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12 • Recent Advances in PK/PD 331
12.4.5 Mechanistic, Multiscale PK/PD and
PBPK Modeling for In Vitro to In Vivo
Correlation (IVIVC) and Preclinical to
Clinical Translation for CAR‑T Therapy
Singh etal. built a mechanism‑based, multiscale PK/PD modeling framework to bet‑
ter understand IVIVC for CAR‑T efcacy and to potentially guide preclinical to clini‑
cal PK/PD translation for cell therapy [72]. Using a stepwise bottom‑up approach, the
study also aimed at identifying critical determinants for the PK/PD of CAR‑Ts. First,
an in vitro cell‑level PD model was developed to quantitatively investigate the impact of
drug‑specic (CAR density and CAR‑target afnity) and system‑specic (target density
and tumor burden) parameters on in vitro functional readouts such as target cell killing,
CAR‑T cell proliferation, and cytokine release. Previously published comprehensive in
vitro datasets from different afnity variant CAR‑Ts targeting EGFR or HER2 across
different experimental conditions (different E:T ratios, cancer cell lines with varying
target cell density, etc.) were used. As shown in Figure 12.5, the in vitro PD model
assumes that the formation of CAR‑target complexes was governed by afnity‑driven
target‑mediated interactions between the two cell populations (CAR‑T and tumor cells)
and that the CAR‑tumor complexes drive tumor cell depletion, CAR‑T expansion, and
cytokine release. The model was able to characterize comprehensive in vitro datasets
simultaneously and estimate key parameters for tumor cell killing, CAR‑T expansion,
and cytokine release (e.g., IC50, which is dened as ‘the number of CAR‑target com‑
plexes/tumor cells’ required to induce50% of the maximum killing rate of CAR‑Ts’,
K
for killing).
max
Next, a PBPK model was developed to capture the in vivo CK and tissue biodis‑
tribution of CAR‑Ts in xenograft mouse models. Previously published biodistribu‑
tion studies with radiolabeled anti‑EGFR and anti‑CD19 CAR‑Ts in mouse xenograft
models were leveraged for this purpose. The model assumes blood and other major
organs as representative compartments linked via blood and lymphatic ows with
each tissue compartment further sub‑compartmentalized as vascular space and extra‑
vascular space (Figure 12.5). First‑order transmigration organ rates characterizing
the migration or movement of CAR‑Ts from vascular space to extravascular space
while organ‑specic lymphatic ow rates governing their circulation back into the
blood were utilized in the model structure. The developed PBPK model was able
to simultaneously characterize the distribution of multiple CAR‑Ts to major tissues,
including tumor, liver, lung, spleen, kidney, and lymph nodes. Finally, an integrated
PBPK/PD model was established to understand the in vivo expansion of CAR‑Ts and
its relationship with TGI in mouse xenograft efcacy studies. Datasets from mouse
xenograft and efcacy studies with CAR‑Ts targeting EGFR, CD19, BCMA, or HER2
were used. In addition to the PBPK structure, the model now also included a PD com‑
ponent (similar to the in vitro PD model) that assumes afnity‑driven target‑mediated
332 Biopharmaceutical Informatics
FIGURE12.5 (a) A schematic diagram of a cell-level pharmacodynamic model for CAR-T
cell activity: A dynamic population of CAR-T cells and tumor cells was assumed in an in vitro
system. Upon target-mediated interaction among the two cell populations, there is the formation of CAR-target complexes, which simultaneously mediate the tumor cell depletion,
expansion of CAR-T cells, and release of cytokines. (b) A schematic diagram of a physiologically based pharmacokinetic (PBPK) model to characterize the disposition of CAR-T cells:
The model is compartmentalized into blood and relevant tissues, anatomically arranged
via blood ows (red arrows) and lymphatic ows (green arrows). Each tissue is further subcompartmentalized into vascular and extravascular spaces. A rst-order elimination of
CAR-T cells (solid black arrow) is characterized from liver extravascular space. In a typical tissue, CAR-T cells extravasate from vascular space to extravascular space via rst-order transmigration (JOrgan) rates, eventually circulating back to the bloodstream via organ-specic
lymphatic ow. Within the tumor extravascular space, there is the formation of CAR-target
complexes, whereas only unbound CAR-T cells can circulate back via lymphatic ow.
(c) A schematic diagram of the PBPK-PD model to characterize CAR-T cell expansion and
tumor growth inhibition: The diagram illustrates only the ‘tumor compartment’ of the full
PBPK model structure, where upon the formation of CAR-target complexes in tumor extravascular space, there is expansion of total (unbound + tumor-bound) CAR-T cells and depletion of total tumor volume (TVtotal), which comprises vascular and extravascular spaces.
Only the unbound CAR-T cells can leave the tumor tissue via lymphatic (LTumor) ows. The
‘number of CAR-target complexes per tumor cells’ undergoes a series of signal transduction
steps (K1–K4), before they ultimately induce killing of inherently growing tumor cells (Kg) to
induce TGI. Reproduced from [72].
12 • Recent Advances in PK/PD 333
interactions between CAR‑T and tumor cells and that the CAR‑tumor complexes drive
TGI. The model was able to characterize the unique, multiphasic expansion kinetics
of CAR‑Ts observed in the mouse studies. Besides, the TGI proles were simultane‑
ously captured well and in vivo killing potency parameters, specic to each CAR‑T,
were estimated.
The IVIVC analysis showed that the in vitro potency parameters were consistently
estimated to be ~10‑ to 20‑fold higher as compared to the in vivo estimates, which
could be attributed to the higher probability of CAR‑Ts to come in direct contact and
interact with tumor cells in the in vitro static conditions as compared to the in vivo situ‑
ation. Additional model‑based simulations suggested a ‘threshold dose’, below which
there was no response, above which there was a steep dose‑exposure‑response for a
narrow dose range, and after that the dose‑exposure‑response relationship was at.
In contrast, tumor burden was predicted to be a more sensitive parameter for CAR‑T
expansion kinetics as compared to the cell dose, which is consistent with several pub‑
lished studies. Similarly, sensitivity analysis demonstrated CAR afnity, CAR density,
and antigen density to be positively correlated with CAR‑T expansion. Overall, the
developed multiscale PK/PD modeling framework can be used to determine the ideal
properties of a CAR‑T lead (e.g., CAR‑target afnity and CAR density), compare and
select lead candidate(s), better understand IVIVC, establish the PK/PD relationship in
a preclinical setting, and nally translate the learnings to the clinical setting for CAR‑T
therapies.
12.4.6 QSP Model for Preclinical to Clinical
Translation of CD3 Bispecic Antibodies
A translational QSP model was developed for a CD3 bispecic antibody (bsAb),
P‑cadherin/CD3 DART® (Pcad‑LP‑DART), targeting P‑cadherin for solid tumor
indications [34]. CD3 bsAbs can simultaneously engage with the CD3 receptors on
the cytolytic T cells and target antigen on the tumor cells, which then leads to the for‑
mation of trimolecular complexes and subsequently T‑cell activation and tumor cell
lysis. The model was used to characterize the PK/PD relationship for Pcad‑LP‑DART
in preclinical mouse efcacy studies and eventually translate to humans to predict
ef cacy.
As shown in Figure12.6, the model incorporated the PK of Pcad‑LP‑DART, T‑cell
distribution in the central compartment (systemic circulation) and tumor, and binding
of the drug to the T cells and soluble P‑cadherin in the systemic circulation. In addi‑
tion, the model assumed the binding of Pcad‑LP‑CART to CD3 receptors on T cells
and target on the tumor cells to form the trimolecular complexes or immune synapses
within the tumor, which are then linked to the tumor cell killing. Data, including PK of
Pcad‑LP‑DART, T‑cell distribution, TGI, and binding afnities of the drug to the target
and T cells and target and CD3levels on tumor and T cells, respectively, were used to
build the model. Overall, the preclinical QSP model was able to characterize the PK/PD
data, relevant parameters were estimated, and TSC (dened as minimum trimer concen‑
tration required for efcacy) was calculated across mouse models. Next, the preclinical
334 Biopharmaceutical Informatics
FIGURE12.6 A diagram showing a translational QSP model for CD3 bispecic antibodies with key events including distribution of drug to different compartments, binding of
the drug to target antigens on tumor cells and CD3 receptors on T-cells, and formation of
trimers between drugs, T-cells, and tumor cells which is linked to tumor cell killing. Figure
adapted from [34].
QSP model was translated to humans by integrating predicted human PK and their clini‑
cally relevant estimates for T‑cell concentration at the tumor site, tumor volumes, levels
of target, and CD3 receptors, as well as soluble P‑cadherin in patients. Here, the human
PK was predicted from a cynomolgus monkey using conventional two‑compartmental
modeling and allometric scaling approaches. The impact of soluble P‑cadherin on the
PK of Pcad‑LP‑DART was evaluated, and potential clinically efcacious doses were
predicted. The model‑based simulations identied target levels and T‑cell inltration at
the tumor site as sensitive parameters that severely impacted the efcacious dose projec‑
tions in humans.
Overall, the translational mechanistic model integrated in silico, in vitro, and in
vivo datasets, characterized the PK/PD relationship, and can be used to potentially pre‑
dict efcacy in the clinic. Such a modeling framework can be used at different stages
of discovery and development of CD3 bispecics, including to guide molecule design
(e.g., binding afnity), triage different leads, and facilitate ideal lead selection, as well as
support preclinical to clinical translation for dose projections and guide the FIH clinical
study design.
12 • Recent Advances in PK/PD 335
12.4.7 QSP Model for mRNA Therapeutic
Lipid Nanoparticle for Preclinical
to Clinical Translation
Crigler‑Najjar syndrome type 1 (CN1) is an autosomal recessive disease that is caused
by a signicant drop in the activity of the UGT1A1 enzyme. It is hypothesized that
administering hUGT1A1‑modRNA (a modied messenger RNA encoding for UGT1A1)
as a LNP will restore hepatic production of UGT1A1, allowing normal glucuronida‑
tion and elimination of bilirubin in patients. To better understand the mechanisms of
hUGT1A1‑modRNA and to direct the design of the FIH clinical investigations, a QSP
model was proposed that incorporates preclinical data from studies in Gunn rats with
the known physiological distinctions between humans and Gunn rats. The inherent
kinetics of the target plays a major role in the selection of an optimal dose and dosing
regimen, making it difcult to directly apply allometric coefcients derived from large
datasets comprising small compounds or biologics to the modRNA platform [73]. Drug
properties and biological mechanisms (such as the intracellular half‑life of mRNA and
UGT1A1) govern the expected dose regimen, and these factors are not easily scaled
allometrically based on body weights or surface areas. Because QSP models may lever‑
age datasets from several contexts (e.g., in vitro and in vivo) and multiple species/indi‑
cations (e.g., rats, healthy volunteers, and CN1 subjects), they are anticipated to provide
more predictive power than the empirical PK/PD techniques (Figure12.7) [73].
The model is able to provide projections on the consequences of these parameters,
which in this instance are non‑linear and are not expected to follow typical allometric
scaling laws. In the end, a model with such a mechanistic basis can be utilized to facili‑
tate more informed clinical decision‑making.
12.4.8 QSP Model to Gather Mechanistic Insights
for Gene Delivery in Sickle Cell Disease
To better understand the interplay between erythropoiesis, gene therapy, and autologous
stem cell transplantation, authors built a multiscale mathematical model [74]. The model
was used to simulate the effects of a novel exogenous globin that generates anti‑sickling
hemoglobin on patients with sickle cell disease (SCD). In most cases, SCD is caused by
a deciency in a single gene and cannot be treated at this time. Therefore, it is a promis‑
ing candidate for gene therapy. Preclinical research shows that anti‑sickling behavior
is conferred by the insertion of an alternative globin gene. However, clinical data dem‑
onstrating the quantitative relationship between therapy parameters and post‑treatment
results are limited. Understanding these connections and developing a logical frame‑
work to create and improve gene therapies for SCD were the primary objectives of this
case study [74].
Red blood cells (RBCs) with an anti‑sickling hemoglobin should be produced by
these stem cells indenitely. There is a lack of patient data from early clinical studies,
and the cost of this sophisticated, multi‑step treatment is prohibitive. The goal was to
336 Biopharmaceutical Informatics
FIGURE12.7 Schematic representation for the quantitative systems pharmacology (QSP)
model of hUGT1A1-modRNA. The model outlines the clearance of lipid nanoparticles (LNP)
from plasma due to liposomal instability, their uptake via endocytosis into liver hepatocytes,
the release of mRNA from endosomes into the cytoplasm, subsequent translation of mRNA
to synthesize uridine-diphosphate-glucuronosyltransferase (UGT1A1 protein), and the glucuronidation processes forming diglucuronides (DG) and monoglucuronides (MG) (Figure
adapted from [73]).
assess the effect of treatment factors on engraftment success, peripheral RBC counts,
and anti‑sickling hemoglobin levels over time. These parameters include initial stem
cell dose, lentiviral transduction effectiveness, and bone marrow preconditioning inten‑
sity. The model of RBC formation from progenitor cells in the bone marrow and of
12 • Recent Advances in PK/PD 337
hemoglobin assembly from its constituent globin monomers is based on ordinary dif‑
ferential equations. RBC and hemoglobin levels seen in healthy and SCD phenotypes
are reected in the model. The kinetics of stem cell engraftment and RBC carrying the
therapeutic gene product can be predicted using treatment simulations. Following ther‑
apy, there is an initial phase of reconstitution caused by short‑lived stem cells, followed
by a sustained RBC production from steady engraftment of long‑lived stem cells [74].
Relationships between treatment parameters and efcacy were assessed using sensitiv‑
ity analysis of the model. Predicted long‑term success is highest when the initial dose of
transduced stem cells and the intensity of myeloablative bone marrow preconditioning
are maximized. Using a QSP method, this study demonstrated the efcacy of SCD gene
treatments.
12.5 CONCLUSIONS AND FUTURE PERSPECTIVES
To overcome the challenges in drug discovery and development and to deconvolute
the complexities of novel biotherapeutic modalities, innovative approaches are needed.
Mathematical modeling is a key tool which has been shown to increase efciency and
effectiveness in drug discovery and development and can be used to facilitate molecule
design, lead selection, and preclinical to clinical translation and to optimize clinical tri‑
als for biotherapeutics. In this chapter, two different types of mathematical modeling are
reviewed: PK/PD modeling, which involves tting of data in a ‘top‑down’ manner, and
QSP modeling, which integrates data from disparate sources in a ‘bottom‑up’ approach,
to examine the relationships between a drug, the biological system, and the disease
process. These modeling tools are not mutually exclusive, and the appropriate method
should be implemented to address the question in hand.
PK/PD modeling and QSP modeling are particularly useful tools for quantita‑
tive understanding of biotherapeutics as these drugs have some unique challenges.
Biotherapeutics have evolved very rapidly over the last two decades and consist of a
diverse set of therapies, including antibodies and their derivatives such as multispecic
antibodies and ADCs, modied RNA molecules, cell and gene therapies, and vaccines.
Each of these modalities has unique PK/PD behaviors, which are reviewed in this chap‑
ter. For example, the PK and PD of mAbs are often interdependent due to processes
such as TMDD and immunogenicity. For bispecic antibodies such as T‑cell retargeting
drugs, which cross‑link immune cells and tumor cells, the formation of a trimolecular
complex between the mAb, the T cell, and the tumor cell drives the PD (and toxicody‑
namic) responses and not drug concentration alone. This leads to interesting mechanistic
complexities, including bell‑shaped concentration‑response relationships. Cell therapies
such as CAR‑T cells are even more complex as they are ‘living drugs’ which proliferate,
differentiate, actively trafc between tissues, and engage in two‑way communication
with the patient’s immune system. The resultant pharmacology is different from that of
small molecules or mAbs, as there is little relationship between administered dose and
338 Biopharmaceutical Informatics
exposure. In the face of these complexities, PK/PD modeling and QSP modeling have
become key quantitative tools to guide biotherapeutic design and development.
Consistent with the evolution in biotherapeutic modalities, PK/PD modeling and
QSP modeling are now routinely used across all stages of drug discovery and devel‑
opment, from very early discovery programs to large‑scale phase 3/4 patient studies.
The principles and methods underpinning the quantitative approaches remain relatively
constant across this continuum, but what changes are the questions that are asked. The
scope and impact of the application of PK/PD and QSP modeling and simulation are
showcased in the case studies that are presented in this chapter. For example, at early
stages, the questions may include ‘What is the best target to invest exploratory resources
in?’ and ‘What are the optimal design properties for my biotherapeutic drug?’. This is
exemplied in a case study applying mechanistic PK/PD models for early feasibility
analyses to inform key decisions for biotherapeutics in early drug discovery before the
collection of data [66]. Once a lead molecule has been identied and is being progressed
toward clinical studies, the question may become ‘How do I integrate in vitro and
in vivo data collected in the preclinical phase to translate to humans and predict safe and
effective clinical doses?’. Case studies presented herein showcase mechanistic modeling
frameworks applied for preclinical to clinical translation of T‑cell engager molecules
[44], CAR‑T cells [43], and a LNP delivering a modied mRNA [73]. In clinical devel‑
opment, the questions become ‘What dose and patient population do we select for the
phase 3 study?’ or ‘How can I use data from one indication to inform optimal dose and
regimen for a second indication?’. This is exemplied in a case study where a mechanis‑
tic model is applied for an ADC to treat NHL and used to recommend a different regi‑
men for ALL [44]. In addition to answering specic questions, perhaps a more nuanced
impact of applying a modeling‑based strategy in the discovery and development of bio‑
therapeutics is the mechanistic understanding that comes from a rigorous examination
of the system dynamics and the impact of the drug in perturbing this system.
To conclude, modeling and simulation approaches will continue to evolve as a criti‑
cal component to tackling attrition in the drug discovery and development process.
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