Model solution
The model equations were solved
numerically using ANSYS Fluent v. 2020R2 software and the finite volume
method (FVM). A computational domain was defined, considering the drops
and the external fluid in which the glioblastoma cells absorb (consume)
the drug (DOX) released from drops of emulsions DOX-E1 and DOX-E2. Based
on the analysis of the number of drops per unit volume (drops + the
external surrounding fluid), the simulation domain was determined as the
relationship between the radius of the drops and the radius of the
external fluid into which the drug was released.
Due to the spherical geometry and
axial symmetry, the computational domain was defined and discretised in
cylindrical coordinates.
3. RESULTS AND DISCUSSION
3.1 The controlled anti-cancer drug release from the pH-responsive
multiple emulsion and elimination by GBM cells: experiments and
simulations
The experimental data and simulations of the release rates of DOX from
multiple emulsions DOX-E1 and DOX-E2 in the cancer cell environment
(LN229 and U87 MG) are presented in Fig. 2 (c, d, f, g) as a cumulative
mass of DOX released vs time for two DOX concentrations in emulsions.
The experimental results showed that the release rates of DOX are
influenced by the drop sizes and emulsion structures in the presence of
the tumour environment characterised by acidic pH. The diffusional
release of DOX from the emulsion with smaller drops (DOX-E2) was faster
than those from the emulsion with larger drops (DOX-E1). Faster release
from DOX-E2 resulted from a larger interfacial related to the smaller
drop sizes of these emulsions. In addition, the internal structure of
emulsion DOX-E2 (single droplet in a drop-Fig. 2b) shortened the DOX
diffusion path to the drops’ interface and outside, and so thus led to a
faster release compared to the emulsion DOX-E1, structured as many
internal droplets in a drop (Fig. 2a). Our previous results related to
the release rates of DOX from multiple emulsions in pH=6.3 simulating
the biological system of cancer cells confirmed a faster release of DOX
in comparison with pH=7.4 representing healthy cells. The release of DOX
from multiple emulsions is based on a pH-dependent mechanism, shown in
Fig. 3a.
This idea was realised by introducing pH-responsive biopolymer (sodium
carboxymethylcellulose - CMC-Na) into the external phase of multiple
emulsions, which bring forth spatial conformational changes influencing
drug release.31 As the biopolymer (CMC-Na) is an
adhesive polymer, its molecules are present not only in the external
phase but also on the surfaces of drops.32 As shown in
Fig. 3a, under lower pH conditions, the chains of CMC-Na are coiled and
form aggregates that interact with one another weakly, facilitating drug
release. At a higher or neutral pH, the polymer stretches to form
long-loose chains, which interact strongly, leading to overlapping and
ultimately hindering the drug release (Fig. 3 a). The spatial
conformation changes in polymer chains also promote changes in some of
its physicochemical properties.31 Our measurements
demonstrated differences between viscosities under acidic and slightly
base pH levels for emulsions and their external phases (Fig. 3 b, c).
Moreover, viscosity changes affect the values of the diffusion
coefficient of the drug. Due to the low concentration of Na-CMC (0.2 wt.
%) the changes in the viscosity were small but significant enough to
observe the difference in the diffusional transport of DOX both within
and out of the drops (Table 3). The drug release rates also depend on
the amount of its elimination by cancer cells. Drug elimination is
determined by its physicochemical properties, formulation, type of the
cells, route of administration, and rate of drug transport to the brain.
In general, drugs can be eliminated including mechanisms such as
degradation, metabolism, permeation, local internalisation or binding,
and through blood capillaries.33 The drug (DOX)
depletion due to elimination by GBM cells was determined based on the
experimental data of the mass fraction of DOX released from emulsions
with and without cancer cells (Fig. 2 c, d, e and f, g, h). A more
general model of drug binding in the biological tissue was used to
determine the elimination rate constant of DOX, according to the
kinetics of an irreversible first-order reaction.9 On
this basis, the elimination rate constants of DOX (k) by LN229 and U87
MG cells for the emulsions DOX-E1 and DOX-E2 were calculated and
compared with those for the DOX in the solution representing classical
therapy (DOX in a solution), (Tab. 2). The obtained values of (k) have
demonstrated that exposing cancer cells to DOX in emulsions led to
higher drug elimination, as compared to classical therapy. Higher values
of the consumption rate constants of DOX in emulsion implied a greater
effectiveness of the emulsion form of the drug administration, which was
confirmed by cytotoxicity studies of both forms of the drug (DOX in
emulsion and DOX in a solution). The experimentally obtained values of
the drug elimination rate constants (k) were further used in
simulations. The simulations of
the drug (DOX) release in the GBM cells environment were based on a
diffusion model with a chemical reaction (representing
elimination/consumption of the DOX by cancer cells).
Model equations (eqs. 1-13) were
solved for parameters D32, d32,
kLa, φ, De, De,z, k,
calculated based on the experimental data (Table 3) to find the
spatiotemporal drug concentration distribution and then averaged to a
defined volume for simulating the cumulative mass of DOX released vs
time in the presence of GBM cells. The results of the release rates
simulations in comparison to experiments for both investigated emulsions
and cell lines (LN229 and U87 MG cells) are presented in Fig. 2 (c, d,
f, g). Simulations predicting release rates of DOX from the emulsion
implant showed good agreement with experimental data. These results
proved that the developed model may be a vital tool in the planning and
evaluating brain oncotherapy. One of the stages is, among others,
determining the dose and duration of therapy and whether and when the
implant should be replaced with a new portion of the emulsion - a new
implant. Then, based on the simulation results, it is possible to
determine the time of the complete release of the drug and thus the time
after which it is necessary to replace the inserted implant with a new
portion of the emulsion, i.e. the time when the consumption of DOX by
the cells ceases to increase or increases insufficiently. Moreover, by
having a process model, the prediction of the drug release rates in the
tumour cellular environment is feasible over a longer time scale,
concerning the treatment time, compared to experimental studies. In
vitro studies of the DOX release from the emulsion in the presence of
cells were carried out for a maximum of 24 h due to the specific nature
and limitations of tests with biological material related to the
cell-culturing under conditions of anti-cancer therapy. The use of this
model avoids long-term and costly experimental studies that require work
with highly toxic chemotherapeutic agents and biological material. In
addition, having then basic data on cell viability (from cytotoxicity
study) connected with drug elimination, the effectiveness of the therapy
may be easily evaluated based on the model predictions.
3.2 The modelling of the spatiotemporal drug concentration distribution
within drops of the emulsion implant and external environment with
glioblastoma cells
The numerical simulations also included the spatial concentration
distribution of DOX within drops and the surrounding fluid with cancer
cells LN229 at a given time for emulsion DOX-E1 (Fig. 4a) and DOX-E2
(Fig. 4b). As shown in exemplary simulations in Fig 4, the concentration
of DOX released outside the drop, in the presence of GBM cells, achieved
a relatively fast (within 50 seconds) and practically constant value
within an already small distance from the surface of the implant
(representative drop of emulsion) and within the bulk phase. This is the
advantage of the drug emulsion-based implant, which ensures a constant
concentration of the drug in the tumour environment controlled by
emulsion structures and drop sizes. Simulations enable the prediction of
the required drug concentration, and thus the dose of the anti-cancer
drug for any cancer cells based on comparing the concentration
distribution of DOX within the emulsion implant and the concentration of
DOX in the cancer cells environment (external fluid). As shown in Fig. 4
(a, b), despite the same dose of DOX in both emulsions, the gradient of
DOX in emulsions DOX-E2 (containing smaller drops) changes faster, due
to faster diffusional release, providing smaller values of the drug
concentration within and outside the drop, compared to emulsion DOX-E1
(with larger drops) at the same release time. This feature of the
emulsion-based implant as a local drug delivery system may be important
for planning individualised and tailored drug dosing, and also for
achieving the desired therapeutic efficacy and avoiding undesired
effects.
3.3 Cytotoxicity of the drug
encapsulated in multiple emulsions for GBM cell lines
The in vitro cytotoxicity of the multiple emulsions with and without
encapsulated DOX, and DOX in a solution (classical chemotherapy), were
tested in the presence of glioblastoma multiforme (GBM) cell lines: U87
MG and LN229, after different contact times (24h, 48h, 72h) with cells
(Fig. 5).
Firstly, the cytotoxicity of the emulsion without DOX (emulsions E1 and
E2) was verified. Reduction in the viability of cells after 72 h contact
with the emulsion was observed (for 87 MG max. to 55%, Fig. 5 a-d; for
LN229 max to 45% Fig. 5 e-h), but this effect disappeared within a
maximum of 7 days cell culturing after removal of the emulsion.
Secondly, the cytotoxic effect of
DOX introduced as an emulsion implant was compared with DOX in a
solution (classical therapy) for GBM cells of both lines, and two doses
of DOX (0.1 µM and 0.2 µM). At the lower dose of DOX (0.1 µM), a
reduction in cell viability within 24-72 h for both routes of the drug
administration was observed in the range: (i) U87 MG to 15-69% for DOX
in emulsions, and to 58-77% for DOX in solution (Fig. 5 a, c), (ii)
LN229 to 39-69% for DOX in emulsion, and to 54-67% for DOX in solution
(Fig. 5 e, g). Whereas at the higher dose of DOX (0.2 µM), a reduction
in cell viability was in the range: (i) U87 MG to 25-71% for DOX in
emulsions and to 56-70% for DOX in solution (Fig. 5 b, d), (ii) LN229
to 36-60% for DOX in emulsion and to 27-54% for DOX in solution (Fig.
5 f, h). For the tested doses of DOX, a greater cytotoxic effect of DOX
in emulsions (max. reduction by 85%) was observed compared to DOX in a
solution (max. reduction by 43%) for 0.1 µM DOX in emulsion DOX-E1, and
U87 MG cell line. These results revealed that DOX delivered as an
emulsion provides a greater cytotoxic effect, and therefore increases
the efficacy of the therapy compared to classical chemotherapy. Also,
these results confirmed the significance of the routes of drug
administration for the final effect of this therapy. Our previous
studies with a wider range of DOX concentration (0.01-1 µM) for U87 MG
cells also demonstrated greater effectiveness of DOX therapy based on a
drug in an emulsion compared with the classical drug
administration.26 In addition, DOX in emulsion-based
therapy was shown to be effective for the lowest doses of DOX in the
range studied, which were ineffective with the classical therapy (DOX
solution). Next, the cytotoxic effect between the emulsion form of DOX
(DOX-E1 and DOX-E2) was compared. In case of line U87 MG cells, cell
viability after DOX administration in emulsion were (i) for DOX-E1:
15-57% for the 0.1 µM DOX dose and 25-63% for the 0.2 µM DOX dose
(Fig. 5 a-b), and (ii) for DOX-E2: 50-69% for the 0.1 µM DOX dose and
46-71% for the 0.2 µM DOX dose (Fig. 5 c-d). For the LN229 cell line,
cell viability after DOX administration in emulsion achieved (i) for
DOX-E1: 36-46% for the 0.1 µM DOX dose and 36-49% for the 0.2 µM DOX
dose (Fig. 5 e-f), and (ii) for DOX-E2: 53-69% for the 0.1 µM DOX dose
and 48-60% for the 0.2 µM DOX dose (Fig. 5 g-h). Emulsion DOX-E1
demonstrated greater efficacy of reduction in viability of the tested
GBM cell lines compared to DOX-E2. The DOX-E1 and DOX-E2 systems
differed in the drop sizes and internal structures, as well as in the
composition of the external phases, and the volume fraction of the
dispersed phases. Differences between emulsions DOX-E1 and DOX-E2
affected the release rates of DOX, which contributed to the different
efficacy in reducing cancer cell viability. More cytotoxic and thus
effective was emulsion DOX-E1 with larger membrane phase drops with a
structure of many small internal droplets, from which DOX release is
slower than from emulsion DOX-E2. This proved that the drug release rate
from a delivery system has a direct impact on cancer cell viability and
thus on the final therapeutic
effect.
4. CONCLUSIONS
This paper presents results of a promising strategy for the efficient
local delivery of an anti-cancer drug (doxorubicin-DOX) to brain tumours
based on an injectable three-phase liquid implant in the form of W1/O/W2
multiple emulsion. The multiple emulsions have structures of droplets in
drops, therefore protecting healthy cells by encapsulating an aggressive
anti-cancer drug within their internal droplets surrounded by larger
drops of patient-friendly oil. The drug is gradually released by
diffusion at predetermined rates from the internal droplets of the
emulsions-based implant containing biopolymer (sodium
carboxymethylcellulose) in response to the acidic tumour
microenvironment, and is then transported to the tumour. The implant was
designed to sustainably deliver therapeutics for up to 100 hours or
longer, depending on the parameters of the emulsion: drop sizes,
structure, viscosity, and the encapsulated drug dose. The comprehensive
experimental study included drug release, in the presence and absence of
glioblastoma multiforme (GBM) cell lines (LN229, U87 MG), and cell
viability to evaluate the effectiveness of the proposed therapy. Also, a
diffusion–reaction model has been adapted to analyse and predict
doxorubicin release kinetics and drug elimination by glioblastoma cells
to evaluate the proposed therapy. The model equations include parameters
that take into account the structure of the emulsion (drop size and
packing volume fraction), drug absorption (elimination rate constant) by
cancer cells, and drug diffusion coefficients inside the emulsion drops
and in the tumour environment. Drug elimination was modelled assuming
first-order reaction kinetics. The numerical simulations of the drug
concentration distribution in time and space were performed for the
release process from emulsions DOX- E1 and DOX-E2 in the presence of
glioblastoma cells (U87 MG and LN229) according to model parameters
based on the experimental data. The CFD numerical simulation confirmed
that the drug release process is controlled by the parameters of the
emulsion structures. The obtained fractional release of the
chemotherapeutic drug showed a faster release rate, from the emulsion
DOX-E2, of smaller drops (higher interfacial area) compared to the
emulsion DOX-E1 (bigger drops - smaller interfacial area) in the
presence of the tested cancer cell lines. In addition, simulations of
the spatiotemporal drug concentration distribution outside the drops of
the emulsion implant confirmed a constant drug concentration, close to
the implant surface and in the bulk phase, essential for the
effectiveness of the therapy. Maintaining a constant concentration of
the drug in the cancer cells environment confirmed the advantage of
multiple emulsion as an implant delivering the drug. The validation of
this model by comparison with experimental data showed good agreement
under a variety of conditions (emulsions drop sizes and structures:
DOX-E1 and DOX-E2, DOX concentration and types of cancer cells). The
best effectiveness of the therapy was experimentally confirmed by a
significant reduction in the GBM cell viability by 85% for emulsion
DOX-E1, whereas for DOX in a solution (classical chemotherapy) by 43%
depending on the dose of the drug. This was also confirmed by the higher
drug elimination rate constants by cancer cells treated with a
chemotherapeutic in a multiple emulsion compared to classical
chemotherapy. Moreover, emulsion-based therapy, even with the lowest
dose of DOX responded with reduced cell viability, whereas for the
traditionally delivered drug this dose was ineffective. The obtained
results showed some considerable promise and proved that emulsion-based
implant anti-cancer drugs delivery might succeed in the unequal fight
against brain tumours. The adapted
diffusion-reaction model has several potential uses, especially in early
pre-clinical development in the planning of optimal oncotherapy,
including drug dose and release kinetics and treatment duration. This
model, supported by experimental data, also provides insights into the
relevant mechanisms and parameters, which quantitatively describe the
complex processes accomplished by drug release in a biological system.
ACKNOWLEDGMENT
Research was funded by (POB Biotechnology and Biomedical Engineering) of
Warsaw University of Technology within the Excellence Initiative:
Research University (IDUB) programme (project BIOTECHMED-2) and by the
National Science Centre – Poland (grant number: 2014/13/B/ST8/04274).
REFERENCES
- Lu CT, Zhao YZ, Wong HL, Cai J, Peng L, Tian XQ. Current approaches to
enhance CNS delivery of drugs across the brain barriers. Int J
Nanomedicine. 2014;9:2241-2257.
- Tan AC, Ashley DM, López GY, Malinzak M, Friedman HS, Khasraw M.
Management of Glioblastoma: State of the Art and Future Directions. CA
Cancer J Clin. 2020;70:299–312.
- Kasinathan N, Jagani HV, Alex AT, Volety SM, Rao JV. Strategies for
drug delivery to the central nervous system by systemic route. Drug
Deliv. 2015;22:243-257.
- Chakroun RW, Zhang P, Lin R, Schiapparelli P, Quinones‐Hinojosa A, Cui
H. Nanotherapeutic systems for local treatment of brain tumors. WIREs
Nanomed Nanobiotechnol. 2018;10(1):e1479.
- Haumann R, Videira JC, Kaspers GJL, van Vuurden DG, Hulleman E.
Overview of Current Drug Delivery Methods Across the Blood–Brain
Barrier for the Treatment of Primary Brain Tumors. CNS Drugs.
2020;34:1121–1131.
- Mueller E, Himbert S, Simpson MJ, Bleuel M, Rheinstadter MC, Hoare T.
Cationic, Anionic, and Amphoteric Dual pH/Temperature-Responsive
Degradable Microgels via Self-Assembly of Functionalized Oligomeric
Precursor Polymers. Macromolecules. 2021;54(1):351-363.
- Gerlee P. The model muddle: in search of tumor growth laws. Cancer
Res. 2013;73(8):2407-2411.
- Preziosi L. Cancer modelling and simulation (1st edition). Chapman &
Hall, CRC, 2003.
- Weiser JR, Saltzman WM. Controlled release for local delivery of
drugs: barriers and models. J Control Release. 2014;190:664-673.
- Siepmann J, Siepmann F. Modeling of diffusion controlled drug
delivery. J Control Release. 2012;161(2):351-362.
- Kim M, Gillies RJ, Rejniak KA. Current advances in mathematical
modeling of anti-cancer drug penetration into tumor tissues. FRONT
ONCOL. 2013;3:278.
- Montigny JD, Iosif A, Breitwieser L, Manca M, Bauer R, Vavourakis V.
An in silico hybrid continuum-/agent-based procedure to modelling
cancer development: interrogating the interplay amongst glioma
invasion, vascularity and necrosis. Methods. 2020;185(4):94-104.
- Chen J, Weihs D, Vermolen FJ. A Cellular Automata Model of Oncolytic
Virotherapy in Pancreatic Cancer. Bull Math Biol. 2020;82(103):1-25.
- Metzcar J, Wang Y, Heiland R, Macklin P. A Review of Cell-Based
Computational Modeling in Cancer Biology. JCO Clin. Cancer Inform.
2019;3(3):1-13.
- Trucu D, Lin P, Chaplain MA, Wang Y. A multiscale moving boundary
model arising in cancer invasion. Multiscale Model. Simul.
2013;11(1):309-335.
- Ramis-Conde I, Chaplain MAJ, Anderson ARA. Mathematical modelling of
cancer cell invasion of tissue. Math. Comput. Modelling.
2008;47:533–545.
- Dluska E, Hubacz R, Wronski S, Kamienski J, Dylag M, Wojtowicz R. The
influence of helical flow on water fuel emulsion preparation. Chem.
Eng. Commun. 2007;194(10): 1271–1286.
- Dluska E, Markowska-Radomska A, Metera A, Kosicki K. Hierarchically
structured emulsions for brain therapy. Colloid Surf. A Physicochem.
Eng. Asp. 2019;575:205-211.
- Eugenia Carlotti M, Gallarate M, Sapino S, Ugazio E, Morel S. W/O/W
Multiple Emulsions for Dermatological and Cosmetic Use, Obtained with
Ethylene Oxide Free Emulsifiers. J Dispers Sci Technol.
2005;26(2):183-192.
- Loya-Castro MF, Sánchez-Mejía M, Sánchez-Ramírez DR, Domínguez-Ríos R,
Escareño N, Oceguera-Basurto PE, Figueroa-Ochoa ÉB, Quintero A, del
Toro-Arreola A, Topete A, Daneri-Navarro A. Preparation of PLGA/Rose
Bengal colloidal particles by double emulsion and layer-by-layer for
breast cancer treatment. J. Colloid Interface Sci. 2018;518:122-129.
- Dluska E, Metera A, Markowska-Radomska A, Tudek B. Effective
cryopreservation and recovery of living cells encapsulated in multiple
emulsions. Biopreserv Biobank. 2019;17(5):468-476.
- Mutaliyeva B, Grigoriev D, Madybekova G, Sharipova A, Aidarova S,
Saparbekova A, Millere R. Microencapsulation of insulin and its
release using w/o/w double emulsion method. Colloids Surf. A
Physicochem. Eng. Asp. 2017;521:147–152.
- Bozkir A, Hayta G. Preparation and evaluation of multiple emulsions
water-in-oil-in-water (w/o/w) as delivery system for influenza virus
antigens. J. Drug. Target. 2004;12:157-164.
- Soriano-Ruiz JL, Suner-Carbo J, Calpena-Capmany AC, Bozal-de Febrer N,
Halbaut-Bellowa L, Boix-Montanes A, Souto EB, Clares-Naveros B.
Clotrimazole multiple W/O/W emulsion as anticandidal agent:
Characterization and evaluation on skin and mucosae. Colloids Surf. B
Biointerfaces. 2018;175:166-174.
- McClements DJ, Decker EA, Weiss J. Emulsion-based delivery systems for
lipophilic bioactive components. J Food Sci. 2007;72(8):109-124.
- Dluska E, Markowska-Radomska A, Metera A, Tudek B, Kosicki K. Multiple
emulsions as effective platforms for controlled anti-cancer drug
delivery. Nanomedicine. 2017;12(18):2183-2197.
- Dluska E, Cui Z, Markowska-Radomska A, Metera A, Kosicki K.
Cryoprotection and banking of living cells in a 3D multiple
emulsion-based carrier, Biotechnology Journal. 2017;12(8):1–7.
- Dluska E, Markowska-Radomska A. Regimes of multiple emulsions of
W1/O/W2 and O1/W/O2 type in the continuous Couette-Taylor flow
contactor. Chem. Eng. Technol. 2010;33(1):113–120.
- Markowska-Radomska A, Dluska E. An evaluation of a mass transfer rate
at the boundary of different release mechanisms in complex liquid
dispersion. Chem Eng Process. Process Intensification. 2016;101:56-71.
- Markowska-Radomska A, Dluska E. The Multiple Emulsion Entrapping
Active Agent Produced via One-Step Preparation Method in the
Liquid-Liquid Helical Flow for Drug Release Study and Modeling. Progr
Colloid Polymer Sci. 2012;139:29-34.
- Khaled B, Abdelbaki B.
Rheological and electrokinetic properties of
carboxymethylcellulose-water dispersions in the presence of salts.
Int. J. Phys. Sci. 2012;7(11):1790-1798.
- Friedman D, Schwartz J, Amselem
S. Bioadhesive emulsion preparations for enhance drug delivery. US
Patent Number: USOO5744155A, 1998.
- Weiser JR, Saltzman WM. Controlled release for local delivery of
drugs: barriers and models. J Control Release. 2014;190:664-673.
- Li J, Carr PW. Accuracy of empirical correlations for estimating
diffusion coefficients in aqueous organic mixtures. Anal. Chem.
1997;69:2530-2536.
- Bartzatt R. Identification of doxorubicin and an imine derivative from
liquid and solid samples utilizing liquid chromatography. J Liq
Chromatogr Relat Technol. 2006;29:2303-2312.
- Yan N. A mass transfer model for type-II-facilitated transport in
liquid membranes. Chem. Eng. Sci. 1993;48:3835-3843.
- Lian G, Malone ME, Homan JE, Norton IT. A mathematical model of
volatile release in the mouth from the dispersion of gelled emulsion
particles. J. Control. Release. 2004;98:139–155.
- Happel J. Viscosity of suspensions of uniform spheres. J. Appl. Phys.
1957;28:1288-1292.