Defining the resolving power and detection depth of the DiffMag handheld probe

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1 Faculty of science and technology

Defining the resolving power and detection depth of the DiffMag

handheld probe

Bas Bloemendaal B.Sc. Thesis

July 2020

Supervisors:

dr. ir. L. Alic E.R. Nieuwenhuis M.Sc.

dr. E. Groot Jebbink

Magnetic Detection and Imaging group

Faculty of science and technology

University of Twente

P.O. Box 217

7500 AE Enschede

The Netherlands

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Samenvatting

Momenteel wordt in meerdere zorgcentra de schildwachtklier (SKW) biopsie (SKWB) procedure gebruikt voor het diagnosticereen van de lymfeklierstatus bij hoofd-hals kanker. De SKW’s zijn de lymfeklieren die de grootste kans hebben op een uitza- aiing afkomstig van de primaire tumor. Daarom spelen deze SKW’s een cruciale rol in het maken een prognose. De SKWB procedure bestaat uit het opsporen, operatief verwijderen en het diagnosticeren van een eventuele tumoruitzaaiing naar de SKW’s. Na verwijdering van de SKW wordt deze naar de pathologie gebracht om uiteindelijk een prognose over de kanker te geven. Momenteel wordt de SKW opgespoord met behulp van radio-actieve tracers en een gamma probe of met behulp van blauwkleuring. Echter, deze opsporingsmethoden brengen logistieke problemen en veiligheidsproblemen door de radio-actieve tracer en verstoring van het operatie veld van de chirurg door de blauwkleuring. Tevens, radio-active tracers brengen een

”shine-through” fenomeen mee, waardoor het signaal dat gemeten wordt met een gamma probe minder accuraat is in het detecteren van SKW’s. Om deze bijkomende nadelen te overkomen wordt er een nieuwe methode met magnetische detectie on- twikkeld.

Deze nieuwe magnetische detectie methode is vergelijkbaar met de radio-actieve methode alleen bestaat de magnetische tracer uit superparamagnetische ijzeroxide- nanodeeltjes (SPIONs). Deze deeltjes wordern peritumoraal ingespoten en vervol- gens opgespoord met een magnetische handheld probe in de omliggende schildwachtk- lieren. De magnetische detectie handheld probe exploiteert de niet-lineaire eigen- schappen van de ingespoten SPIONs om deze op te sporen in een diamagnetische (lineaire-) omgeving. Dit concept wordt differenti¨ ele magnetometry (DiffMag) ge- noemd. Deze DiffMag handheld probe bestaat uit een excitatie-en detectiespoel. De excitatiespoel exciteert een magnetisch AC-excitatieveld dat gemoduleerd is met een pulssequentie. Deze pulssequentie geeft het exciatieveld een offset mee die ervoor zorgt dat alleen de response van de SPIONs gemoduleerd wordt waardoor diamag- netische deeltjes niet gemeten worden. De response van de deeltjes wordt vervolgens door de detectiespoel gemeten. Hierdoor is een selectieve methode voor het deterc- teren van SPIONs mogelijk.

Voordat deze DiffMag handheld probe voor klinische doeleinden kan worden ge-

bruikt, moet deze aan een aantal klinische voorwaarden voldoen. De meest be-

langrijke voorwaarden zijn het onderscheidend vermogen en de maximale detectie

diepte. Om deze voorwaarden te evalueren voor de DiffMag handheld probe is een

MATLAB

^®

simulatiescript van de probe ontworpen. Voor het maken van deze sim-

ulatie is rekening gehouden met de exacte technische specificaties van de gegeven

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CHAPTER 0. SAMENVATTING

Eerst is er een simulatie genaakt van het gecre¨ eerde exciatie en detectieveld. Vervol- gens is de respons van de SPIONs op dit exitatiesignaal gesimuleerd. Deze respons is berekend voor verschillende dieptes en laterale afstanden. Met deze respons is vervolgens een verband opgesteld tussen de detectie diepte en het onderscheidend vermogen.

Het model is gevalideerd aan de hand van metingen. Deze metingen zijn vericht aan een sample met MagTrace. De resultaten van de metingen waren niet afdoende om het model te valideren.

De detectie diepte van de DiffMag handeheld probe voldoet niet aan de de klinsiche voorwaarden voor het detecteren van SKW’s. Daarentegen is het oplossend vermo- gen van de DiffMag handheld probe op een maximale axiale afstand van 1.06 cm hoog genoeg om het ”shine-through” fenomeen te overkomen.

iii

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Introduction

On annual basis head and neck cancer (HNC) accounts for 500.000 registered cases worldwide and for 3000 cases in the Netherlands [1, 2, 3]. HNC is the 8th most common tumour for men and the 9th for women [4]. Lymphatic neck metastasis is the most crucial in prognosis and thus of high importance in treatment decision making[5]. The sentinel lymph nodes (SLN) are lymph nodes which have the high- est odds of being drained by a tumour in the head and neck region. [5]. Head and neck carcinoma are often squamous cell carcinomas and contain the pharynx, larynx, paranasal sinuses, nasal cavity, the salivary glands and the oral cavity which consists of i.e. the tongue and the floor of the mouth (FOM) [6]. A sentinel lymph node biopsy (SLNB) is performed for selectively SLN staging. The SLN is removed for histopathological examination to determine the lymph node status. The SLNB procedure is proven for breast cancer while it is viable for head and neck cancer but not commonly utilized yet [7].

The current standard of care of the SLNB is to utilize a radioactive tracer(Technetium- 99

^m

or

^99m

Tc nanocoll) or blue dye that is injected near to the primary tumour. Blue dye is used for visual guidance while the radioactive tracer is detected with a gamma handheld probe. Afterwards the gamma probe is used to find the SLN. Finally, the SLN which contributes most to the measured signal, is removed. A new measure- ment will be performed after removing the SLN in order to inspect if there is still a signal coming from the region of interest or not. For metastatic identification, the dissected SLN(s) are examined by histological protocol [8]. However, the use of radioactive tracers for the SLNB procedure is not ideally as there are issues with safety and logistics as well [9, 10]. Further, blue dye has several drawbacks as well like concealing the intraoperative field of view of the surgeon and leaving a tattoo strain on the skin [10].

Therefore, a new option for SLNB could be magnetic detection with Super Para- magnetic Iron Oxides (SPIONs). This magnetic detection will have advantages compared to the current standard of care of a SLNB procedure. The magnetic de- tection of SPIONs with SentiMag

^®

(Endomagnetics ltd., London, United Kingdom) is already proven feasible for breast cancer and not inferior to the current standard of the SLNB procedure [10]. Nevertheless, this technique depends on the linear magnetic response of the SPIONs and is thus exposed to signal coming from dia- magnetic tissue [11]. To improve the magnetic detection of SPIONs in the SLNB procedure, Differential Magnetization (DiffMag) is currently being researched. This technique exploits the non-linear magnetic characteristics of the SPIONs which can improve the selectivity and sensitivity of intra-oprative magnetic detection for the

1

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CHAPTER 1. INTRODUCTION

SLNB procedure[11]. The difference between the linear and non-linear magnetiza- tion curve is shown in Figure 1.1.

Figure 1.1: Difference between the magnetization for an ideal SPIO nanoparti-

cle(blue) and diamagnetic(red) matter against the same applied magnetic field [11].

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CHAPTER 1. INTRODUCTION 1.1. SHINE THROUGH PHENOMENON

1.1 Shine through phenomenon

Detection of carcinomas situated in the FOM is far more difficult than carcinomas in other sites of the oral cavity [12, 13, 14]. This is due to the shine-through phe- nomenon that causes an inability to differentiate between the signals from SLNs and the primary tumour[12]. This phenomenon is caused by the proximity between the peri-tumoural injection site and the SLNs along with the insufficient resolving power of the current detection techniques as the SentiMag

^®

and gamma probe [12, 14].

The gamma probe has a linear relationship between the resolving power and axial distance [15]. This means that the resolving power becomes worse as the measure- ments are further from the gamma probe. The resolving power is defined as the closest distance at which two point sources can be distinguished. The proximity between the injection site and SLN can be as close as 13 mm [16, 17]. This shine- through phenomenon causes the SLNB to fail. This phenomenon can be illustrated in Figure 1.2.

Figure 1.2: Visual representation of the shine-through phenomenon. T represents the primary tumour whereas the red circle represents a SLN in the close vicinity of the tumour. The yellow circle reflects the focus of the injection site. The yellow circle overshadows the SLN and primary tumour which causes the shine-through phenomenon. As a result, the SLN can not be identified. Figure from [12].

3

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1.2. CONCEPT OF DIFFERENTIAL

MAGNETOMETRY CHAPTER 1. INTRODUCTION

1.2 Concept of Differential Magnetometry

A refinement of the SentiMag

^®

could be the DiffMag handheld probe. Both mag- netometers exists of an excitation and detection coil. The magnetometer excites a magnetic field by putting a current through an alternating current (AC) coil and de- tects signals with a detection coil. The DiffMag handheld probe is a magnetometer with an additional DiffMag procedure [9]. The DiffMag handheld probe technique exploits the non-linear SPION’s behaviour. Because of the different physical be- haviour between the SPIONs and human diamganetic tissue, the response to an applied external magnetic field will be different as perceived in Figure 1.3.

Figure 1.3: Concept of DiffMag. The colors red, blue and green correspond to the offset field -20, 0, +20 respectively. To the left: different response to an applied alternating field. To the right: (C) gives the different magnetization of the SPIONs.

The red and green colors are corresponding to the small amplitude to the lower right graph. (D) represents the time derivative of the magnetization (∆U ), which is equal to the difference between DiffMag signal amplitude with zero offset and non-zero offset. Figure acquired from [18].

An AC modulated field with and without direct current (DC) or offset results in

different signal amplitudes for SPIONs [19]. DiffMag is able to detect this difference

and thus DiffMag can detect the SPIONs in a diamagnetic environment. As pre-

sented in Figure 1.3, the amplitude of the signal is higher with zero DC offset than

with non-zero offset. The DiffMag signal amplitude is now obtained by subtraction

of the signal without DC offset minus the signal with DC offset. Now, the SPIONs

show a high signal compared to the approximate zero signal of the diamagnetic

tissue.

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CHAPTER 1. INTRODUCTION

1.2. CONCEPT OF DIFFERENTIAL MAGNETOMETRY

The excitation coil of the DiffMag handheld probe generates a magnetic field that can be described with Equation 1.1 [9]:

H = H

AC

sin(ωt) + H

DC

(1.1)

The SPIONs’ response is measured in the detection coil of the DiffMag handheld probe according to Faraday’s law of induction[18]. The response of the SPIONs to the applied magnetic field can be approximated by the Langevin Equation:[11, 19, 18]:

M = M

_s

L(x), with L(x) = coth(x) − 1/x (1.2) Here, M

_s

is the saturation magnetisation in A/m. Due to the magnetic susceptibility of the SPIONs, the magnetization of the SPIONs will change with the frequency of the excitation signal and will induce a voltage in the detection coil which is proportional to the time derivative of the SPION-specific magnetization [18, 11]:

U = −ωS(z)V

_c

M = dM

dt (1.3)

Here, ω = 2πf in rad/s, S(z) in the coil constant in T/A and V

_c

the core volume

that contains the iron oxide in m

³

.

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1.3. SCOPE OF THIS THESIS CHAPTER 1. INTRODUCTION

1.3 Scope of this thesis

The main clinical application that is focused on is a SLNB, which is intended to resect lymph nodes with highest chance on containing potential metastases. The current standard of care for a SLNB has several drawbacks. A magnetic procedure to perform the SLNB will have advantages like less complex logistics and safety risks.

This new method utilizes SPIONs. These nanoparticles are usually injected peri- tumoural and accumulate in a primary tumour and in (regional) SLNs. Although this magnetic SLNB procedure is proven viable, some false-positive cases could arise due to the shine-through phenomenon as this is the case with the gamma probe.

Ongoing research involves development of detection methods for both open and la-

paroscopic surgery. Some technical specifications must be defined for the differential

Magnetometry (DiffMag) handheld probe, before the probe can be utilized in the

clinic. Hence, the following question: ”What is the resolving power and detection

depth of the simulated DiffMag handheld probe?”. Therefore, the scope of this re-

search is to simulate the detection depth and resolving power with regard to the

DiffMag handheld probe.

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Chapter 2

Methods

A list of clinical requirements is assembled for the DiffMag handheld probe. The detection depth and the resolving power are the most important requirements for clinical employment. First a list of specifications of existing methods is being assem- bled. The list of specifications will be based on the gamma probe and the SentiMag

^®

specifications whereas the list of requirements will be based on the clinical SLNB requirements. An important specification of the handheld probe must be a high resolving power which means a small FWHM is required [11, 20].

2.1 Specifications and Requirements

In order to perform a SLNB in the head and neck area, a localization of the SLN is required. The detection depth is defined as the deepest point in space where SPIONs can be detected. The cervical lymph nodes are rooted 3 ± 1.1 cm deep in the neck [21]. Therefore a maximum depth for transcutaneus detection would be 4.1 cm whereas the minimum depth will be 1.9 cm. The resolving power is defined as the shortest distance between two sources in which these sources can be detected independently. A high resolving power is required to detect a SLN close to the injection site in the neck area [16]. Table 2.1 summarizes the experimentally established detection depth and resolving power for the DiffMag handheld probe, SentiMag

^®

and the gamma handheld probe. The in vivo detection depth of the SentiMag

^®

is 2.5 cm for an uptake of 500 µg of Sienna

⁺^®

, whereas this depth is 1.9 to 2.2 cm for an 50 µg uptake [22].

The detection depth of the DiffMag handheld probe is 1.0 cm for 4 µl of SPIONs[21].

Note that the uptake of SPIONs in a SLN is assumed to be the same as with

radioactive tracers. Therefore, the detection specifications are based on the same

volume of particles as for the gamma probe. In addition the detection depth of the

gamma probe can be very deep but loses its resolution quickly.

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2.1. SPECIFICATIONS AND REQUIREMENTS CHAPTER 2. METHODS

The concentration and volume of iron oxides in the SLN is determinative for the detection depth and resolving power. For clinical applications in the head and neck area, a resolving power between 0.5 and 1.0 cm is required according to an head and neck oncologist from Medisch Spectrum Twente.

Table 2.1: Detection specifications.

Specification DiffMag (50 µL) SentiMag

^®

(50 µL) γ-probe

Detection depth [cm] 1.0 [21] 2.5 [22] 1.0≤ [16]

Resolving power [cm] (depth=0 cm) 1.9 [21] 2.4 [21] ≈3.5 [16]

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CHAPTER 2. METHODS 2.2. MODEL OF DIFFMAG HANDHELD PROBE

2.2 Model of DiffMag handheld probe

The steps for developing the MATLAB

^®

(version 2018b, The MathWorks Inc., Nat- ick, MA, USA) script are run through. A model for simulating the detection depth and the resolving power is developed, with respect to the technical specifications of the DiffMag handheld probe. First, a DiffMag signal is produced alongside the simulation of the excitation and detection magnetic field (Bz). Second, a magnetic particle response will be added to the model. Last, a simulation of the detection depth along with its resolving power at that depth is made.

2.2.1 Simulating the DiffMag signal in MATLAB ^®

First a schematic cross-section of the DiffMag handheld probe tip is illustrated in Figure 2.1. This DiffMag handheld probe contains an integrated system of the excitation and detection coils. The excitation coil produce a magnetic excitation field, called Bz

_ex

in Tesla (T). The concern for the detection coils lie within the coil sensitivity in T/A. This coil sensitivity is a measure for the detection sensitivity and is called Bz in the MATLAB

^®

script.

Figure 2.1: Schematic cross-section of the tip of the DiffMag handheld probe with two detection and compensation coils (orange), two AC excitation coils (green) and one DC excitation coil (blue). Figure enquired from [9].

A set of global variables was created and gathered from [18]. By producing a mag- netic field with and without an offset, an excitation signal was produced according to Equations 2.1 and 2.2. Adding different offsets is possible to change the magne- tization of the SPIONs:

H(t)

_up

= V

c

M s

K

_b

T (of f set + AC

_amp

) (2.1) H(t)

_down

= V

_c

M s

K

_b

T (of f set − AC

_amp

) (2.2)

Here V

_c

is the iron core volume of one particle in m

³

, M

_s

the saturation magnetization

in A/m, K

b

the Boltzmann constant and T the temperature which is set at the

temperature of the human body around 310 K. The offset is the DC signal which

later on can be simulated and is responsible for the early magnetic saturation of

the SPIONs compared to the diamagnetic tissue [18]. Also AC

amp

is the amplitude

of the excitation signal that varies with the distance to the excitation coil. This

variation in signal strength over depth can be approximated by using the magnitude

of that magnetic field (Bz) at that exact same depth. This Bz field is induced

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2.2. MODEL OF DIFFMAG HANDHELD PROBE CHAPTER 2. METHODS

by the excitation coil of the handheld probe and is simulated with the help of Soleno(in-house build, written in MATLAB

^®

, C++) according to Ampere’s law which describes the characteristics of the magnetic field originated from the changing electrical current[9].

The SPION magnetization can be calculated with the help of the Langevin equation.

The response of the SPIONs to excitation signal is equal to the time derivative of the magnetization:

d

dt M (t) = nM

_s

V

_c

f L(ξ

₊

) − L(ξ

−

) (2.3) Here L(ξ

₊

) and L(ξ

−

) are respectively the excitation fields with the highest and lowest offsets. These field parameters can be described with regard to Equations 2.1 and 2.2 and is given by:

L(ξ

₊

) = M

_s

(coth(H(t)

_up

) − 1

H(t)

_up

(2.4)

L(ξ

−

) = M

_s

(coth(H(t)

_down

) − 1

H(t)

_down

(2.5)

Here, H is the dimensionless applied magnetic field. Substituting Equations 2.4 and 2.5 into 2.3 results in:

M

_spions

= nf V cM s(coth(ξ

_up

) − 1/(ξ

_up

) − coth(ξ

_down

) + 1/(ξ

_down

)) (2.6) with ’n’ the SPION density number in m

⁻³

[19]. Equation 2.6 is written by Max Rietberg in MATLAB

^®

(version 2020a) and adjusted to fit into the model for simu- lating the SPION response. With the mentioned SPION’s magnetization response, the signal voltage (U

det

, V) can now be calculated with the following Equation:

U

_det

/S

_coil

= − d

dt M (t) (2.7)

Here, S

_coil

is the coil sensitivity which varies over different depths. Plotting this against the offset, generates a signal that represents the response of the SPIONs.

2.2.2 Simulating the detection depth and resolving power of the handheld probe in MATLAB ^®

In Section 2.2.1 a set-up was made to provide simulations. First an excitation signal was created followed by a response from the SPIONs to this signal. In this section the magnetic field produced by handheld probe is simulated in MATLAB

^®

with the Soleno function ’soleno calcB’. The input values can be found in Appendix 2.3.

The output values are 100x100 matrices containing the excitation magnetic field and the detection coil sensitivity for Bz

_ex

and Bz respectively. These output values are given for axial distances lateral distances as described in Table 2.2.

First, an orientation for the axes can be perceived in Figure 2.2. The axial distance

represents the distance from the surface of the probe while the lateral distance

represents the distance to the axial axis.

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CHAPTER 2. METHODS 2.2. MODEL OF DIFFMAG HANDHELD PROBE

Figure 2.2: Axes frame orientation with respect to a handheld probe.

Keeping this frame in mind, a 3D plot can be simulated with an induced magnetic field. This plot is constructed from magnetic field strength, produced by the DiffMag handheld probe and by a grid of lateral and axial distances from the handheld probe.

The specifications of the handheld probe are described in Table 2.3. According to Visscher et al., the background noise can be set to 10

⁻⁷

V which is equal to 10 counts and is can be represented by a transverse (x,y = z) plane in the 3D representation.

Table 2.2: Grid of lateral and axial distances.

Axial distance in cm Lateral distance in cm Number of steps

0.1 to 4 -4 to +4 100

Table 2.3: Handheld probe specifications R

in

[m] R

out

[m] Z

low

[m] Z

high

[m] N

windings

# 0.0060 0.0095 -0.0016 0.0000 380 0.0060 0.0095 -0.0196 -0.0180 -380

The Full Width Half Maximum (FWHM) of the SPIONs response is calculated for

each step in the depth (Z-) direction, in order to calculate the resolving power. This

is provided by taking the values of the detection signal amplitude for each depth at

each distance from the probe’s surface.

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2.3. VALIDATION CHAPTER 2. METHODS

2.3 Validation

Two separate measurements are required to validate the MATLAB

^®

model as de- scribed in Section 2.2.1. Calibration is performed prior to each measurement. All measurements will be performed using the DiffMag handheld probe. The offset was changed to 30 mT only. Resolving power measurements are single measurements.

A sample with MagTrace SPIONs will be used for the measurements. Furthermore, all counts are written down in Excel

^©

(Microsoft, Washington, United States) after each measurement.

2.3.1 Detection depth

The measuring set-up, developed by Fleur van Wezel is utilized for the detection depth measurements. This set-up is illustrated in Figure 2.3. A volume of 50 µL pure MagTrace with a concentration of 28 µg/µL of iron nanoparticles is used.

The whole set-up for detection depth measurements is illustrated in Figure 2.4. The measurement with 50 µL sample is placed in the first hole (0 cm) and a measurement is run. The measurements are performed in duplo and shown in Figure 3.1. The measurement protocol for the axial distance is as follows:

1. Make a sample with 50 µL MagTrace with a concentration of 28 µg/µL.

2. Balancing DiffMag with a sensitivity of 100 nV.

3. Put the handheld probe in the standard.

4. Put the sample in the first hole of the foam measurement set-up.

5. Put the handheld probe in the foam measurement set up as well.

6. Start the measurement.

7. Write down the amount of counts into Excel.

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CHAPTER 2. METHODS 2.3. VALIDATION

Figure 2.3: Set-up for detection depth measurements. The 1.6 cm holes are de- signed to pin the DiffMag handheld probe. the small holes in the bottom contain the samples. the holes are 0.0, 0.5, 0.7, 1.0, 1.3, 1.5, 1.7 and 2.0 cm far from the probe [21].

Figure 2.4: Complete measurement set-up for detection depth measurements.

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2.3. VALIDATION CHAPTER 2. METHODS

2.3.2 Resolving power

Two tubes are filled with respectively 50 and 2.4 µL MagTrace. The tube with 50 µL represents the primary tumour whereas the 2.4 µL represents the SLN with a 4.8% uptake. This is percentage is based on the radioactive tracer uptake in the SLN which depends on the particle’s size[12, 22]. One measurement consists out of three parts:

1. Measurement with 50 µL.

2. Measurement exactly in between both samples (0.5*distance).

3. Measurement with 2.4 µL.

These three parts and the set-up are presented in Figure 2.5. These measurements are repeated for 10 different lateral distances. The distances are measured with a digital ruler.

Figure 2.5: Complete measurement set-up for lateral measurements. The numbers

in the probe represent the step that is described as above.

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Chapter 3

Results

Visual representations of the calculations by the developed MATLAB

^®

script are shown. All results are based on the technical specifications of the DiffMag handheld probe. The simulation results will consist of representations of the excitation and detection field, the response of the SPIONs to this field and the final resolving power over different detection depths.

3.1 Simulation results

An induced magnetic excitation field in vacuum, responsible for the excitation of the SPIONs is produced. This excitation field is shown in Figure 3.1. The figure below is a simulation of the magnetic field over the axial and lateral direction. Note that this field begins at 0.1 cm instead of 0 cm because of the cover thickness of around 0.1 cm over the coils. The different colors of the field lines represent the strength of the magnetic field at that exact coordinate. The maximum field strength at the origin or center of the excitation coil is 6.15 mT while the minimum field strength is 0.23 mT at 2.39 cm axial distance.

-4 -3 -2 -1 0 1 2 3 4

lateral distance [cm]

0.5 1 1.5 2 2.5 3 3.5 4

axial distance [cm]

1 2 3 4 5 610^-3

Figure 3.1: Produced magnetic excitation field by DiffMag handheld probe. The

different colors of the field lines represent the magnitude of the magnetic field in T.

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3.1. SIMULATION RESULTS CHAPTER 3. RESULTS

In Figure 3.2, the produced magnetic detection field by the DiffMag handheld probe is simulated. What can be extracted from this plot is the strength or magnitude of Bz along the axial and lateral axis. Figure 3.2(a) represents how the magnetic field is behaving along the lateral axis. Figure 3.2(b) shows a smooth graph of the behavior of the magnetic field in the axial direction. Last, Figure 3.2(c) shows the magnetic field in all possible directions and has a maximum magnitude of Bz= 0.036 T at 0.1 cm depth.

(a) Bz superior view.

(b) Bz side view.

(c) Bz oblique view.

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CHAPTER 3. RESULTS 3.1. SIMULATION RESULTS

Next, the simulation of the SPION response to the excitation signal with different offsets, is presented in Figure 3.3. The response of the SPIONs is decreasing due to an increasing offset.

Figure 3.3: Detected signal in counts 100 nV against an increasing offset in mT.

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3.1. SIMULATION RESULTS CHAPTER 3. RESULTS

A representation of the SPION response to the magnetic field from Figure 3.2 can be perceived in Figure 3.4. The maximum amount of counts at 0.1 cm distance from the SPIONs is 40880 as can be perceived in Figure 3.4(b). The noise is simulated as a dark blue transverse plane with a magnitude of 10 counts. It is hard to see where the signal of the SPIONs stops and the SNR becomes too low. The response is plotted along the axial and lateral axis of the DiffMag handheld probe. The response of the SPIONs will be maximal when there is no distance between the probe and the SPIONs as can be seen in Figure 3.4. Also when the lateral distance increases, the signal amplitude in counts will decrease exponentially. What can be perceived in Figure 3.4(a) is a view of the behaviour of the received signal along the lateral axis. Figure 3.4(b) shows a smooth graph of the behavior of the magnetic field in the axial direction.

(a) SPION response top view. (b) SPION response side view.

(c) Zoomed in representation of (a). (d) Zoomed in representation of (b).

Figure 3.4: SPION response, top(a) and side(b) view with zoomed in representa-

tions.

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CHAPTER 3. RESULTS 3.1. SIMULATION RESULTS

The maximum axial distance value can be found in Figure 3.5. The maximum distance is 1.06 cm as this is where the signal to noise ratio (SNR) becomes too low.

(a) Maximum axial distance where Bz ≥ noise.

(b) Maximum axial distance where Bz ≥ noise.

Figure 3.5: Maximum axial distance top view and side direction, where Bz ≥

noise. Color values expressed in T.

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3.1. SIMULATION RESULTS CHAPTER 3. RESULTS

Nevertheless, it is still hard to exclude the direct relation between the resolving power and the detection depth. Therefore, the FWHM is calculated for each increase in axial distance and plotted along the axial axis as shown in Figure 3.6(b).

0 0.5 1 1.5 2 2.5 3 3.5 4

Axial [cm]

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Lateral [cm]

(a) Lateral versus axial distance.

-4 -3 -2 -1 0 1 2 3 4

Lateral [cm]

0.1 0.15 0.2 0.25 0.3 0.35 0.4

Axial [cm]

(b) Axial versus lateral distance.

Figure 3.6: Resolving power of the DiffMag handheld probe in both axial and lateral direction.(a) The lateral versus axial distance and (b) Axial versus lateral distance.

The dependency of the resolving power on the marginal increase of the axial distance

is shown in Figure 3.6(a). What can be seen is a linear increase, starting at 0.57

cm deep, of the nearest detectable SPION. An increase in distance represents a

decrease in resolving power. The beginning of the graph is remarkable. The graph

first decreases and increase linearly afterwards. This suggest that the resolving

power first increases and decreases later on. The dependency on the maximal axial

distance per increase of the lateral distance is shown in Figure 3.6(b). What can

be seen is a parabolic relationship. This graph represents the maximum detection

depth for every lateral distance from the axial axis. Remarkable about this graph is

that the maximum dept at which measurements can be done is around 0.4 cm deep.

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CHAPTER 3. RESULTS 3.1. SIMULATION RESULTS

The detection coil of the handheld probe with the SPIONs’ response is simulated for an increasing current in Figure 3.7. Through Figure 3.7(a) to 3.7(d) the current increases with 5 Ampere. The other views can be found in the appendix. What can be extracted is the increasing detection depth and inherently a broader lateral range.

(a) SPION response superior view 5 A. (b) SPION response side view 10 A.

(c) SPION response front view 15 A. (d) SPION response front view 20 A.

Figure 3.7: SPION response with increasing current from 5 to 20 A.

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3.2. VALIDATION RESULTS CHAPTER 3. RESULTS

3.2 Validation results

Data acquired according to the protocol reported in Section 2.3.1 is illustrated in Figure 3.8. The exact mean values with their standard deviation (std) of the axial measurements can be found in Table 3.1.

Table 3.1: Average axial measurements with standard deviation.

Axial cm Signal Std.

0.0 6191 173.5

0.5 626 86.5

0.7 229 29.5

1.0 89 17.5

1.3 48 1.5

1.5 43 2

1.7 40 2

2.0 38 0.5

The graph of the axial measurements show a decrease in counts between 0.0 and 0.5 cm. Thereafter, a more gradual decrease in counts between 0.5 and 1.3 cm is perceived in the zoomed in frame. In this frame, the signal does not cross the noise line. The amount of counts do approximate the noise line closely between the 1.3 and 2.0 cm axial distance.

Figure 3.8: Axial measurements result with a zoomed in frame.

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CHAPTER 3. RESULTS 3.2. VALIDATION RESULTS

Data acquired according to the protocol reported in Section 2.3.2 is illustrated in Figure 3.9. The bars in Figure 3.9 represent the number of counts in that position.

The exact values of all measurements can be found in Appendix A.3. The bars that correspond to the 50 µL sample at position 1 have the most counts whereas the counts at position two have the least amount of counts. Especially the measurement with a distance of 4.0 cm has very little counts at position two. This represents that there is almost no signal measured in between the samples. This applies also for the 3.0 cm distance. Important is that the bars at position 3 must be higher than the bars at position two in order to distinguish both sample from each other. The value where this distinction is minimal but still existing is for the 2.0 cm distance. The orange line represents the limit for the distinction between the two samples.

Figure 3.9: Lateral measurements result. Numbers 1, 2, 3 on the horizontal axis

correspond to the positions of the DiffMag handheld probe as perceived in Figure

2.5. Number 1 corresponds to the 50 µL sample and the 2.4 µL sample corresponds

with number 3. Number two is a measurement exact in between the two samples.

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Chapter 4

Discussion

The developed model is based on two crucial assumptions:

1. The model is based on the Langevin equation. This equation is a simplification of how the SPIONs really respond to the applied magnetic field with its offset.

The Langevin function lacks of taking the interaction between SPIONs and the polydispersity (i.e. not all particles are exactly of the same size and shape) of the particles into consideration.

2. The model is not based on volume of a sample, but on iron concentration.

Therefore, the influence of the injected volume of SPIONs can not be simulated and thus the resolving power and the detection depth are not directly linked to a volume. The resolving power and maximum axial distance of the real DiffMag handheld probe is dependent on the volume of the sample. This causes a discrepancy between the real DiffMag handheld probe and the model.

The maximal axial distance can only be defined up to 1.06 cm deep due to the signal to noise ratio (SNR). Therefore, the resolving power can only be defined for axial distances between 0 and 1.06 cm. This maximal distance is not in accordance with the clinical requirement of a minimum axial distance of 1.9 cm.

The values of the SPIONs’ response signal should be a factor x10

³

less in order to validate the the relationship between the resolving power and detection depth.

This will show a clear transition between the signal and noise. Thereby, the relation between 0 and ± 1 cm in Figure 3.6(a) was expected to be linear. This linear rela- tion was assumed for the DiffMag handheld probe, as the relation between resolving power and axial distance is linear for the gamma probe. It appears that this is not true for an axial distance between 0 and ± 1 cm. This is caused by the difference between the gamma probe and the DiffMag probe. The DiffMag probe must first induce a signal while the gamma probe only has to measure the radiation. Further- more, the characteristicsof the magnitude of the magnetic field is different from the intensity of the radiation and therefore the relationship between the resolving power and axial distance is different.

Further, the relationship between the axial distance versus the resolving power sug-

gests that the maximum axial distance, that can be measured, is 0.4 cm. This is

not true as the the validation measurements show that the DiffMag handheld probe

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CHAPTER 4. DISCUSSION

This is due to a possible mistake in the calculation of the FWHM for the axial dis- tance. These axial FWHM calculations were not made till the exact 1.06 cm, but up till 0.4 cm.

The model is validated with measurements with the DiffMag handheld probe and MagTrace. The validation is not maximal reliable because of the following points:

1. For both, the axial and lateral measurements, the amount of data points is very limited. This is due to limited laboratory time and the use of standard measurement set-ups as well.

2. It was not possible to measure the counts with a simultaneous increase of both the axial distance and lateral distance.

3. The measurements for the resolving power are not provided with a very solid measuring set up. The samples are measured each time with a different dis- tance between the two samples. The distance is measured between the sample and a measurement is done. However the samples were not pinned so they could have moved closer or further from each other. This could explain some failures in the measurment results. It was very hard to fixate the two samples exactly at the give distance because it was done manually.

4. The maximum detection depth was depending on the MagTrace volume in the sample. This volume dependency is not included in the MATLAB

^®

model and therefore hard to validate if the model is correct or not.

Further, the maximal axial distance that can be reached seems to be more than 2 cm. However, at 1.3 cm deep the signal is very close to the noise line and therefore a clear distinction between the signal and the noise can not be made. Although the signal is twice as high as the noise here, the graph has a dip here and is flattening from point 1.3 cm. This means that this small decrease in counts can not only be addressed to an increasing axial distance but also to reading errors and a heated DiffMag handheld probe.

Additionally, the maximum resolving power is defined as 2.0 cm at an axial distance

of 0 cm. The resolving power at 1.3 cm axial distance would be 0.7 cm, according

to the MATLAB

^®

model, while, the maximum resolving power is 2.0 cm according

to the resolving power measurements. Taking the resolving power and the maximal

axial distance into consideration, the MATLAB

^®

model is not in accordance with

the developed DiffMag handheld probe. Thereby, the measurements with the Diff-

Mag handheld probe shows that it does not meet the clinical requirements for the

resolving power and maximal axial distance.

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Chapter 5

Conclusion

What is the resolving power and detection depth of the simulated DiffMag handheld probe?

The maximum resolving power and detection depth that can be defined is respec-

tively 0.64 cm at a axial distance of 1.06 cm. Comparing this result to the require-

ments from the clinic, it turns out that the resolving power is sufficient to distinguish

two SLNs and overcome the shine-through phenomenon at a maximum axial dis-

tance of 1.06 cm as this requires a resolving power of ≤ 1.3 cm. Nevertheless, the

maximum axial distance is not sufficient as this requires a distance of 1.9 cm. There-

fore, the DiffMag handheld probe is not clinical applicable for the SLNB procedure

in the head and neck area.

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Chapter 6

Recommendations

The DiffMag handheld probe is very promising for the SLNB procedure for head and neck cancer. Although the DiffMag handheld probe could not overcome the shine-through phenomenon because of the limited resolving power in the head and neck area, There are some improvements possible to improve the simulation and make it more reliable.

The first improvement would be to rewrite the Langevin function. This is important in order to make this simulation depending on the SPION volume. With volume de- pendency, a simulation could be provided for different amount of SPIONs. This will give the exact resolving power for different axial distances. This can later be used for reversed calculation which means that an input of the required resolving power can be used to calculate the amount of SPIONs that is needed to meet this requirement.

Furthermore, a more accurate approximation than the Langevin equation can be used to simulate the SPIONs’ response. This equation may be too simple to simu- late the SPIONs’ response and therefore result in different values for the maximal axial distance and resolving power. This approximation can be expanded taking the sample volume, the polydisperity and the interaction between SPIONs into account.

Furthermore, the axial FWHM calculations must be provided up till at least 1.06 cm. This can be done by changing the axial FWHM calculation section in the script.

This can be done using a different approach for the FWHM calculation.

The validation of the model needs to be done more specifically. A better practice would be if the measurements are performed as follows: For each step in axial dis- tance, measurements for each lateral distance must be performed. Herewith, a plot with the exact relation between the resolving power and axial distance can be made and compared to the relationship of the model. Herewith, the model can be com- pared to the measurements and therefore reliably validated.

Furthermore, the resolving power measurement must be provided with a more stable measurement set-up. Both the samples should be pinned so that they can not move anymore when the distance between them is noted down and the measurement starts.

This can be done by making a phantom with fixed distances between the samples.

It is important that there are enough data points in this set-up. Distances between

0.5 and 4.5 cm with a step size of 0.3 cm is being advised.

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CHAPTER 6. RECOMMENDATIONS

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BIBLIOGRAPHY BIBLIOGRAPHY

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[16] D. A. Heuveling, K. H. Karagozoglu, A. Van Lingen, O. S. Hoekstra, G. A. Van Dongen, and R. De Bree, “Feasibility of intraoperative detection of sentinel lymph nodes with 89-zirconium-labelled nanocolloidal albumin PET-CT and a handheld high-energy gamma probe,” EJNMMI Research, vol. 8, pp. 6–11, 2018.

[17] G. B. Flach, E. Bloemena, W. M. C. Klop, R. J. Van Es, K. P. Schepman, O. S. Hoekstra, J. A. Castelijns, C. R. Leemans, and R. De Bree, “Sentinel lymph node biopsy in clinically N0 T1-T2 staged oral cancer: The Dutch multicenter trial,” Oral Oncology, vol. 50, no. 10, pp. 1020–1024, 2014.

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sentinel lymph node biopsy,” AIP Advances, vol. 7, p. 56720, 2017.

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Appendix A

A.1 Experimental validation

Table A.1: First Axial measurements Axial cm Signal

0.0 6017

0.5 539

0.7 258

1.0 71

1.3 46

1.5 41

1.7 38

2.0 37

Table A.2: Duplo axial measurements.

Axial cm Signal

0.0 6364

0.5 712

0.7 199

1.0 106

1.3 49

1.5 45

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APPENDIX A. APPENDIX A

A.2. LIST OF SYMBOLS, UNITS, ELEMENTARY CONSTANTS AND QUANTITIES Table A.3: Resolving power. Numbers represent counts in 100 nV.

50 µL in between 2.4 µL 5 cm

4012 52 563

4.5 cm

4116 54 558

4.0 cm

4111 46 474

3.5 cm

4146 60 548

3.0 cm

4111 99 539

2.5 cm

4106 402 525

2.0 cm

4000 421 556

1.5 cm

3970 1058 548

1.3 cm

4230 1470 560

1.1 cm

4166 2688 591

0.8 cm

4156 2246 727

A.2 List of symbols, units, elementary constants and quantities

Table A.4: List of symbols, units, elementary constants and quantities

T 300.15 Kelvin [K]

µ

0

2π · 10

⁻⁷

Vacuum magnetic permeability [N/A

²

] Kb 1.38064852·10

⁻²³

Boltzmann constant in [J/K]

Ms 8.7535·10

⁵

Saturation magnetization [Am

²

] u

0

· M s 0.55 [T] for Fe3O4/Fe2O3

Dc 17.6·10

⁻⁹

Resovist average diameter [m]

Vc 2.8545·10

⁻²⁴

Iron core volume [m

³

]

n 1.5·10

¹³

SPIO nano-particle density [#/m

³

]

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A.3. MATLAB

^®

SCRIPT USAGE APPENDIX A. APPENDIX A

A.3 MATLAB ^® script usage

The variable ’N’ are the number of steps that the script is running. This can be changed to any value. The more steps the more precisely the simulations are. The number is set to 1000 as the standard. Further, the input values for the excitation and detection coil can be changed in the following part of the script as represented in table A.5. Because the excitation part of the handheld prob is only one excitation coil, the values are single.

Table A.5: DiffMag handheld probe variables for the excitation and detection coil HH probe field DETECTION:

Scoil = 37.8e-3; [mT/A]

Rin = [0.0060,0.0060]; Internal radius [m]

Rout = [0.0095,0.0095]; Outer radius [m]

Zlow = [-0.0016,-0.0196]; Detection coil height [m]

Zhigh = [0.0000,-0.0180]; Detection coil separation [m]

Nturn = [380,380]; Number of windings

I = [1,1]; Current through one winding [A]

Nloop = [5,5]; Number of layers

Itot = Nturn.*I; Total current [A]

HH probe field EXCITATION:

Rinex = 0.0051; Internal radius [m]

Routex = 0.0096; Outer radius [m]

Zlowex = -0.0166; Detection coil height [m]

Zhighex = 0.0000; Detection coil separation [m]

Nturnex = 182; Number of windings

Iex = 1.14; Current through one winding [A]

Nloopex = 5; Number of layers

Itotex = Nturnex.*Iex; Total current [A]

Lastly, the following line must be ’un-commented’ in order to calculate the maximum

axial distance per lateral distance step. This is to set all values to zero that are

lower than the FWHM. This part of the script must be commented to calculate the

resolving power per axial distance step.

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APPENDIX A. APPENDIX A

A.4. SPIONS’ RESPONSE FOR DIFFERENT CURRENTS

A.4 SPIONs’ response for different currents

(a) Oblique view of Figure 3.7(a). (b) Side view of Figure 3.7(a).

Figure A.1: Oblique and side view of Figure 3.7(a). Color values expressed in T.

(a) Oblique view of Figure 3.7(b). (b) Side view of Figure 3.7(b).

Figure A.2: Oblique and side view of Figure 3.7(b). Color values expressed in T.

(a) Oblique view of Figure 3.7(c). (b) Side view of Figure 3.7(c).

Figure A.3: Oblique and side view of Figure 3.7(c). Color values expressed in T.

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A.4. SPIONS’ RESPONSE

FOR DIFFERENT CURRENTS APPENDIX A. APPENDIX A

(a) Oblique view of Figure 3.7(d). (b) Side view of Figure 3.7(d).

Figure A.4: Oblique and side view of Figure 3.7(d). Color values expressed in T.

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List of Figures

1.1 Difference between the magnetization for an ideal SPIO nanoparti- cle(blue) and diamagnetic(red) matter against the same applied mag- netic field [11]. . . . 2 1.2 Visual representation of the shine-through phenomenon. T represents

the primary tumour whereas the red circle represents a SLN in the close vicinity of the tumour. The yellow circle reflects the focus of the injection site. The yellow circle overshadows the SLN and primary tumour which causes the shine-through phenomenon. As a result, the SLN can not be identified. Figure from [12]. . . . 3 1.3 Concept of DiffMag. The colors red, blue and green correspond to

the offset field -20, 0, +20 respectively. To the left: different re- sponse to an applied alternating field. To the right: (C) gives the different magnetization of the SPIONs. The red and green colors are corresponding to the small amplitude to the lower right graph. (D) represents the time derivative of the magnetization (∆U ), which is equal to the difference between DiffMag signal amplitude with zero offset and non-zero offset. Figure acquired from [18]. . . . . 4 2.1 Schematic cross-section of the tip of the DiffMag handheld probe with

two detection and compensation coils (orange), two AC excitation coils (green) and one DC excitation coil (blue). Figure enquired from [9]. . . . 9 2.2 Axes frame orientation with respect to a handheld probe. . . 11 2.3 Set-up for detection depth measurements. The 1.6 cm holes are de-

signed to pin the DiffMag handheld probe. the small holes in the bottom contain the samples. the holes are 0.0, 0.5, 0.7, 1.0, 1.3, 1.5, 1.7 and 2.0 cm far from the probe [21]. . . 13 2.4 Complete measurement set-up for detection depth measurements. . . 13 2.5 Complete measurement set-up for lateral measurements. The num-

bers in the probe represent the step that is described as above. . . 14 3.1 Produced magnetic excitation field by DiffMag handheld probe. The

different colors of the field lines represent the magnitude of the mag- netic field in T. . . 15 3.2 Bz, superior side and oblique view. All magnitudes are given in T. . 16 3.3 Detected signal in counts 100 nV against an increasing offset in mT. . 17 3.4 SPION response, top(a) and side(b) view with zoomed in representa-

tions. . . 18

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LIST OF FIGURES LIST OF FIGURES

3.5 Maximum axial distance top view and side direction, where Bz ≥ noise. Color values expressed in T. . . . 19 3.6 Resolving power of the DiffMag handheld probe in both axial and

lateral direction.(a) The lateral versus axial distance and (b) Axial versus lateral distance. . . . 20 3.7 SPION response with increasing current from 5 to 20 A. . . . 21 3.8 Axial measurements result with a zoomed in frame. . . 22 3.9 Lateral measurements result. Numbers 1, 2, 3 on the horizontal axis

Defining the resolving power and detection depth of the DiffMag handheld probe

1

Faculty of science and technology