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Targeted drug delivery of magnetic microbubble for abdominal aortic aneurysm: an in silico study

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Abstract

Targeted drug delivery (TDD) to abdominal aortic aneurysm (AAA) using a controlled and efficient approach has recently been a significant challenge. In this study, by using magnetic microbubbles (MMBs) under a magnetic field, we investigated the MMBs performance in TDD to AAA based on the amount of surface density of MMBs (SDMM) adhered to the AAA lumen. The results showed that among the types of MMBs studied in the presence of the magnetic field, micromarkers are the best type of microbubble with a −\(50\%\) increase in SDMM adhered to the critical area of AAA. The results show that applying a magnetic field causes the amount of SDMM adhered to the whole area of AAA to increase −\(1.54\) times compared to the condition in which the magnetic field is absent. This optimal and maximum value occurs for Definity MMBs with − 3.3 μm diameter. Applying a magnetic field also increases the adhesion surface density by − \(1.27\), − \(1.14\), and −\(1.11\) times for the Micromarker, Optison, and Sonovue microbubbles, respectively, relative to the condition in which the magnetic field is absent. It was shown that using MBBs under magnetic field has the best performance in delivery to AAA for patients with negative inlet blood flow. Also, we have exposed that in an efficient TDD to AAA using MMBs, decreasing the density of MMBs increases drug delivery efficiency and performance. When density is − \(3500 {\text{Kg}}.{\text{m}}^{ - 3}\), there is the highest difference (about − 75%) between the SDMM adhered to AAA in the presence of a magnetic field and in the absence of a magnetic field.

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Data Availability

All data, models, or code generated or used during the study are available from the corresponding author upon reasonable request.

Abbreviations

AAA:

Abdominal aortic aneurysm

ALE:

Arbitrary Lagrange–Eulerian

AMG:

Algebraic multigrid

BDF:

Backward differentiation formula

CT:

Computerized tomography

DICOM:

Digital imaging and communications in medicine

FSI:

Fluid–structure interaction

GNF:

Generalized Newtonian fluid

GMRES:

Generalized minimal residual

MMBs:

Magnetic microbubbles

MUMPS:

Multifrontal massively parallel sparse

NPs:

Nanoparticles

SDMM:

Surface density of magnetic microbubbles

TDD:

Targeted drug delivery

\({\varvec{A}}\) :

Magnetic vector potential (T.m)

\(a\) :

Power law index

\({\varvec{B}}\) :

Magnetic flux density (T)

\({{\varvec{B}}}_{\mathrm{rem}}\) :

Remanent magnetic flux (T)

\({C}_{10}\) :

Material constant (Pa)

\({C}_{20}\) :

Material constant (Pa)

\(d\) :

Parameter of non-residency of material

\({d}_{p}\) :

Particle diameter (m)

\({\varvec{E}}\) :

Electrical field (V.m−1)

\({\varvec{F}}\) :

Volumetric force (N)

\({F}^{s}\) :

Dislodge force parameter

\({{\varvec{F}}}_{B}\) :

Brownian force (N)

\({{\varvec{F}}}_{D}\) :

Drag force (N)

\({{\varvec{F}}}_{G}\) :

Gravitational force (N)

\({{\varvec{F}}}_{L}\) :

Lift force (N)

\({{\varvec{F}}}_{\mathrm{mp}}\) :

Magnetophoretic force (N)

\({\varvec{H}}\) :

Magnetic field intensity (A.m−1)

\({h}_{0}\) :

Maximum distance of particle from the wall (m)

\({I}_{1}\) :

First strain variable (Pa)

\({\varvec{J}}\) :

Current density (A.m−2)

\({{\varvec{J}}}_{\mathrm{e}}\) :

External current density (A.m−2)

\({\varvec{J}}_{{{\text{el}}}}\) :

Elastic volume ratio (A.m−2)

\({K}_{a}^{0}\) :

Continuity constant

\({K}_{B}\) :

Boltzmann constant (m2.kg.s−2.k−1)

\(l\) :

Separation distance (m)

\({\varvec{M}}\) :

Magnetization vector (A.m−1)

\({m}_{l}\) :

Surface density of ligand (m−2)

\({m}_{m}\) :

Particle mass (Kg)

\({{\varvec{m}}}_{\mathrm{eff}}\) :

Effective dipole moment (A.m2)

\({m}_{r}\) :

Surface density of receptor (m−2)

\(p\) :

Static pressure (Pa.s)

\({P}_{a}\) :

Adhesion probability

\({r}_{0}\) :

Radius of circular section (m)

\(T\) :

Temperature (K)

\({T}^{s}\) :

Dislodge torque parameter

\({\varvec{u}}\) :

Fluid velocity vector (m.s−1)

\({\varvec{v}}\) :

Particle velocity vector (m.s−1)

\(V\) :

Volume (m3)

\({{\varvec{W}}}_{\mathrm{iso}}\) :

Strain energy density (MPa)

\(\beta \) :

Reactive compliance (Å)

\(\gamma \) :

Aspect ratio

\(\dot{\gamma }\) :

Local shear rate (s−1)

\({\delta }_{\mathrm{eq}}\) :

Equilibrium bond length (m)

\({\eta }_{0}\) :

Zero-shear viscosity (Pa.s)

\({\eta }_{\infty }\) :

Infinite-shear viscosity (Pa.s)

\({\eta }_{\mathrm{app}}S\) :

Wall shear stress (MPa)

\(\lambda \) :

Time constant (s)

\({\mu }_{0}\) :

Magnetic permeability of vacuum (N.A−2)

\({\mu }_{p}\) :

Magnetic permeability of particle (N.A−2)

\({\mu }_{r}\) :

Magnetic permeability (N.A−2)

\(\rho \) :

Density (Kg.m−3)

\(\sigma \) :

Electrical conductivity (Ω.m)

\({\varvec{\tau}}\) :

Stress tensor of the fluid (MPa)

\(\chi \) :

Magnetic susceptibility

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Acknowledgements

The authors declare that they have no known competing for financial interests or personal relationships that could have influenced the work reported in this paper.

Funding

The authors have no relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript.

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Authors and Affiliations

  1. Nano-Bioengineering Lab, School of Mechanical Engineering, Sharif University of Technology , Azadi Ave., Tehran, Iran

    Amir Shamloo, Sina Ebrahimi, Ghazal Ghorbani & Mojgan Alishiri

  2. Stem Cell and Regenerative Medicine Center, Sharif University of Technology, Tehran, Iran

    Amir Shamloo, Sina Ebrahimi, Ghazal Ghorbani & Mojgan Alishiri

Authors
  1. Amir Shamloo
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  2. Sina Ebrahimi
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  3. Ghazal Ghorbani
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  4. Mojgan Alishiri
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Contributions

Amir Shamloo initiated the idea, designed the simulations, analyzed the data, and wrote the paper; Sina Ebrahimi designed the simulations, analyzed the data, and wrote the paper; Ghazal Ghorbani ran the simulations and wrote the paper. Mojgan Alishiri, ran the simulations and revised the paper.

Corresponding author

Correspondence to Amir Shamloo.

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Shamloo, A., Ebrahimi, S., Ghorbani, G. et al. Targeted drug delivery of magnetic microbubble for abdominal aortic aneurysm: an in silico study. Biomech Model Mechanobiol 21, 735–753 (2022). https://doi.org/10.1007/s10237-022-01559-4

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  • DOI: https://doi.org/10.1007/s10237-022-01559-4

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