Supplemental Pharmacokinetic model of breast milk

Chapter 4: Bedaquiline exposure in pregnancy and breastfeeding in women with

4.6 Supplemental Pharmacokinetic model of breast milk

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87 Figure s4. 1: Pharmacokinetics profile of bedaquiline and M2 of the two individuals contributing breast milk samples. Bedaquiline concentrations are plotted in blue and M2 in green. The solid line represents the model-predicted plasma concentration, while the dashed lines represent the breast milk concentrations. The circles represent the observed breast milk concentrations, while the triangles represent the observed plasma concentrations.

As a second step, we fixed the individual plasma PK parameters and used the model-predicted plasma concentration profile as an input (forcing function) for the model fitting the breast milk concentrations. This is called a sequential modelling approach, and Zhang et al. (L. Zhang et al., 2003) showed that it performs as well as the simultaneous modelling method, which was not feasible in our scenario, since the plasma PK model showed a systematic over- prediction at population level.

To characterise the link between plasma and milk concentrations, we used an effect compartment approach ( Upton & Mould, 2014), as shown in the diagram in Figure s4.2

88 depicting the structural model. This paradigm describes the concentrations of bedaquiline (and M2) in human milk as dependent on plasma concentrations, but it assumes no significant transfer of drug between plasma and breastmilk (negligible mass transfer), so that the movement of drug into the breastmilk compartment does not affect the amount in the central compartment.

Figure s4. 2: Schematic representation of the PK model of bedaquiline and M2 in plasma and human milk. The plasma PK model is as reported by Brill et al., 2017. The absorption is described with a series of transit-compartments (NN) and mean transit time (MTT) to capture the delay in absorption, and a rate constant ka. Drug transfer between the central and peripheral compartments is defined by intercompartmental clearance Q1 and Q2. Bedaquiline and M2 clearances are denoted by CL and CLM2, respectively. Kmilk is the plasma and human milk equilibration rate constant and Rmilk and M2_Rmilk are bedaquiline and M2 accumulation ratios, respectively

The equation describing the concentration in breastmilk is:

𝑑𝐶_{𝑚𝑖𝑙𝑘}

𝑑𝑡 = 𝐾_{𝑚𝑖𝑙𝑘}∙ (𝑅_{𝑚𝑖𝑙𝑘}∙ 𝐶_{𝑝𝑙𝑎𝑠𝑚𝑎}− 𝐶_{𝑚𝑖𝑙𝑘})

where Cmilk is the concentration in human milk, Cplasma is the plasma concentration, Kmilk is the first-order plasma-to-breastmilk equilibration rate constant, and Rmilk is the accumulation

89 ratio between plasma and breastmilk, previously referred to as pseudo-partition coefficient (Egbelowo et al., 2021; Sheiner et al., 1979). Kmilk describes the “delay” in the transfer of drugs from plasma to milk. It can also be parameterised as a half-life (T1/2milk = In(2)/Kmilk) which can be interpreted as the time required to achieve 50% of the equilibrium target between human milk and plasma. Rmilk is the ratio between the concentrations in human milk and plasma at equilibrium. Two separate effect compartments were fit, one for bedaquiline and the other M2.

The model parameters are presented in Table s4.2. The final model did not find any significant difference for Kmilk of BDQ and M2, so a single parameter was estimated. The model supported between-subject variability (BSV) in bedaquiline Rmilk (ΔOFV=5.05) and only proportional error for both bedaquiline and M2. The model-predicted profile and the individual PK profile of the plasma and milk concentration are depicted in Figure s4.1, showing satisfactory goodness of fit.

Table s4. 2: Final pharmacokinetic parameter estimates for bedaquiline and M2 in human milk.

Parameter Typical Value

(%RSE)

Between-Subject Variability ^a, %CV

T1/2milk - half-life of delay in plasma to milk equilibration (h)

8.15 (36.5)

Rmilk - BDQ accumulation ratio (.) 13.6 (10.1) 10.9 (34.2)

M2_Rmilk - M2 accumulation ratio (.) 4.84 (5.10)

BDQ Proportional error (%) 16.0 (21.1)

M2 Proportional error (%) 13.3 (27.5)

a Variability was modelled with log-normal distribution and is presented as an approximate percentage CV.

The model estimated a bedaquiline milk to plasma accumulation ratio of 13.6 and M2 milk to plasma ratio of 4.84. A single Kmilk with a half-life of 8.15 was estimated for both bedaquiline and M2. However, the large delay in the milk to plasma equilibration might be driven by a

90 single unexpectedly low plasma concentration in the first 6 hours, hence should be interpreted with caution.

Table s4. 3: Characteristics of 13 HIV-positive women treated for rifampicin-resistant tuberculosis

TB treatment

regimen ART regimen

Gestational age at birth,

wks

Time on bedaquiline, days Time from delivery to Postpartum

PK, days

Breastfeeding status Antepartum

PK

Postpartu m PK LZD, BDQ, hdINH,

LFX, CFZ, PZA, EMB

TDF, FTC,

NVP 33 19 81 44 Yes

INH, PZA, EMB, BDQ, LVX, Moxy

TDF, FTC,

NVP 38 84 201 46 No

INH, PZA, CFZ, LZD, BDQ, LVX

TDF, FTC,

NVP 37 96 166 48 No

LZD, BDQ, hdINH, LFX, CFZ, PZA, EMB

TDF, FTC,

NVP 37 57 No

INH, PZA, EMB, ETH, CFZ, LZD, BDQ,

TDF, FTC,

NVP 40 13 No

PZA, TRZ, CFZ, LZD, BDQ, DLM

TDF, FTC,

NVP 39 15 No

LZD, BDQ, hdINH,

LFX, CFZ, PZA, EMB 3TC+RIT+LPV 38 31 No

LZD, BDQ, hdINH, LFX, CFZ, PZA, EMB

TDF, FTC,

NVP 40 27 184 44 Yes

LZD, BDQ, hdINH, LFX, CFZ, PZA, EMB

TDF, FTC,

NVP 39 17 No

LZD, BDQ, DLM, LFX, CFZ, PZA, EMB, TRZ, PAS

TDF, FTC,

NVP 39 25 No

LZD, BDQ, DLM, LFX, CFZ, PZA, EMB, TRZ, PAS

TDF, FTC,

NVP 38 31 143 44 No

LZD, BDQ, hdINH, LFX, CFZ, PZA, EMB

DTG, TDF,

3TC 34 35 81 46 No

LZD, BDQ, hdINH, LFX, CFZ, PZA, EMB

DTG, TDF,

3TC 36 18 No

LZD: linezolid; BDQ: bedaquiline; DLM: delamanid; hdINH: high-dose INH; INH: isoniazid; CFZ: clofazimine, PZA: pyrazinamide, EMB:

ethambutol; ETH: ethionamide; DLM: delamanid; TRZ: terizidone; LFZ: levofloxacin; PAS: para-aminosalycylic acid; TDF: tenfovir; 3TC:

lamivudine; FTC: emtricitabine; RIT: ritonavir; LPV: lopinavir; DTG: dolutegravir

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Chapter 5: Pharmacokinetics of high-dose isoniazid for treatment of