Shuang J. Zhu Mechanical Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia e-mail:
[email protected]
Eric K. W. Poon Mechanical Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia
Andrew S. H. Ooi Mechanical Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia
Stephen Moore IBM Research Collaboratory, Victoria Life Sciences Computation Initiative, The University of Melbourne, Parkville, Victoria 3010, Australia
Enhanced Targeted Drug Delivery Through Controlled Release in a Three-Dimensional Vascular Tree “Controlled particle release and targeting” is a technique using particle release score map (PRSM) and transient particle release score map (TPRSM) via backtracking to determine optimal drug injection locations for achieving an enhanced target efficiency (TE). This paper investigates the possibility of targeting desired locations through an idealized but complex three-dimensional (3D) vascular tree geometry under realistic hemodynamic conditions by imposing a Poiseuille velocity profile and a Womersley velocity profile derived from cine phase contrast magnetic resonance imaging (MRI) data for steady and pulsatile simulations, respectively. The shear thinning non-Newtonian behavior of blood was accounted for by the Carreau–Yasuda model. One-way coupled Eulerian–Lagrangian particle tracking method was used to record individual drug particle trajectories. Particle size and density showed negligible influence on the particle fates. With the proposed optimal release scoring algorithm, multiple optimal release locations were determined under steady flow conditions, whereas there was one unique optimal release location under pulsatile flow conditions. The initial in silico results appear promising, showing on average 66% TE in the pulsatile simulations, warranting further studies to improve the mathematical model and experimental validation. [DOI: 10.1115/1.4028965] Keywords: computational fluid dynamics, blood flow, drug targeting, nanoparticles, controlled release
1
Introduction
Targeted drug delivery is a technique of delivering drugs to specific cells, tissues, or organs of the patient’s body exclusively. Targeted medicine should in theory efficaciously attack pathogens yet remain harmless in healthy tissues [1]. There are many different approaches to targeted drug delivery, which generally can be divided into three categories: passive targeting, active targeting, and physical targeting. Passive targeting is based on drug accumulation in the areas around the tumors with leaky vasculature, which commonly referred to as the enhanced permeation and retention effect [2]. It was found that a blood vessel wall might become leaky under certain circumstances [3,4] and drugs can be delivered into the tumor affected area. The drug carriers used should demonstrate the ability to circulate for a long period of time in the blood to provide a sufficient level of target accumulation [5]. Active targeting directs drugs to the intended area through the use of antigen-specific antibodies or cell-specific ligands that interact with specific surface molecules of the desired target cell. For example, antibodies to the specific antigens expressed by tumors can be attached to the drug as ligands so that the drug will be delivered and localized in the tumor through the antigen–antibody reaction [6]. Not only antibodies but also integrins, transferrins, vitamins, and hormones may be used as ligands, which makes active targeting more sophisticated and more attractive. Therefore, substantial research efforts have been put in this area [7–10]. Physical targeting refers to a strategy that releases a drug when exposed to an abnormal variation in microenvironment in the
Manuscript received September 4, 2013; final manuscript received October 29, 2014; published online January 29, 2015. Assoc. Editor: Francis Loth.
Journal of Biomechanical Engineering
pathological area such as pH value [11] or temperature [12]. Magnetic targeting also falls in this category, where magnetic particles are injected into the bloodstream and draw toward a target location via an external magnetic field to subsequently release the therapeutic drug that they contain. There exists a rich variety of compositions and methods of synthesis [13–19], allowing for the composition, size, morphology, and surface chemistry to be tailored for a particular application. Kleinstreuer and Zhang [20] introduced the concept of “controlled particle release and targeting” in designing suitable inhalers for optimal drug aerosol delivery in the human respiratory system. The specific release positions of aerosols to be delivered to the tumor are predetermined via “backtracking” and then release-controlled aerosol streams are generated so that most aerosols deposit in desired lung target regions [21]. The study was carried out numerically in a four-generation symmetrically bifurcating rigid lung airway model with hemispherical tumors. It was shown that the drug aerosol deposition fractions increase dramatically at desired target sites but decrease at the healthy airway epithelium. Kleinstreuer et al. [22] extended study by combining an oral airway model with the lung airway model. Recently, numerical investigation has been extended to study the transport and targeting of yttrium-90 microspheres through optimal catheter positioning and controlled release toward liver tumor regions in a complex geometric tree model [23–27]. Experimental work by Richards et al. [28] validated the simulation methodology for achieving targeted microsphere distributions in a known geometry under steady flow conditions. Two possible approaches to in silico work investigating targeted drug delivery are to either treat the suspended drug particles in the blood as a second homogeneous fluid phase intermingled with the primary phase and include additional terms in the standard Navier–Stokes equations governing the motion of a fluid [29–32], or particles are treated as dispersed phase and tracked in
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the Lagrangian mode through the fluid medium [20,23,29,33]. As the human vascular system exhibits complicated and tortuous morphology, the goal of the present study is to investigate the possibility of drug targeting through a complex vascular tree under realistic hemodynamic conditions. A suitable idealized vascular tree geometry will subsequently be presented as well as an algorithm to determine the optimal release locations.
2
Methodology
2.1 Description of the Idealized Vascular Tree. The key design features deemed relevant for testing the concept of “controlled particle release and targeting” were that the idealized 3D vascular tree geometry includes a number of out-of-plane bifurcations and branches that span a range of diameters and lengths (Fig. 1). The initial diameter of the root branch was chosen to be 2.5 mm, approximately the size of a major cerebral artery [34,35]. The length to diameter ratio of each branch in the tree was chosen to be 20 as human coronary arteries show a ratio between 10 and 35 [36]. For each bifurcation, the ratio between the daughter and parent diameters was chosen to be 0.8 [37–40]. The bifurcation angle between two daughter segments was chosen to be 30 deg [41,42] and the plane of each bifurcation was designed to be rotated 90 deg from the plane of the bifurcation immediately upstream. These parameters create a tree with similar level of complexity as the human vascular system. A total of five bifurcation levels were included, resulting in a total of 32 terminal branches. The geometry was created with the commercial computer-aided design software SOLIDWORKS (DS SolidWorks Corp., Concord, MA) using a procedure described in Ref. [43]. The computational mesh was created with the software ANSYS ICEM CFD (ANSYS, Inc., Canonsburg, PA) comprising approximately 10 106 tetrahedral cells, which was found to give a mesh independent solution. 2.2 Fluid Modeling. The blood flow within the vasculature was simulated using the incompressible Navier–Stokes equations. These equations were solved using an open source finite-volume code OpenFOAM with the Gauss linear corrected, Gauss self-filtered central differencing, and Crank–Nicolson discretization schemes for the convective, diffusive, and unsteady terms,
Fig. 2 The mean flowrate and flowrate waveforms used in the steady and pulsatile simulations, respectively. Illustrated are 11 key times within the cardiac cycle where planar particles were released.
respectively. Convergence was considered as attained when the velocity and pressure residuals fell below 105 and 106, respectively. The OPENFOAM solver with the discretization schemes mentioned was tested against the Poiseuille solution for a fully developed pipe flow. The Carreau–Yasuda model was implemented as a custom shared library, which accounts for the aggregation and deformation of red blood cells as a function of shear rate. The zero shear viscosity and the infinite shear viscosity are taken as 0.22 Pa s and 0.0022 Pa s, respectively, [44,45]. For steady simulations, a Poiseuille velocity profile was imposed at inlet of the tree with a flowrate of 100 mlmin1 [46]. For pulsatile simulations, a Womersley velocity profile derived from cine phase contrast MRI data [43] was imposed (Fig. 2) and implemented as a custom shared library. At each terminal branch outlet, a zero velocity gradient was imposed along with a prescribed fixed pressure of 95 mmHg. No-slip boundary conditions were applied on arterial walls.
Fig. 1 The idealized 3D vascular tree geometry used in the present study showing the definition of the anatomical positions, the origin of the Cartesian coordinate system and key design parameters in the root branch of the tree. The naming convention for the 32 outlet branches is shown in the inferior view for clarity.
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2.3 Description of the Drug Particles. Therapeutic nanoparticles play an important role in the development of targeted drug delivery due to their unique physicochemical properties. Particle size has a significant impact on the circulation time, biodistribution, and drug accumulation. Smaller particles (50–300 nm) have slower removal from the circulation [47]. Fang et al. [48] observed that nanoparticles (
