) and lymph node pools (dashed line) vs. time profile for one subject in all
`sessions.
`
`DISCUSSION
`
`The circadian rhythm of cortisol concentrations in humans is often
`asymmetric and variable. The patterns of‘ the basal cortisol secretion rate of
`each individual are different. A single cosine function may not be sufficient
`to describe such a complex pattern. This issue has been illustrated in studies
`that compared various modeling approaches for biorhythmic basal cortisol
`concentrations (16,20). In this model, we utilized the Fourier Lzflnorm ana—
`lytical approach (19,20) to generate the appropriate circadian harmonic
`function for the cortisol secretion rate profile of each subject. This approach
`is flexible, accurate, and stable over time. Therefore, it was used as a part of
`the model for driving the cortisol-induced changes in T-helper cell rhythms.
`The majority of lymphocytes in the human body reside in lymph nodes,
`spleen, thymus, and bone marrow. Only about 2% of the total lymphocytes
`are found in the blood (22). Among the lymphoid tissues, the lymph nodes
`and spleen are the main compartments in lymphocyte trafficking (1). Circul-
`ating blood disseminates lymphocytes to various regions of the body. The
`extravasation process of lymphocytes is rapid. It takes about 15 min from
`the initiation of contact of lymphocytes with endothelial cells to diapedesis
`of the lymphocytes into tissue (29). The lymphocytes accumulate in either
`the white pulp of spleen or the high endothelial venule (HEV) of the lymph
`nodes (30). Cells in lymph nodes complete their journey and return to the
`bloodstream via the thoracic duct. Our three-pool model was structured
`
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`572
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`Chow, Sharma, and Jusko
`
`accordingly with the kBE value found as expected to be much larger than
`the other rate constants.
`
`Different types of lymphocytes follow a specific trafficking pathway.
`Peripheral
`lymph nodes retain mostly the T lymphocytes (3|,32), while
`Spleen retains mostly the B lymphocytes (23) from the recirculating pool.
`Therefore, we considered only the lymph node pool as a model compart~
`merit apart from the extravascular site for T-helper cell
`trafficking. By
`including these two compartments along with a recirculation system, this
`model provides a more plausible and physiological mechanism or T lympho-
`cyte trafficking. However, with the increase of model complexity, the rela-
`tive sizes of the model compartments determine the rate process of the T-
`helpcr cell migration between each site. Therefore, published values of rela-
`tive lymphocyte distribution in healthy volunteers (22) were assigned for the
`sizes of the T-helpcr cell pools in lymph nodes and extravascular sites under
`steady-state conditions. The influence of disease status on T lymphocyte
`
`distribution should be considered when this model is used to estimate drug
`effects on cell trafficking in patients. Our asthmatic patients were otherwise
`relatively healthy and could be well characterized with this model.
`The T-cell production and degradation rates are important factors in
`our attempt to quantify the temporal changes in these model compartments
`over several days. In normal conditions, these rate processes occur at sites
`other than blood and lymph nodes. Hellerstein et al. (24) measured the
`kinetics of circulating T lymphocytes in normal humans. By intravenously
`infusing the stable isotope-labeled metabolite 2H—glucose to healthy volun—
`teers and following the rate of its disappearance, they Were able to estimate
`the normal life-span of T-helper cells by calculating the rate constant of
`replacement of unlabeled by labeled DNA strands in blood. Since the loss
`of labeled DNA strands would not be affected by cell proliferation during
`the postlabeling period, the estimated production rate and life-span from
`this study represent the true kinetics of T—helper cells in humans. Therefore,
`these synthesis and degradation rates of T—cells were used in our model.
`However, in the same study, when the life-span of T-helper cells were com-
`pared in healthy subjects with those in HIV patients, the degradation pro-
`cess was faster in HIV patients.
`Our model provides a physiologic approach to determine the potency
`of a therapeutic agent for suppressing T lymphocyte trafficking. However,
`it is not possible to obtain appropriate parameter estimates without the
`prior understanding of T lymphocyte distribution and production and
`degradation rates.
`This model considered the dynamics of recirculating T-‘nelper cells with
`a simple three-compartment loop system. Although it is a simplified version
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`Dynamics of TuHelper Cell Trafficking
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`573
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`of the physiological system, our model contains the main components of T-
`helper cell dynamics in humans. With use of some information about T-
`helper cell pools and production from the literature, we were able to con-
`struct this model to describe (i) the biorhythmic nature of T-helper cells in
`blood under the influence of basal cortisol concentrations; (ii) the acute
`suppression of T-helper cells after a single MP dose; (iii) the suppression of
`T-helper cells after multiple MP doses; (iv) the increase of blood T-helper
`cells during multiple MP doses; and (v) the restoration of the normal T-
`helper cell biorhythm after cessation of therapy.
`In basic indirect response models (IRM) (ll), zero-order input and
`first-order output rate constants for a single compartment are used to
`describe the dynamics of a physiological response. Drugs are assumed to
`modulate one of these rate processes. A natural extension of [RM is a two-
`compartment catenary IRM. Sharma et a1. (33) explored precursor-depen-
`dent indirect response models (PIRM) with a zero-order rate in the precur-
`sor preceding the response compartment. A first-order
`rate constant
`connects the precursor to the response compartment while the response was
`dissipated via a first—order process. When drug suppresses or enhances the
`formation rate of response,
`the model predicts tolerance or
`rebound
`phenomena upon repeated dosing. Our current model is partly an extension
`of these PlRM allowing the phenomenon of rebound to be predicted with
`a suppressive drug effect. New developments presented in our models are
`the use of a third dynamic compartment, the description of the production
`and loss of response on the third compartment (THEV )3 and the recircu-
`lation system of these pools (i.e., THEV to THm to THBL and return to
`THE, ). This third compartment is needed when the natural production rate
`(km) of the dynamic response is not associated with the precursor compart-
`ment, and /or the dissipation of response from the response compartment
`(THBL) is not the natural degradation process (kdcgm). Furthermore, a
`threecompartment loop system provides a delay of cell movement in that
`a cell leaving the blood compartment requires time for trafficking through
`the EV site before it becomes available for the blood compartment. There-
`fore, this model is most suitable to describe physiological trafficking pro-
`cesses of T-helper cells where the site of main drug effect is not at the
`synthesis and degradation steps. Additional features of this model are the
`exploration of the intricacies of methylprednisolone and cortisol effects on
`T-cells.
`
`ACKNOWLEDGMENT
`
`The authors thank Dr. Wojciech Krzyzanski
`discussion.
`
`for his
`
`insightful
`
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