treatment of peritoneal cancer
Analysis of magnetic implants for the improved
Academic year 2019-2020
Master of Science in Engineering Physics
Master's dissertation submitted in order to obtain the academic degree of Counsellor: Rikkert Van Durme
Supervisors: Prof. dr. ir. Luc Dupré, Dr. ir. Annelies Coene Student number: 01409279
treatment of peritoneal cancer
Analysis of magnetic implants for the improved
Academic year 2019-2020
Master of Science in Engineering Physics
Master's dissertation submitted in order to obtain the academic degree of Counsellor: Rikkert Van Durme
Supervisors: Prof. dr. ir. Luc Dupré, Dr. ir. Annelies Coene Student number: 01409279
A
UTHOR
’
S PERMISSION
"The author gives permission to make this master dissertation available for consultation and to copy parts of this master dissertation for personal use. In all cases of other use, the copyright terms have to be respected, in particular with regard to the obligation to state explicitly the source when quoting results from this master dissertation."
"De auteur geeft de toelating deze masterproef voor consultatie beschikbaar te stellen en delen van de masterproef te kopiëren voor persoonlijk gebruik. Elk ander gebruik valt onder de bepalingen van het auteursrecht, in het bijzonder met betrekking tot de verplichting de bron uitdrukkelijk te vermelden bij het aanhalen van resultaten uit deze masterproef."
Fien Vanden Hautte, June 2020
P
REFACE
First and foremost, I would like to thank my promoters Prof. Dupré and Dr. Annelies Coene for making this thesis possible. It was a pleasure to be introduced into the world of biomedical engineering, in particular magnetic nanoparticles. A special thanks to An-nelies for making me feel at ease from the very first meeting and creating a constructive and enjoyable environment to discuss and create this thesis. I would also like to thank my counsellor Rikkert, thank you for many fruitful and interesting discussions, and for sharing your experience.
I want to thank my fellow students and friends for all their help throughout my stud-ies, including this thesis, and for all of the fun we’ve had.
I am extremely grateful to Wouter, for supporting me from the thesis choice to the very end, and suggesting some interesting ideas for this thesis. Finally, I would like to thank my family. My parents for making my studies possible and guiding me through it with love and care. And my siblings, for believing in me and for helping me to place things into perspective.
Fien Vanden Hautte, June 2020
Department of Electrical Energy, Metals, Mechanical Constructions and Systems Faculty of Engineering and Architecture
Analysis of magnetic implants for the improved treatment
of peritoneal cancer
by
Fien Vanden Hautte
Supervisors: Prof. dr. ir. Luc Dupré, Dr. ir. Annelies Coene Counsellor: Rikkert Van Durme
Master’s dissertation submitted in order to obtain the academic degree of MASTER OFSCIENCE INENGINEERINGPHYSICS
Academic year 2019-2020
Abstract - Magnetic targeting of drug-carrying magnetic nanoparticles (MNPs) has been proposed as a possible treatment for peritoneal surface malignancy. Targeting is achieved by applying magnetic field gradients, causing magnetic forces to be exerted on the MNPs. Unfortunately, using a single magnetic field source yields forces that are inherently weak. Using a magnetised implant that generates a local field with large gradient at the target region, in combination with a homogeneous external field to magnetise the carriers, as well as this implant, could significantly increase the targeting forces. A mathematical model was developed to study the delivery of drug-carrying MNPs to such a magnetic implant in the peritoneum. Using this model, a sensitivity analysis was performed to examine the effect of MNP size and magnetisation curve, external magnetic field strength and direction, implant geometry and finally, the in-traperitoneal fluid velocity.
Keywords - Peritoneal cancer treatment, Magnetic nanoparticles, Magnetic force, Targeted delivery, Magnetic implants, Modelling
Analysis of magnetic implants for the improved
treatment of peritoneal cancer
Fien Vanden Hautte
Supervisor(s): Rikkert Van Durme, Annelies Coene, Luc Dupr´e
Abstract— Magnetic targeting of drug-carrying magnetic nanoparticles (MNPs) has been proposed as a possible treatment for peritoneal surface malignancy. Targeting is achieved by applying magnetic field gradients, causing magnetic forces to be exerted on the MNPs. Unfortunately, using a single magnetic field source yields forces that are inherently weak. Using a magnetised implant that generates a local field with large gradient at the target region, in combination with a homogeneous external field to mag-netise the carriers, as well as this implant, could significantly increase the targeting forces. A mathematical model was developed to study the deliv-ery of drug-carrying MNPs to such a magnetic implant in the peritoneum. Using this model, a sensitivity analysis was performed to examine the effect of MNP size and magnetisation curve, external magnetic field strength and direction, implant geometry and finally, the intraperitoneal fluid velocity.
Keywords— Peritoneal cancer treatment, Magnetic nanoparticles, Mag-netic force, Targeted delivery, MagMag-netic implants, Modelling
I. INTRODUCTION
Peritoneal cancer, commonly originating from primary can-cers of organs embedded in the peritoneal cavity, is difficult to treat with conventional systemic chemotherapy due to the large surface and poor vascularisation of the peritoneum [1]. Intraperitoneal (IP) chemotherapy has shown significant advan-tages over intravenous drug administration since it facilitates di-rect drug delivery while mitigating adverse effects [2]. Hyper-thermic intraperitoneal chemotherapy (HIPEC) is an example of a local chemotherapy which combines a cytoreductive surgery with an IP perfusion of a heated chemotherapeutic solution. Yet, because of the poor drug penetration, HIPEC (and similar proce-dures) can only be applied if remaining tumours are sufficiently small. And even still, recurrence rates remain high [3]. Recently, nanoparticles (NPs) have been utilised as drug car-riers in IP chemotherapy with the hope of augmenting the IP residence time, and therefore the drug penetration [4]. IP use of nanoparticles has introduced a so called ”size dilemma”: the larger the NPs size, the larger the IP residence time, since larger particles cannot leave the peritoneal cavity through the lymphatic system. However, drug penetrating efficiency re-duces with increasing size [4]. One possible approach to resolve this dilemma is to exploit drug-carrying magnetic nanoparticles (MNPs). Magnetised MNPs particles are subjected to magnetic forces when a magnetic field gradient is present. These forces can be exploited to target them to the region of interest, an approach referred to as Magnetic Drug Targeting (MDT) [5]. However, a severe drawback of MDT is the inherent weakness of the magnetic forces: these forces depend on both the pres-ence of a far-reaching magnetic field to magnetise the carriers, and a strong magnetic field gradient. But, a magnetic field with strong gradient is by definition rapidly decaying and therefore not able to magnetise the bulk of the carriers. To resolve this problem, this research proposes to deploy a magnetised implant
that generates a local field (Bm) with large gradient at the
tar-get region, in combination with a homogeneous external field (B0) to magnetise the carriers as well as this implant. This
ap-proach is referred to as Implant-Assisted Magnetic Drug Target-ing (IA-MDT), and the specific IP application is schematically represented in Fig. 1. The magnetic implant is proposed to con-sist of a gridded structure, referred to as the magnetic mesh. This mesh may be placed during the cytoreduction, additionally serv-ing as a form of abdominal wall reconstruction. Thereafter, the MNPs could be inserted in the peritoneal cavity, solved in the hyperthermic perfusion fluid, while a uniform magnetic field is applied through the patient. This work aims to develop a math-ematical model to analyse the working principles of this cap-turing technique. This model will be described in section II. It includes a model for the MNP motion dynamics, the general simulation set-up, a model for the field created by the magne-tised mesh, and the introduction of a performance measure. Af-terwards, some generic results for a set of representative param-eter values will be discussed in section III-A. Additionally, this work aims to perform a sensitivity analysis in order to reveal the influence of some key parameters, such as MNP size and magnetisation curve, external magnetic field strength and direc-tion, implant geometry and IP fluid velocity. This analysis is discussed in section III-B.
Fig. 1: Intraperitoneal implant-assisted magnetic drug targeting set-up.
II. IA-MDTMATHEMATICAL MODEL
In this section we will describe the model used to analyse implant-assisted MNP capture. The four main components of this model are: the MNPs and their motion dynamics, the
sim--1 -0.5 0 0.5 1 B [T] -10 -5 0 5 10 M [kA/m] -300 -200 -100 0 100 200 300 M [kA/m] MNP1 MNP2 MNP3
Fig. 2: Magnetisation curves for three different kinds of MNPs. MNP1 and MNP3 based on
Ref. [6], MNP2 on Ref. [7] Fig. 3: Reference system with magnetic meshand external field set up.
-1 -0.5 0 0.5 1 B [T] -80 -60 -40 -20 0 20 40 60 80 M [kA/m] -1500 -1000 -500 0 500 1000 1500 M [kA/m] SS 304 SS 304L SS 340
Fig. 4: Magnetisation curves for three SS materials. SS 340 and SS304L based on Ref. [6] and SS 340 on Ref. [6]
ulation set-up of the magnetic mesh, the field generated by the magnetised implant, and the capture efficiency as a performance measure.
A. Modelling MNPs and their motion dynamics In our model, we will assume the MNPs to exhibit superpara-magnetic behaviour, meaning their magnetisationMpstrongly
increases until saturation is achieved when an external mag-netic field is applied, but they are non-magmag-netic in absence of an applied field [8]. In this work we analysed three magneti-sation curves based on literature, as shown in Fig. 2. We will assumeMpto be constant throughout the volume Vpof a
parti-cle [9]. Therefore the magnetic moment of one partiparti-cle is given bymp = RRRV
pMp(r)dV = VpMp. When placed in a mag-netic fieldB, this magnetic moment is subjected to a torque τp=mp× B, which will align the particle with this field,
al-lowing us to write
mp=|mp|B
|B|= m(|B|) B
|B|, (1)
Where |B| is the Euclidean norm of the magnetic field vector. The force exerted on the MNPs due to the magnetic field they are embedded in, will be referred to as the magnetic force, denoted asFm, and is defined by [10]
Fm= (mp· ∇)B . (2)
Combining this with Eq. (1) and some basic vector calculus we obtain Fm= µ0m(|B|) |B| ∇ 1 2B · H . (3)
This last equation relates the magnetic force to the differen-tial of the magnetostatic field energy density1
2B · H,
demon-strating that this force acts in the direction of steepest ascent of this magnetic energy density. This implies that when a particle is subjected to a homogeneous field, no forces are exerted on it, but by creating a magnetic energy gradient the magnetic force can be used to manipulate MNPs to a certain target region. Be-sides the magnetic force, the hydrodynamic drag force, or “fluid
force”, denoted asFf, should be taken into account as well [11].
Ffwill be calculated using Stokes’ approximation for a
spheri-cal particle in laminar flow [12]
Ff= 6πrpηf(vf− vp) , (4)
where rpandvpare the radius and velocity of a MNP,vfis
the fluid velocity, and ηfis the viscosity of the fluid. This fluid
was modelled to possess a uniform velocity profile parallel to the magnetic mesh, along the positive y-direction.
While many other forces affect the MNP motion dynamics, such as the gravitational forces, floatage because of buoyancy and the interactions between nearby particles, these will be ne-glected in our model due to their small magnitude compared to the dominant forces listed above [12]. Using Newton’s equation of motion we obtain a second order differential equation for the position of a particle as a function of time
mpdr
dt2=Fm(r) + Ff(r) . (5)
Because the mass mpof the MNPs is so small, the inertia term
is neglected [12], leading to an equation that yields the particle velocity as a function of the position dependent magnetic field
vp= 1 6πrpηf m(|B|) 2|B| ∇|B| 2+v f. (6)
We will discretise our simulation domain, using Eq. (6) to cal-culate the velocity at the centre of every voxel, and assume this centre value to apply over the entire voxel. Subsequently, we can investigate the discretised particle concentration distribution as a function of time by applying an Euler integration scheme.
B. The magnetic mesh set-up
We will consider a limited simulation domain of 1.5 × 1.5 × 0.5 cm, and a magnetic mesh that fits inside this domain, as shown in Fig. 3. The mesh will be positioned in the XY-plane and is constructed out of a biocompatible stainless steel (SS), with possible magnetisation curves as shown in Fig. 4. The ex-ternal magnetic field is assumed to be perfectly uniform and per-pendicular to this mesh. Note that the chosen magnetic mesh
size is not realistic for an IP application, so edge effects will be over-represented. Yet, it allows qualitative conclusions that are independent of magnetic mesh size and edge effects, and are therefore expandable to realistic magnetic mesh sizes.
C. Modelling the magnetised mesh field The method used to calculate the field created by the magne-tised mesh,Bm, will be referred to as the dipole superposition
method. In this method we divide the magnetised volume V into small volumes Vi. In our case, the magnetic mesh volume will
be divided into rods with a length lrodsimilar to the diameter of
the threads that constitute the magnetic mesh. With each rod i, a magnetic momentmi = ViM positioned at the centre of this
rod,rc,i, will be associated. As an additional simplification, we
assume the SS magnetisation not to depend onBm, in order to
avoid an implicit equation:M(B(r)) = M(Bm(r) + B0(r)) ≈
M(B0(r)) = M(B0). Since the magnetic flux density generated
by one magnetic dipole positioned at the origin is given by [13] Bm(r) = µ0 4π 3r(m · r) r5 − m r3 , (7)
the magnetic flux density from one rod is given by Bi(r) = µ0 4π 3(r − rc,i)(M · (r − rc,i)) |r − rc,i|5 − M |r − rc,i|3 Vi. (8) Finally, we obtain the total magnetic field as
B(r) = B0(r) + Bm=B0(r) + N
X
i=1
Bi(r), (9)
where N is the amount of volumes Vi.
D. Performance measure
To evaluate the success of the IP IA-MDT we introduce the capture efficiency (CE); the fraction of particles initially present in the simulation domain that got “captured” in the plane of the magnetic mesh. “Captured” here simply means they reached the XY-plane, we will not take into account any of the underlying bi-ological phenomena causing specific adhesion and detachment rates. Note that our definition of the CE is time-dependent since our simulation allows an evaluation of the amount of captured particles at each point in time. The capture efficiency is a widely used parameter in literature, both for simulations [12, 14, 15] and experiments [6, 16, 17]. The initial condition of the particle distribution has a large influence on the capture efficiency. Tak-ing into account that we will generally assume the fluid to move with the positive y-direction, we will assume a sheet of particles with a concentration of 3 × 1014m−3“entering” from the most
negative y position [18]. This is visualised in Fig. 5a. The fluid velocity was chosen to equal 1 mm s−1since this velocity is of
the same order as the downward particle velocities, such that fluid drag and magnetic attraction will be competitive.
(a) t = 0 s.
(b) t = 0.5 s.
(c) t = 5 s.
Fig. 5: Particle number density in m−3after different simulation
times.
III. RESULTS
A. Generic case
We start by examining some generic results for a fixed set of representative parameters, presented in Tab. I. The two-dimensional slice (for x = −35 mm) of the magnetostatic en-ergy density shown in Fig. 6 indicates that generally there is an increasing energy density towards the magnetic mesh, which means the magnetic force will guide MNPs towards the mesh, at least particles located above it. An overview of particle trajec-tories in a stationary fluid, shown in Fig. 7, confirms this result. However, from both figures it is clear that particles outside, or at the edges of the mesh are in first instance repelled. Also, parti-cles that are located between two threads of stainless steel in the vicinity of the mesh are repelled. Nevertheless, while the repul-sion causes a detour, which may cause the particles to get “lost” in reality, due to physical obstacles in the peritoneal cavity that block their detour, in theory all particles will be captured over time in our simulation domain. In Fig. 8 the z-component of the velocity gives additional info about how fast particles move towards, or away from, the magnetic mesh. The particle tra-jectories for a fluid velocity ofvf= 1 mm s−1eyare shown in
Fig. 9. For a non-stationary case it is no longer true that all particles will be captured eventually. On the other hand, some particles may be captured sooner because of the moving fluid. Fig. 5 shows frames of the particle number density distribution at different points in time.
TABLE I: Representative parameters used to obtain general sim-ulation results.
Parameter Symbol Value
MNP
MNP radius rp 1µm
MNP density ρp 5× 103kg m−3
MNP Msat 112 kA m−1
B0 Magnitude external fieldDirection external field |BeB00| 0.5 Tez
Simulation domain 1.5× 1.5 × 0.5 cm
Voxel dimension hx× hy× hz 0.1× 0.1 × 0.1 mm
Simulation time step dt 0.5 s
Mag.
Mesh
Magnetic Mesh Surface 1× 1 cm
Rod length lrod 200µm
Rod radius rrod 100µm
Period of magnetic mesh 400µm
Material magnetic mesh SS 340
Fluid
Fluid viscosity ηf 0.6913× 10−3Pa s
Fluid velocity vf 0 or 1 mm s−1ey
Fig. 6: Magnetic energy density slice, in kJ m−3.
B. Sensitivity analysis
In the following, we will discuss the influence of different pa-rameters on the capturing process. It is important to note that the combination of interdependent parameters and the fact that our model is a serious simplification of reality requires a careful interpretation of our results.
A first example of an independent parameter is the MNP volume. Since the magnetic moment is proportional to the third power of the particle radius, the magnetic force is as well (Fm ∝ rp3). Seeing as the hydrodynamic force is only
pro-portional to the first power (Ff ∝ rp), the particle velocities
are proportional to the second power (apart from a constant): vp∝ rp2. This is reflected in the increasing capturing efficiencies
in Fig. 10. An important result is the fact that a rescaling of the particle velocities results not only in increasing attracting forces, but also in increasing repulsive forces. This is illustrated by the
trajectories in Fig. 16. The unexpected saturation of the CE at a non-100% value is most likely attributed to the repulsion of in-coming particles who will be “lost” upon leaving the simulation domain, and therefore not physical. Yet, these results are defi-nitely an incentive to use MNPs with maximised volumes. How-ever, while this parameter is not interdependent with any of the other parameters in our model, the reality is more complicated: most importantly, large particles have inferior tumour penetra-tion qualities and may cause adhesions. Then again, larger par-ticles may increase the IP residence time, which is a desired property.
The MNP saturation magnetisation is another independent parameter. The magnetic force is linearly dependent: Fm ∝
Msat,p, and therefore Msat,pshould be maximised as well. Yet,
the particles are required to be biocompatible, which limits the possible Msat,pvalues.
The influence of the SS saturation magnetisation is slightly more complicated: though the magnetised mesh field scales lin-early with Msat,SS(Bm ∝ Msat,SS), the factor ∇B · H
intro-duces mixing between the mesh- and uniform magnetic field, and therefore the magnetic force dependence is generally not simply linear. Yet, we can state that in general larger values of Msat,SSyield larger magnetic forces, and therefore we conclude
that strongly magnetisable implants are generally superior for IA-MDT. On the other hand, the design is again limited since the mesh should be biocompatible. Moreover, very strong mag-netisable implants would be impractical since they would ren-der it impossible to safely perform MRI procedures in the future [19].
The influence of the magnitude of the external magnetic field within our model is delicate as well. For increasing |B0|, m(|B|)
increases (see Fig. 2) and sinceFm∝ m(|B|), this will lead to
increased capture. The SS magnetisation also increases with |B0| (see Fig. 4), and since Fm = mp· ∇B ≈ mp· ∇Bm,
this will lead to an increased capture as well. Therefore, we conclude that |B0| should be sufficiently large to magnetically
saturate both the MNPs and the SS, but further increase will not have any influence. Since this saturation may happen at rela-tively low fields, IA-MDT does not require high fields, which is a significant advantage over conventional MDT. Fig. 11 (simu-lated with SS 304L) indeed indicates saturation at about 0.75 T, where both MNPs and SS are saturated.
From our simulation for different directions of the external mag-netic field, we conclude that the attraction to the magmag-netic mesh reduces with an increasing angle between the normal to the mag-netic mesh and the direction of the externally applied magmag-netic field. This result is shown in Fig. 12. Since the peritoneum is a bended rather than a flat surface, applying a uniform magnetic field through the patient will inevitably create a non-zero angle between this uniform field and the normal to some part of the magnetic mesh, which could reduce the attraction. Possibly an adapted external magnetic field pattern, perpendicular the the magnetic mesh at all points, may be a solution. Further simula-tions are needed to investigate this effect.
Fig. 7: Slice of particle trajectories forvf=0.
Fig. 8: Slice of z-component of the
particle velocity, in mm s−1. Fig. 9: Slice of particle trajectoriesforvf= 1 mm s−1ey.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 MNP radius [µm] 0 20 40 60 80 CE in % Fig. 10: CE as a function of MNP radius. 0 0.5 1 1.5 | B0| [T] 0 5 10 15 20 CE in %
Fig. 11: CE as a function of exter-nal field magnitude |B0|.
0 20 40 60 80 in ° 0 5 10 15 20 CE in %
Fig. 12: CE as a function of the an-gle betweenB0and the normal to
the magnetic mesh.
0 5 10 15 20 25 30 length [mm] 10 15 20 25 30 35 40 CE in %
Fig. 13: CE as a function of the magnetic mesh length.
40 60 80 100 120 140 160 180 rod radius [µm] 20 30 40 50 60 70 80 90 CE in %
Fig. 14: CE as a function of rod ra-dius. 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 period [mm] 55 60 65 70 75 80 85 CE in %
Fig. 15: CE as a function of mag-netic mesh period.
(a) rMNP= 0.5µm (b) rMNP= 1µm (c) rMNP= 2µm
The magnetic mesh parameters are interdependent. Gener-ally, the threads that constitute the mesh should be as thick, and as close to each other, as possible. This is clear from Fig. 14 and 15, presenting the CE as a function of the magnetic mesh thread radius, and the the distance between two consecutive threads respectively. However, it is not clear how these parameters in-teract: should the threads be further apart so they can be thicker, or the other way around? The CE as a function of the magnetic mesh length (and therefore surface area) is shown in Fig. 13. When the magnetic mesh becomes larger than the simulation domain (1 cm), the CE drops. This may be attributed to the fact that particles are now attracted to regions outside of the simula-tion domain. Moreover, this may cause particles to be repelled from regions inside the simulation domain, hence lowering the CE. Therefore, we conclude that targeting to a specific region is not enhanced by placing a magnetic mesh in the neighbourhood of this region, on the contrary, this may cause particles to be re-pelled from the desired region.
Finally, for the velocity of the fluid that surrounds the par-ticles we found that a non-zero fluid velocity is advantageous for dragging particles at large distances to the neighbourhood of the mesh, and conquering repelling edge effects, but disadvan-tageous for particles already close to the magnetic mesh, since they may be dragged passed it instead of being captured as they would have been without a fluid velocity. This is an incentive to alter between a moving and non-moving fluid during the pro-cedure, or to carefully monitor the fluid velocity to an advanta-geous range.
At the risk of oversimplifying, we conclude that the two most important parameters are rp and |B0|, since these parameters
achieve the largest increase in capture efficiency over a realistic range of their values. For r0it is important to note that small
radii yield a capture that is nearly zero, while the CE keeps in-creasing (even more rapidly) for larger values. |B0| is important
due to the large initial increase of the CE: with “little effort” a large difference is made.
IV. CONCLUSION
In summary, a mathematical model was developed to anal-yse the behaviour of MNPs in the neighbourhood of a magnetic mesh, for an improved treatment of peritoneal cancer. In this model, the MNP motion dynamics is governed by magnetic at-traction and hydrodynamic drag. The magnetic force attracts particles to regions of high magnetostatic energy density. The field generated by the magnetised implant is calculated by split-ting its volume into rods and regarding every rod as a magnetic moment with associated induction field. According to our sim-ulation results, the magnetic force is indeed generally directed towards the magnetic mesh, attracting the particles. However, between the threads of the mesh, outside, or at the edges of the mesh, a repulsive force is created. Our sensitivity analysis re-vealedFm ∝ r3,Fm ∝ Msat,p and that |B0| should be
suf-ficiently large to magnetically saturate MNPs and SS. Further-more, the magnetic mesh threads should be as thick as possible and as close to each other as possible, and applying a mesh in
the neighbourhood instead of target region itself may repel parti-cles from the desired region. Finally, an increased fluid velocity parallel to the magnetic mesh is beneficial for particles who are not located above the magnetic mesh.
In future work, the current model could be used to continue the analysis by investigating, for example, different magnetic mesh geometries, fluid profiles and the interdependence of all param-eters. While the current model offers a computational proof of concept for the implant-assisted targeting of magnetic particles, it possesses room for improvement on many levels. First, the inclusion of the tumour’s pathophysiology seems of vital im-portance to analyse the intratumoural drug penetration. Second more accurate computational methods, such as the finite element method, may significantly improve the resemblance between model and reality. Third, a more realistic simulation domain size will improve the reliability of the CE calculations. Alterna-tively, the individual particle trajectories could be used to yield a CE, therefore eliminating the limited simulation domain issues. Finally, consultation with clinicians to discuss the practical fea-sibility and limitations of such an implant is crucial to adapt the design in a useful way.
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CONTENTS
Author’s permission iii
Preface iv
Title and abstract v
Extended abstract vi
Contents xiii
List of Figures xv
List of Tables xix
Nomenclature xix 1 Introduction 1 1.1 Motivation . . . 1 1.2 Problem description . . . 2 1.3 Objectives. . . 2 1.4 Methods . . . 3
2 Peritoneal cancer and its treatments 4 2.1 The Peritoneum. . . 4 2.2 Peritoneal cancer . . . 5 2.3 Treatments . . . 6 2.3.1 Comfort treatments . . . 6 2.3.2 Chemotherapy . . . 6 2.3.3 Radiotherapy. . . 6 2.3.4 Cytoreduction . . . 7 2.3.5 HIPEC . . . 7 2.3.6 PIPAC . . . 8 2.4 Conclusion . . . 10 3 Magnetic Nanoparticles 11 3.1 Definition and applications . . . 11
3.2 Magnetic Properties. . . 14
3.3 Magnetic nanoparticle dynamics . . . 15
3.3.1 Motion of a MNP. . . 18
3.3.2 Advection-Diffusion Equation . . . 18
3.4 Magnetic Implants as a solution for magnetic drug targeting limitations . . 19 xiii
xiv CONTENTS
4 Modelling implant-assisted magnetic nanoparticle capture 23
4.1 Magnetic Nanoparticles. . . 23
4.2 External magnetic field . . . 26
4.3 Magnetic mesh . . . 26
4.4 Mesh field. . . 28
4.4.1 Finite Element Method . . . 28
4.4.2 The infinite Magnetic Mesh . . . 29
4.4.3 Dipole superposition method . . . 30
4.5 Fluid . . . 35
4.6 Particle Motion Dynamics . . . 35
4.7 Capture efficiency. . . 43
4.8 Simulation Result for a generic case. . . 45
4.9 Conclusion . . . 53
5 Sensitivity Analysis 54 5.1 External Magnetic Field . . . 54
5.1.1 Magnitude of the external magnetic field . . . 54
5.1.2 Direction of the external magnetic field . . . 60
5.2 Magnetic Nanoparticles. . . 63 5.2.1 Size . . . 64 5.2.2 Magnetisation Curve. . . 65 5.3 Magnetic Mesh . . . 66 5.3.1 Thickness of Threads. . . 67 5.3.2 Period of Threads . . . 68
5.3.3 Magnetic Mesh Surface Area . . . 69
5.3.4 Thread Material . . . 72 5.4 Fluid Velocity . . . 74 5.5 Conclusion . . . 75 6 Conclusion 79 Bibliography 83 Appendix 87
L
IST OF
F
IGURES
1.1 Schematic overview of intraperitoneal implant-assisted drug targeting. . . 2 2.1 The peritoneum . . . 5 2.2 Schematic representation and surgical procedure of Hyperthermic
Intraperi-toneal Chemotherapy (HIPEC), figure by Shariati et al. [1] . . . 8 2.3 Schematic representation and surgical procedure of Pressurized
Intraperi-toneal Aerosol Chemotherapy (PIPAC), figure by Shariati et al. [1] . . . 9 3.1 Nanomedicine based intraperitoneal therapies. . . 13 3.2 Magnetisation curves for different magnetic materials. . . 15 3.3 Schematic illustration of the use of a magnetic stent versus an
imperme-able magnetic patch for intravascular IA-MDT. . . 21 4.1 Magnetisation curves for three different kinds of MNPs. . . 24 4.2 External magnetic field B0, generated by Helmholtz-coil (left) or assumed
uniform (right). Magnetic field lines shown in black, coils shown in grey (dot-out of paper, cross- in paper). Simulation domain, containing the peritoneum, indicated in red. . . 26 4.3 Scanning Electron Microscopy (SEM) image of the stainless steel mesh used
by Yellen et al. [2] . . . 27 4.4 Reference system with magnetic mesh and external field set-up. . . 27 4.5 Magnetisation curves for three SS materials. . . 28 4.6 Geometry and reference frame for the mesh field of an infinite magnetised
cylinder. . . 30 4.7 Division of the magnetic mesh into small rods. . . 32 4.8 Geometry and reference frame for one single magnetised rod. . . 33 4.9 Norm of mesh field of magnetised rod, calculated as an integration over its
volume (equation 4.13) and by approximating the integrand to be constant throughout the rod (equation 4.15). r is defined in Fig. 4.8. . . . 33 4.10 Geometry and reference system for the comparison between infinite
cylin-der and finite cylincylin-der mesh fields. . . 34 4.11 x-component of the mesh field of infinite and finite cylinders. . . . 34 4.12 Absolute difference between x-component mesh field of infinite and finite
cylinders. . . 35 4.13 Relative difference between x-component mesh field of infinite and finite
cylinders. . . 35 4.14 Visualisation of central differentiation (blue arrows) and single-side
differ-entiation (green arrows) in one-dimension. . . 37 xv
xvi LIST OFFIGURES
4.15 Visualisation of the analytical gradient method. . . 38
4.16 Visualisation of linear concatenation method. . . 39
4.17 Visualisations of Euler based particle number density updating procedure. 41 4.18 Initial particle number density as a homogeneous sheet. Fluid velocity in-dicated with a black arrow. . . 44
4.19 |B| and magnetic field values of B as red arrows. . . . 46
4.20 Slices of |B| and magnetic field lines of B as red arrows. . . . 46
4.21 Slices of |Bm| and magnetic field lines of Bmas red arrows. . . 46
4.22 Magnetic energy density slice, in kJm−3. . . . 47
4.23 Magnetic energy density zoom-in, in kJm−3. . . . 47
4.24 z-component of the magnetic field gradient ∇|Bm| with gradient field lines visualised as black arrows. . . 48
4.25 Trajectory of a MNP in a stationary fluid with initial condition r0= −2mmex+ 3mmey+ 4.5mmez. . . 48
4.26 z-component of the trajectory of a MNP in a stationary fluid with initial condition r0= −2mmex+ 3mmey+ 4.5mmez, as a function of time. . . 49
4.27 Velocity along the trajectory of a MNP in a stationary fluid with initial con-dition r0= −2mmex+ 3mmey+ 4.5mmez, as a function of time. . . 49
4.28 Slice of particle trajectories for a stationary fluid. . . 50
4.29 Slice of z-component of the particle velocity. . . . 50
4.30 Slice of particle trajectories for a moving fluid: vf = 1 mm s−1ey. . . 50
4.31 Slice of norm particle velocity, for a moving fluid: vf = 1 mm s−1ey. . . 50
4.32 particle number density after different simulation times. . . 51
4.33 Capture efficiency in percent as a function of simulation time for different time steps d t. . . . 52
4.34 Capture efficiency in percent as a function of time step d t. . . . 52
4.35 Calculation time in minutes for a 15 s simulation as a function of time step d t. . . 52
4.36 Capture efficiency in per cent as a function of simulation time. . . 52
5.1 ∂z∂(Bm,z) in Tm−1 . . . 57
5.2 ∂z∂|Bm|2in T2m−1 . . . 57
5.3 ∂|B|∂z2 for different values of the magnitude of the external magnetic field. . 58
5.4 Magnetic field-lines of the mesh field, Bm, and the norm of the mesh field, |Bm|. . . 59
5.5 Particle trajectories (indicated as blue arrows) and the magnitude of the particle velocity along the z-axis, for different values of B0, with vf = 0. . . 59
5.6 Particle trajectories (indicated as blue arrows) and the magnitude of the particle velocity along the z-axis, for different values of B0, with vf = 1 mm s−1ey. 59 5.7 Capture efficiency for different values of the external field magnitude |B0|. 60 5.8 Definition of the angleθ. . . . 60
5.9 Magnetic field-lines of the total magnetic field, B, and the norm of the total magnetic field, |B|. . . . 61
5.10 Magnetic field-lines of the mesh field, Bm, and the norm of the mesh field, |Bm|. . . 61
LIST OFFIGURES xvii 5.11 Magnetic field-lines of the mesh field Bmin three-dimensions. . . 61
5.12 Particle trajectories (indicated as blue arrows) and the magnitude of the particle velocity along the z-axis, for different directions of B0, with vf = 0. 62
5.13 Particle trajectories (indicated as blue arrows) and the magnitude of the particle velocity along the z-axis, for different directions of B0, with vf =
1mms−1e
x. . . 62
5.14 Particle trajectories (indicated as blue arrows) and the magnitude of the particle velocity along the z-axis, for different directions of B0, with vf =
1mms−1e
y. . . 63
5.15 Capture efficiency for different directions of B0. . . 63 5.16 Particle trajectories (indicated as blue arrows) and the magnitude of the
particle velocity along the z-axis, for different values of rM N P, with vf =
1mms−1e
y. . . 64
5.17 Capture efficiency for different MNP radii. . . 65 5.18 Particle trajectories (indicated as blue arrows) and the magnitude of the
particle velocity along the z-axis, for different values of Msat,p, with vf =
1mms−1e
y. . . 66
5.19 Capture efficiency for different MNP magnetisation curves. . . 66 5.20 Particle trajectories (indicated as blue arrows) and the magnitude of the
particle velocity along the z-axis, for different values of the rod radius, with vf = 1 mm s−1ey. . . 68
5.21 Capture efficiency in % for different MNP rod radii. . . 68 5.22 Magnetic mesh geometries for different periods. . . 69 5.23 Particle trajectories (indicated as blue arrows) and the magnitude of the
particle velocity along the z-axis, for different thread periods, with vf =
1mms−1e
y. . . 69
5.24 Capture efficiency for different magnetic mesh periods. . . 69 5.25 Magnetic mesh geometries for different lengths. . . 70 5.26 Particle trajectories (indicated as blue arrows) and the magnitude of the
particle velocity along the z-axis, for different values of the magnetic mesh length, with vf = 1 mm s−1ey. . . 70
5.27 Capture efficiency in % as a function of the magnetic mesh length. . . 71 5.28 Magnetic mesh geometries of length 7.8 mm (total red) and 4.8 mm (total
black). . . 71 5.29 Definition of “square strip”: difference between mesh of length 7.8 mm and
4.8 mm. . . 71 5.30 Magnetic field-lines of the mesh field, Bm, and the norm of the mesh field,
|Bm|. . . 72
5.31 Magnetic field-lines of the mesh field, Bm, and the norm of the mesh field,
|Bm|. . . 72
5.32 Particle trajectories (indicated as blue arrows) and the magnitude of the particle velocity along the z-axis, for different values of Msat,SS, with vf =
1mms−1e
y. . . 73
5.33 Capture efficiency as a function of time for different magnetic mesh mate-rials. . . 73
xviii LIST OFFIGURES 5.34 Particle trajectories (indicated as blue arrows) for different values of vf,y. . 77 5.35 Capture efficiency as a function of the fluid velocity vf = vyey. . . 78
L
IST OF
T
ABLES
4.1 Saturation Magnetisation for three different kinds of MNPs. . . 24 4.2 Saturation Magnetisation for three SS materials. . . 28 4.3 Representative parameters used to obtain generic simulation results. . . . 45 5.1 Value of the magnetic field by which saturation is reached for 3 different
stainless steel materials. . . 55
N
OMENCLATURE
Abbreviations
CRS Cytoreductive Surgery
HIPEC Hyperthermic IntraPEritoneal Chemotherapy IA-MDT Implant-Assisted Magnetic Drug Targeting
IP Intraperitoneal
MDT Magnetic Drug Targeting
MNP Magnetic Nanoparticle
NP Nanoparticle
PCI Peritoneal Cancer Index
PIPAC Pressurized Intraperitoneal Aerosol Chemotherapy
SPM Superparamagnetic SS Stainless Steel
Greek symbols
τp torque on a particle χv volumetric susceptibility ηf fluid viscosityµ0 magnetic permeability in a vacuum
ρp mass density of a particle
τc computation time
ε0 permittivity in a vacuum
Other symbols
Am magnetic vector potential of magnetised mesh
B magnetic induction, magnetic flux density
B0 homogeneous external magnetic field
NOMENCLATURE xxi
Bm magnetic field generated by magnetised mesh, or mesh field
E electrical field
eB0 Unit vector of external magnetic field
eM Unit vector magnetisation
ei Unit vector along direction i
Ff hydrodynamic- or fluid force
Fm magnetic force
H magnetic field
JA advective particle flux
JD diffusive particle flux
M magnetisation
Mp MNP magnetisation
Msat,p SS saturation magnetisation
Msat,SS MNP saturation magnetisation
mp MNP magnetic moment
rc,i point vector centre of rod with index i
vf fluid velocity
vp MNP velocity
Bsat value of the magnetic field for which a magnetisation curve saturates
D diffusion constant
d t time step
hx distance between two points of discretised space along direction x
kb Boltzmann constant
L(x) Langevin function
lrod length of a rod
mp MNP mass
n particle number density
xxii NOMENCLATURE
rp MNP radius
rrod radius of a rod
T temperature
Um magnetic potential
Vi Volume of a part of the magnetic mesh
1
I
NTRODUCTION
1.1. M
OTIVATION
Peritoneal cancer, commonly originating from primary cancers of organs embedded in the peritoneal cavity, is generally a poor prognosis indicator [3]. Because of poor ther-apeutic response, survival rates are small and systemic chemotherapy treatments are mainly applied as palliative care [4, 5]. Intraperitoneal (IP) chemotherapy has shown significant advantages over intravenous drug administration for the treatment of peri-toneal malignancies [3]. However, the inadequate drug penetration in the notoriously penetration resistant peritoneal nodules limits the efficacy of this treatment. Recently, nanoparticles (NPs) have been utilised as drug carriers in IP chemotherapy with the hope of augmenting the IP residence time, and therefore the drug penetration. This applica-tion has introduced a so called “size dilemma”: the larger the NPs size, the larger the IP residence time, since larger particles cannot leave the peritoneal cavity through the lymphatic system. However, drug penetrating efficiency reduces with increasing size [6]. It is proposed to resolve this dilemma by exploiting drug-carrying magnetic nanoparti-cles (MNPs), which can be targeted to the region of interest by external magnetic forces, an approach referred to as Magnetic Drug Targeting (MDT). In this way, one can bene-fit from the enhanced residence time of the larger particles, while retaining acceptable penetration depths. However, a severe drawback of MDT is the inherent weakness of the magnetic forces: these forces depend on both the presence of a far-reaching magnetic field to magnetise the carriers, and a strong magnetic field gradient. Yet, a magnetic field with strong gradient is by definition rapidly decaying and therefore not able to magnetise the bulk of the carriers. To resolve this problem, it is proposed in this research to deploy a magnetic implant that generates a local field gradient at the target region, in combi-nation with a homogeneous external field to magnetise the carriers. This approach is referred to as Implant-Assisted Magnetic Drug Targeting (IA-MDT) [7]. The aim of this work is to develop a mathematical model for the delivery of drug-carrying MNPs to a magnetic implant in the peritoneum, and to use this model to analyse the influence of different parameters.
1
2 1. INTRODUCTION
1.2. P
ROBLEM DESCRIPTION
In IA-MDT, a magnetisable implant, for example, a ferromagnetic wire, is placed in-side the body at the target site. When an external homogeneous magnetic fields is ap-plied, this implant will become magnetised and therefore generate its own magnetic field. Since this field has a large gradient in the direct neighbourhood of the implant, it will locally increase the magnetic force exerted on the the nearby MNPs. In addition to magnetising the implant, the external magnetic field can magnetise the bulk of the MNPs, enhancing the magnetic forces exerted on them as well. Several enlightening theoretical, experimental, and animal model studies have shown the feasibility of this technique [8]. However, research on an intraperitoneal application of IA-MDT is, to our knowledge, limited, if not non-existent. A schematic overview of the proposed treatment is shown in Fig. 1.1. The external homogeneous field applied throughout the peritoneal cavity is denoted as B0. The implant is proposed to consist of a gridded structure, which we will refer to as the magnetic mesh. The local field it creates when magnetised is re-ferred to as the mesh field, and denoted as Bm. In this thesis, a mathematical model will
be developed to gain insight into the working principle of the MNP targeting, and the parameters influencing the success of the treatment.
Figure 1.1: Schematic overview of intraperitoneal implant-assisted drug targeting.
1.3. O
BJECTIVES
Firstly, this text aims to frame IA-MDT in the bigger picture of peritoneal cancer treat-ments. We briefly mention the main advantages and limitations of both conventional and state-of-the-art treatments, leading us to IA-MDT as a possible improvement. Sec-ondly, a we aim to develop a mathematical model for the delivery of drug-carrying MNPs to a magnetic implant in the peritoneum. While this model will necessarily be a simplifi-cation of reality, it should capture the main physical phenomena governing the particles’ movement and therefore allow for a range of qualitative conclusions about the working principles and important parameters. In addition, this model should include the
calcu-1.4. METHODS
1
3lation procedure for a parameter that represents the success of certain simulation con-ditions, for example a certain implant geometry. This parameter will be referred to as the capturing efficiency. Finally, our goal is to use this mathematical model to analyse some general characteristics of the IA-MDT set-up, as well as the influence of different simula-tion parameters on the MNP behaviour and capturing efficiency. So, we want to obtain a model such that we can associate a number (the capture efficiency) with every simula-tion set-up. This number reflects the performance of the set-up and should therefore be optimised. For a set of parameters determining the set-up, we want to obtain this per-formance number as a function of realistic values for the analysed parameter, such that we have not only a way to tell which value of this parameter maximises performance, but also which parameters achieve the largest increase in performance over a realistic range. Parameters we want to analyse are: MNP size and magnetisation curve, external magnetic field strength and direction, implant geometry and finally, the intraperitoneal fluid velocity.
1.4. M
ETHODS
In Chapter 2, a brief introduction to the peritoneum and peritoneal cancer is followed by an overview of the most important treatments. We introduce NPs and their use in peritoneal cancer treatments in Chapter 3. In this same chapter, we turn to the use of MNPs, particularly in MDT. We will describe their magnetic properties, as well as their motion dynamics, using Newton’s equation of motion for a single particle’s trajectory, or the advection-diffusion equation for the particle number density dynamics. This chap-ter is concluded by introducing IA-MDT as a solution for MDT limitations, supported by some basic size order calculations. Chapter 4 is devoted to the development of a mathematical model, combining similar models from literature with an intraperitoneal environment. At the end of this chapter, the model will be used to generate some generic results under representative simulation conditions, providing a proof of concept for the targeting technique. In Chapter 5 the model is then used for a sensitivity analysis: differ-ent parameters will be varied to investigate their influence on the MNP behaviour, using both analytical formulas and simulations.
2
P
ERITONEAL CANCER AND ITS
TREATMENTS
In this chapter, a brief description of the peritoneum and peritoneal cancer is presented. This is followed by a condensed overview of the most important treatments, starting from more conventional approaches, like systemic chemotherapy, to some state-of-the-art treatments.
2.1. T
HE
P
ERITONEUM
The peritoneum is a membrane: a thin layer of tissue, that covers most of the abdominal organs – amongst others, the stomach, liver, bowel, uterus, ovaries and fallopian tubes. The peritoneum helps protect and support the organs it covers and produces a lubricat-ing fluid that helps these organs move smoothly. The peritoneum is made of epithelial cells supported by a thin layer of connective tissue, and has a surface of about 1.5 m2on average [9]. The peritoneum consists of an outer layer and an inner layer: the parietal -and visceral peritoneum, with a potential space between them: the peritoneal cavity or space. The outer layer separates the peritoneal cavity from the abdominal wall and the inner layer is wrapped around the organs, separating them from the peritoneal cavity. Both layers, the space between them, and the organs wrapped in the visceral peritoneum are illustrated in Fig. 2.1.
2.2. PERITONEAL CANCER
2
5Figure 2.1: The Peritoneum, figure adapted from Macmillan cancer support [10].
2.2. P
ERITONEAL CANCER
There are two types of peritoneal cancer that differ from each other by the way they arise. Primary peritoneal cancer develops when certain cells of the peritoneum undergo a transformation into cancerous cells, but this happens very rarely. In most cases, peri-toneal cancer occurs when cells from other tumours metastasize to the peritoneum: sec-ondaryperitoneal cancer. Primary tumours from which the cancer cells metastasize are often located in the abdomen. It is estimated that 15 % to 20 % of the colorectal cancer patients and 10 % to 15 % of the stomach cancer patients will develop peritoneal metas-tasis. For 60 % to 80 % of women with ovarian cancer, peritoneal metastases are already present at the time of diagnosis [11]. However, the cancer cells can also reach the peri-toneum through the blood or the lymphatic system and in this way originate from any other tumour [12].
Peritoneal cancer can occur anywhere on the 1.5 m2peritoneum, but some places are more common than others [12]. The Peritoneal Cancer Index (PCI) is an objective method to score the presence and size of macroscopic tumours in 13 different abdominal re-gions, with a maximum score of 39 (13 × 3) [13].
Symptoms of peritoneal cancer are limited as long as the nodules are small in size and quantity. When the disease grows, there can be an accumulation of fluid in the abdomen and obstruction of the bowels because of the nodules pressing against them [12]. Because of the ineffectiveness of systemic therapy as a treatment for peritoneal cancer, the mean survival time using this treatment alone is only around 12 months, causing peritoneal cancer to be regarded as a final disease stage. While new local therapies have significantly increased life expectancy, long term survival rates remain an issue [11].
2
6 2. PERITONEAL CANCER AND ITS TREATMENTS
2.3. T
REATMENTS
In this section, a brief review of the most important peritoneal cancer treatments is pre-sented. Starting from the most conventional ones, like chemotherapy, we move on to state-of-the-art treatments. For a detailed and complete overview of peritoneal cancer treatments, the reader is referred to “Peritoneal Carcinomatosis: A Multidisciplinary Ap-proach” by Wim Ceelen et al. [14]
2.3.1. C
OMFORT TREATMENTSBesides cancer treatments as discussed below, the patient can be treated to improve comfort, by reducing symptoms. Examples of these comfort treatments are the drain-ing of fluid from the abdomen and placement of a stoma [12].
2.3.2. C
HEMOTHERAPYChemotherapy is a cancer treatment in which drugs are admitted via the blood stream. In general, these chemotherapeutic drugs are cytotoxic, meaning they are toxic to liv-ing cells, by interferliv-ing with cell growth and division. Cancer cells are more sensitive to these drugs as they divide markedly faster than normal cells. Though to a significant lesser extent, normal cells can be damaged as well. This leads to the most common ad-verse effects of chemotherapy, like suppression of the immune system, hair loss, nausea, etc. Chemotherapy is a systemic therapy since the drugs are in principle able to reach the cancer at any anatomic location in the body via the bloodstream [15]. There are a multitude of cytotoxic drugs available that differ in their mechanism and side effects. In most cases, a combination of several different cytotoxic drugs is administered in order to optimise treatment effectiveness.
Though chemotherapy keeps evolving, it is difficult to treat peritoneal cancer with sys-temic chemotherapy alone. The drugs do not reach high enough concentrations in the peritoneum due to the large surface and poor vascularization [13, 16]. The treatment is therefore not sufficiently effective, leading to low life expectancy. There is a clear dose-effect relation, but the dose-effective dose often exceeds the toxic dose [13]. In other words, high doses are needed to reach sufficiently high concentrations in the peritoneum in or-der to tackle the intraperitoneal tumours. Yet, these high doses are present throughout the entire body and also affect healthy cells, leading to severe adverse effects.
2.3.3. R
ADIOTHERAPYIn radiotherapy, ionisation radiation is directed at cancerous tissue, damaging its DNA, which will lead to cellular death. Contrary to systemic chemotherapy, this is a local ther-apy, since it targets a specific region. Treating the peritoneum with radiotherapy poses the challenge of obtaining a sufficient dose of radiation in the peritoneum all the while protecting the sensitive organs embedded in it [14]. This obstacle has rendered radio-therapy a less attractive option for peritoneal cancer treatment in the past, but new tech-nologies designed to surpass this challenge create new opportunities [14].
2.3. TREATMENTS
2
72.3.4. C
YTOREDUCTIONA cytoreductive surgery (CRS) is an invasive surgery where all visible tumour nodules are removed surgically. Like radiotherapy, cytoreduction is a local therapy. Patient selection is of utmost importance for CRS to be successful; only patients without metastasis in liver or lungs and a restricted amount of nodules are eligible for this medical interven-tion [12]. The Peritoneal Cancer Index (PCI) as introduced earlier, may be used to pre-vent unnecessary surgery in high risk patients. Accurate patient selection will decrease postoperative morbidity. In most cases, it is necessary to remove part of the organs and parts of the peritoneum that are affected. The cytoreduction of the peritoneum is called a peritonectomy. According to studies, surgery does no succeed in removing the tumour at microscopic level, causing residual or recurrent disease in almost all cases. Gener-ally, patients die of the gastrointestinal malfunction or weakness of the body caused by a severe chronic disease [13].
2.3.5. HIPEC
A treatment that has improved long-term survival of peritoneal cancer is Hyperthermic IntraPEritoneal Chemotherapy or HIPEC. In this treatment the peritoneal cavity is per-fused with heated chemotherapy to treat and prevent recurrence of peritoneal surface malignancies [11].
Advantages There are four main advantages for using HIPEC: Firstly and most impor-tantly, studies have shown an important dose advantage for local intraperitoneal (IP) ad-ministration of chemotherapy compared to systemic intravenous application; as there are fewer side effects for local administration, higher doses can be used, leading to a higher effectiveness [13]. Secondly, since they are sensitive to heat, the heat of the per-fusion fluid causes direct injury to cancerous cells. This phenomenon is referred to as hyperthermia. Healthy cells on the other hand are less sensitive and therefore there is no significant injury to normal tissues, at least for the temperatures used in the HIPEC procedure [11]. Thirdly, at higher temperatures various cytotoxic drugs are more effec-tive, this is referred to as the synergism of hyperthermia and those drugs [13]. And finally, hyperthermia also enhances the penetration of cytotoxic drugs into tumour tissue. Surgery Prior to a HIPEC treatment, there is usually a cytoreductive surgery. The pur-pose of this surgery is to reduce the neoplastic mass and, on the other hand, to create optimal exposure to IP drugs by removing intra-abdominal adhesions [17, 13]. The com-pleteness of this surgery is an important prognostic for survival of peritoneal cancer after the complete HIPEC treatment [17].
Hyperthermic Perfusion After the cytoreduction, the peritoneal cavity is perfused with heated chemotherapy, typically at around 41.4 °C, during 30–120 min [9]. Over time, dif-ferent perfusion techniques have been developed for which there is no consensus as to which is best. There are four main aspects in which the perfusion techniques differ: (1) the technique used to achieve a peritoneal expansion, applied to have an optimal exposure of the intra-abdominal organs, (2) whether the perfusion should happen in a closed model, meaning the perfusion liquid is filtered and then again administered, or
2
8 2. PERITONEAL CANCER AND ITS TREATMENTS
not, (3) the exact hyperthermic temperature and (4) the choice of drugs [13]. Since none of the available chemotherapeutics has been specifically approved for IP administration, off-label agents developed for intravenous administration are used [9]. Fig. 2.2 shows a schematic representation of a closed model HIPEC procedure on the left, and on the right a surgical procedure using an expander to achieve peritoneal expansion, allowing the hands to stir in the abdomen. Besides the perfusion parameters, different centres use HIPEC in different ways, and again there is no consensus, for example, whether or not to use systemic chemotherapy in combination with the CRS HIPEC treatment, which patients are eligible for the HIPEC procedure, whether or not to systematically remove the ovaries of all female patients, etc.
Figure 2.2: Schematic representation and surgical procedure of Hyperthermic Intraperitoneal Chemotherapy (HIPEC), figure by Shariati et al. [1]
Limitations Despite the advantages mentioned earlier in this section, HIPEC also pos-sesses considerable limitations, the most important ones being the poor drug penetra-tion of the perfused chemotherapeutics into the tumours, and inhomogeneous drug dis-tribution throughout the abdominal cavity [1]. The unsatisfactory penetration depths are the reason HIPEC is only effective in patients with minimal residual disease after the cytoreduction: tumour depth should be smaller than 3 mm [13]. Insufficient penetra-tion also increases the risk of recurrent peritoneal disease [9]. The short exposure time of the peritoneum to the rapidly leaking away chemotherapeutics contributes to a high recurrence rate as well [9]. In addition, HIPEC is an invasive procedure and therefore hardly repeatable, as well as costly.
2.3.6. PIPAC
While HIPEC administers chemotherapeutic drugs intraperitonially by solving them in a fluid, it has been proven that the nebulisation of chemotherapeutics is also a well-suited an efficacious drug delivery mode to treat and prevent recurrence of peritoneal sur-face malignancies. This treatment is referred to as Pressurized Intraperitoneal Aerosol Chemotherapy or PIPAC.
Advantages The nebulised chemotherapeutics, or chemo-aerosol, formed in the peri-toneal cavity during the PIPAC procedure behaves in a gas-like manner. This gas-like
2.3. TREATMENTS
2
9state offers four main advantages, compared to liquid IP chemotherapy. Firstly, it could guarantee a more homogeneous pattern compared to the use of a liquid. Secondly, the gas is held at a pressure of 12 mmHg during the PIPAC procedures, which could coun-teract the elevated fluid pressure in tumour nodules. This results in a better drug pen-etration [18]. Therefore, superior intratumoural drug concentrations can be achieved with only 10% of the usual dose, reducing systemic toxicity [18]. Finally, the proce-dure is much less invasive, and the repeatability is thus much higher [1]. Fig. 2.3 shows a schematic representation of the PIPAC procedure on the left, demonstrating the in-creased IP pressure with the help of blue arrows, and the surgical procedure on the right, indeed revealing this procedure to be much less invasive than was the case for HIPEC.
Figure 2.3: Schematic representation and surgical procedure of Pressurized Intraperitoneal Aerosol Chemotherapy (PIPAC), figure by Shariati et al. [1]
Limitations While it is clear that the advantages of PIPAC address most of the HIPEC limitations, some of them remain an issue, and new ones are introduced. Though the ho-mogeneity of spacial drug distribution is improved with respect to HIPEC, it remains one of the important limitations of PIPAC. These inhomogeneities cause a variation in pen-etration depth between different regions in the abdominal cavity. In particular, a large fraction of the aerosol is deposited beneath the nozzle, leading to local aerosol “hot-spots”. Furthermore, the PIPAC procedure demands an extensive preparation and safety measures, and has a high cost. Based on studies and trials, it is suggested that PIPAC is feasible and safe and maintains and/or improves the quality of life in patients with peri-toneal cancer. The first application in humans was introduced in 2011 [18]. However, PIPAC is still in its infancy and is so far only performed as a palliative care in patients who are no longer eligible for CRS and HIPEC.
Variations Recently new types of PIPAC have been developed attempting to address the recurrent limitations. For example, Hyperthermic PIPAC, the combination of the PI-PAC technology with hyperthermia, or Hyperthermic Intracavitary NAnoaerosol Ther-apy (HINAT), which attains a more uniform drug distribution pattern and deeper drug penetration [1]. Another noteworthy example is electrostatic PIPAC (ePIPAC), where the electrostatic precipitation of the therapeutic aerosol was shown to improve the distri-bution pattern and tissue uptake of cytotoxic drugs in the peritoneal cavity, as well as a reduction of the application time, compared to PIPAC alone [5].
2
10 2. PERITONEAL CANCER AND ITS TREATMENTS
2.4. C
ONCLUSION
In conclusion, the ineffectiveness of conventional systematic chemotherapy, due to the large surface and poor vascularisation of the peritoneum, has lead the to way to local peritoneal cancer therapies, which facilitate direct drug delivery while mitigating ad-verse effects.
However, these local therapies still have a high risk of recurrent peritoneal disease be-cause of the poor drug penetration. Thus, there is a need for a peritoneal cancer treat-ment that enables enhanced drug penetration, for example by increasing the IP resi-dence time [9]. One possible approach is the usage of nanomedicine, introducing a new series of possible treatment strategies, as will be elaborated in the next chapter.
3
M
AGNETIC
N
ANOPARTICLES
We will start this chapter by defining nanoparticles (NPs), as well as magnetic nanoparti-cles (MNPs), and discuss some general applications. The use of NPs in peritoneal cancer treatments will be reviewed, followed by a more in depth discussion of magnetic drug targeting (MDT) and the use of MDT in peritoneal cancer treatments. To further un-derstand MDT, we will investigate some MNP properties that are crucial to its working principle: we will describe the magnetic properties and motion dynamics of MNPs. This chapter is concluded by introducing implant-assisted magnetic drug targeting (IA-MDT) as a solution for MDT limitations.
3.1. D
EFINITION AND APPLICATIONS
A nanoparticle (NP) is a small object, ranging from a few nanometres to a few hun-dred nanometres, that behaves as a whole unit in terms of its transport and proper-ties. Nanoparticles have a myriad of biomedical applications since their dimensions are smaller than or comparable to those of a range of biological entities like cells, viruses or genes, making it possible to interact with them [19]. Moreover, their sizes allow them to travel through narrow pathways and reach nearly all parts of the body after being in-jected. Often NPs are coated with a biocompatible surface to enhance their stability. Nanoparticles can be functionalised and thereafter used as carriers for drugs, radio- or gene-therapy. In addition, targeting ligands can be attached to actively localize them at a specific tissue, for example a tumour. Their particular composition and synthesis de-pends on the application.
Magnetic nanoparticles (MNPs) are nanoparticles with cores of a magnetic material, usually magnetite Fe3O4or maghemites (α-Fe2O3orγ-Fe2O3). Because of their mag-netic properties, they can be manipulated by magmag-netic field gradients. In addition, they respond to a time-varying magnetic field, enabling an energy transfer from the exciting field to the tissue they are embedded in, creating heat. These properties introduce a new series of possibilities for biomedical applications. Examples of MNP applications
![Figure 2.1: The Peritoneum, figure adapted from Macmillan cancer support [10].](https://thumb-eu.123doks.com/thumbv2/5doknet/3274779.21402/28.722.129.556.78.353/figure-peritoneum-figure-adapted-macmillan-cancer-support.webp)
