Robust, planning-based targeted locoregional tumour heating in small animals

Objective. To improve hyperthermia in clinical practice, pre-clinical hyperthermia research is essential to investigate hyperthermia effects and assess novel treatment strategies. Translating pre-clinical hyperthermia findings into clinically viable protocols requires laboratory animal treatment techniques similar to clinical hyperthermia techniques. The ALBA micro8 electromagnetic heating system (Med-logix SRL, Rome, Italy) has recently been developed to provide the targeted locoregional tumour heating currently lacking for pre-clinical research. This study evaluates the heat focusing properties of this device and its ability to induce robust locoregional tumour heating under realistic physiological conditions using simulations. Approach. Simulations were performed using the Plan2Heat treatment planning package (Amsterdam UMC, the Netherlands). First, the specific absorption rate (SAR) focus was characterised using a homogeneous phantom. Hereafter, a digital mouse model was used for the characterisation of heating robustness in a mouse. Device settings were optimised for treatment of a pancreas tumour and tested for varying circumstances. The impact of uncertainties in tissue property and perfusion values was evaluated using polynomial chaos expansion. Treatment quality and robustness were evaluated based on SAR and temperature distributions. Main results. The SAR distributions within the phantom are well-focused and can be adjusted to target any specific location. The focus size (full-width half-maximum) is a spheroid with diameters 9 mm (radially) and 20 mm (axially). The mouse model simulations show strong robustness against respiratory motion and intestine and stomach filling ( ∆T90≤0.14 °C ). Mouse positioning errors in the cranial-caudal direction lead to ∆T90≤0.23 °C. Uncertainties in tissue property and perfusion values were found to impact the treatment plan up to 0.56 °C (SD), with a variation on T 90 of 0.32 °C (1 SD). Significance. Our work shows that the pre-clinical phased-array system can provide adequate and robust locoregional heating of deep-seated target regions in mice. Using our software, robust treatment plans can be generated for pre-clinical hyperthermia research.


Introduction
Hyperthermia, which involves heating tumours to 40 °C-43 °C for approximately one hour, can enhance the effectiveness of radio-and chemotherapy in treatment against cancer.The use of such a combination is shown to be successful in treating a variety of cancers, including melanomas, sarcomas, and bladder, recurrent breast, cervix uteri and rectum tumours (Berdov and Menteshashvili 1990, Overgaard et al 1995, Vernon et al 1996, Van Der Zee et al 2000, Issels et al 2010, Longo et al 2016).In addition, hyperthermia has the potential to overcome treatment resistance to conventional treatment modalities in pancreatic ductal adenocarcinoma (Issels et al 2023).Hyperthermia is effective through a variety of mechanisms, e.g.inhibition of DNA-damage repair, altering perfusion and re-oxygenation, affecting macromolecular delivery, inducing a heat shock response and stimulating the immune system (Dewhirst et al 2005, Oei et al 2015, Mahmood et al 2018).These mechanisms become active at different temperature thresholds, and there remains significant uncertainty regarding the complete spectrum of mechanisms and their respective significance (Wust et al 1998, Dewhirst et al 2005, Song et al 2009).As a result, the optimal use of hyperthermia as a cancer treatment modality remains to be fully understood.Preclinical research is essential to provide a thorough understanding of hyperthermia and its working mechanisms since it allows for the examination of different temperature ranges, durations, and modality combinations in a controlled and reproducible environment.At the same time, to ensure the effective translation of pre-clinical results into viable treatment protocols, a key requirement is that the pre-clinical treatment setting closely resembles clinical treatment.This resemblance enhances the predictive validity and clinical translation of the research.It ensures that the findings accurately indicate the effects of the treatment in a clinical environment.This requires not only that the tumour model is closely resembling the in vivo situation, but also that the therapy is representative for clinical practice.For hyperthermia, this means that the pre-clinical heating technique should be performed analogous to patient treatments.
Various heating techniques can be used to induce hyperthermia in small animals.For heating of superficial tumours, techniques such as a hot water bath, cold-light source, near-infrared laser, focused ultrasound and capacitive heating have been used (Priester et al 2021).Hyperthermia for deep-seated tumours can be performed using focused ultrasound, capacitive systems and radio-frequency heating (Salahi et al 2012, Curto et al 2018, Raaijmakers et al 2018, Capistrano et al 2020, Priester et al 2021, Vicentini et al 2022).Capacitive heating is a method that is most commonly used for deep heating in small animals.However, it lacks the ability to accurately focus heating on deep targets, resulting in heating a very large region.An elegant development to deliver precisely focused heating is the use of magnetic nanoparticles (Capistrano et al 2020, Vicentini et al 2022).Unfortunately, practical applications are still facing challenges in achieving a uniform nanoparticle distribution in the tumour and precise temperature control.Focused ultrasound (FU) and radio-frequency heating (RF) are currently most suitable for localised heating of deep targets with RF techniques being well represented in the clinic.Delivering a reliable thermal dose using FU for moderate hyperthermia relies on scanning an intense focused beam through the target region.This is however still challenging in the abdomen and specifically the pelvic area due to the need for tight feedback control and anatomical complexities such as bone and air pockets (Sebeke et al 2021, Zhu et al 2021).
Reliable, focussed deep hyperthermia in small animals is therefore best achieved using RF.Radiofrequency heating is also widely applied for clinical treatments of deep-seated tumours for the same reasons.Clinical RF systems typically employ a phased-array setup that uses constructive interference at 60-434 MHz to focus energy deposition to the desired target area (Kok et al 2020a).Replicating these systems on a smaller scale for small animals would enable more representative pre-clinical hyperthermia studies.Although several RF/MW systems have been developed for preclinical use, these all use a single antenna, miniature high frequency phased-array systems with true focussing capabilities are still lacking.Consequently, the current limitation in achieving truly representative focused deep heating poses a significant barrier to the accurate translation of pre-clinical findings into clinical treatment protocols.
To address this gap, the 1.66 GHz phased array ALBA micro8 pre-clinical hyperthermia system (Med-logix SRL, Rome, Italy) has recently been developed.This novel small-animal phased-array system is composed of eight 1.66 GHz microwave antennas.The phase and amplitudes can be controlled independently, which enables targeted tumour heating similar to human hyperthermia treatments.The system is equipped with a water bolus, which is a temperature-controlled water-filled bag surrounding the mouse.This water bolus serves a dual purpose: it facilitates direct contact between the antennas and the mouse's skin, ensuring efficient coupling of electromagnetic waves to the animal, while also providing skin cooling to prevent overheating.The microwave array therewith provides a realistic hyperthermia system that can be used for investigating the various working mechanisms, evaluating the therapeutic effects and optimise treatments for multi-modality therapies on tumours.
An effective hyperthermia treatment involves heating tumours to therapeutic temperatures in the range of 40 °C-43 °C.At the same time, healthy tissue temperatures should not exceed 45 °C to avoid thermal toxicity.To achieve adequate tumour heating while minimising excessive heating in healthy tissue, suitable antenna settings need to be found, i.e. phase and amplitude settings for all antennas.Hyperthermia treatment planning (HTP) has emerged as a valuable tool in achieving this goal by applying numerical simulations to predict the energy deposition and temperature distribution in tissues, which can then be used to optimise treatment parameters (Kok and Crezee 2021).The HTP process can be broken down into four steps.First, a simulation model is created, which is a combination of a patient model, typically obtained by segmenting an anatomical MRI or CT image, and a model of the heating device.Dielectric and thermal properties are linked to the tissues and materials included in the simulation model.Next, electromagnetic (EM) field and possibly temperature simulations are performed on the simulation model.Finally, the predicted EM-power absorption and/or temperature distributions are used to optimise treatment settings.HTP can be used for both optimisation of initial settings and for online steering guidance during the treatment session (Franckena et al 2010, Kok et al 2018a, 2021, Androulakis et al 2022).HTP simulations were shown to provide accurate qualitative information (Sreenivasa et al 2003, van Haaren et al 2007, Franckena et al 2010, Kok et al 2014, Kok et al 2018b, Aklan et al 2019) and its clinical application is recommended in clinical guidelines for hyperthermia (Bruggmoser et al 2012, Myerson et al 2014).Furthermore, numerical simulations are often performed to better understand the performance of pre-clinical hyperthermia systems (Salahi et al 2012, Curto et al 2018, Raaijmakers et al 2018, Capistrano et al 2020, Vicentini et al 2022).
Treatment planning can also be utilised for the development and evaluation of heating systems (Wust et al 1996, Kroeze et al 2001, Kok et al 2018c, 2020b, Androulakis et al 2021).This approach allows for the assessment of a system's performance through simulated treatments, which is a fast and thorough method that reduces the need for extensive physical experiments that are time-consuming and potentially expensive.For example, the robustness of heating with a specific device can be evaluated by simulating a variety of realistic conditions and scenarios.Potential issues or challenges that may arise during treatment can therewith be identified and potentially averted up-front by adjusting the treatment protocol.Assessing the capabilities of pre-clinical hyperthermia systems is therefore critical in ensuring reliable heating, achieving the desired therapeutic effect and obtaining reproducible study results.
For these reasons, advanced HTP tools and robustness analyses for the miniature phased-array are needed to make high quality loco-regional hyperthermia available in a pre-clinical setting.In this study, the heat focusing properties of the ALBA micro8 are investigated, different optimisation techniques are compared, and the ability for robust locoregional tumour heating under realistic physiological conditions is evaluated.This is achieved using hyperthermia simulations on phantoms and realistic anatomies with an artificial pancreatic tumour.Treatment robustness is evaluated by investigating the impact of mouse-positioning errors, respiratory-induced motion, differences in stomach and intestine filling, and uncertainties in tissue property and perfusion values.

Methods
EM-field simulations were conducted using the proprietary finite difference time domain (FDTD) treatment planning software, Plan2Heat (Amsterdam UMC, the Netherlands) (Kok et al 2017).Based on the simulated EM fields, the temperature distributions were calculated using Pennes' bioheat equation with constant (enhanced) perfusion values (Pennes 1998).All simulations were performed at a resolution of 0.3 × 0.3 × 0.3 mm 3 .Evaluation of the simulations was done based on both Specific Absorbed Rate (SAR) and temperature.

ALBA micro8 simulation model
The ALBA micro8 pre-clinical hyperthermia system consists of an array of eight identical 1.66 GHz waveguide antennas and a water bolus.A single waveguide was modelled as a rectangular box with an aperture of 16 × 10 mm and a depth of 16 mm.The waveguides are filled with deionised water.The EM source is positioned between the choke and the wall.The eight waveguides were arranged to form a ring with an inner diameter of 50 mm.Inside the antenna array ring, a 90 mm long cylinder of deionised water was simulated to represent the water bolus.The model of the system is shown in figure 1.

Phantom simulations
Phantom simulations were performed to characterise the focussing capabilities of the system.A homogeneous, muscle-equivalent phantom was modelled with a diameter of 40 mm and length of 90 mm.Inside this phantom, a spherical target volume of 10 mm diameter was defined.The target was placed at the centre of the phantom and at (X, Y) = (10 mm, 0 mm) and (X, Y) = (10 mm, 5 mm) away from the centre.To create a focus on all locations, the antenna phases were adjusted, based on SAR ratio optimisation as discussed in chapter 2.5.The central target was used for evaluation of the focus size (full-width-half-maximum).The phantom simulation model is depicted in figure 1.

Digital mouse model simulation
To simulate a pre-clinical treatment, the MOBY digital mouse model was used (Segars et al 2004).The MOBY mouse model is a highly detailed anatomical mouse model and provides, among others, the possibility to model anatomical variations due to respiratory induced motion.A spherical target of 10 mm in diameter was added to simulate a tumour inside the pancreatic head, following the approximate size of a PDAC tumour in the KPC mouse (Eser et al 2013, Vohra et al 2018).In total, 24 different tissues were included in the simulation model.The dielectric and thermal tissue properties were based on the IT'IS database (Williams and Leggett 1989, Duck 1990, McIntosh and Anderson 2010, Peyman and Gabriel 2012, Hasgall et al 2018).Thermal stress enhanced perfusion values at average hyperthermic temperatures were used for the muscle tissue, based on Cheng et al (2009).Since pancreatic tumours are known to be poorly perfused, the tumour perfusion was simulated to be half the value of (enhanced) muscle perfusion.Initial simulations showed that the impact of metabolic heat generation, as defined by the IT'IS database, is negligible for our case compared to the large power deposition by the antennas.All tissues and their corresponding tissue property values can be found in table 1.
The baseline simulation model was created using the MOBY model in exhaled state and with filled stomach and intestines.Properties of the stomach and intestine lumen were assumed to be similar to muscle, without perfusion.The baseline model was aligned in cranial-caudal direction such that the tumour is at the axial centre of the temperature focus.The water bolus was set at a constant temperature of 30 °C .The baseline model is visualised in figure 2.

Treatment optimisation
To obtain effective target heating while maintaining heating of healthy tissue below specific thresholds, the phases and amplitudes of all eight antennas are optimised.These treatment parameters, denoted by θ, are optimised by maximising an objective function.In this study, we investigated the effectiveness of the following SAR-based and temperature-based objective functions: • SAR ratio : maximise the ratio of average SAR in the target to the average SAR in the healthy tissues; • Homogeneity: maximise the T 90 with a penalty for heterogeneity; With weight c to tune the relative importance between target heating (T 90 ) and homogeneity.
Optimisation of the aforementioned objective functions was subjected to additional constraints.To avoid clinically unrealistic settings, power constraints were set such that each antenna should contribute at least 5% and at most 20% of the total applied power.To avoid thermal damage to healthy tissue, constraints on healthy tissue temperatures were implemented:  T 45 tissue °C.Tumour target temperatures were maximised until this normal tissue limit is reached.The resulting tumour temperatures therefore vary per objective function and could possibly even exceed hyperthermia goal temperatures.In practice, one will likely aim at a specific target temperature, lower than the attainable limit.For this reason, our simulations were conducted assuming that the actual treatment will be guided by a temperature probe placed at the centre of the tumour and a hyperthermic goal temperature of 43 °C.To allow for a fair comparison, the results of all simulations were therefore powerscaled such that the centre of the target reaches 43 °C.Evaluations were carried out based on T 90 , T , homogeneity coefficient (T 10 -T 90 )/(T 90 −37 °C), focus size (volume with a temperature >41 °C) and visual examination of the SAR and temperature distributions.
The optimisation strategies optimise the phases and amplitude settings for all antennas.Another degree of freedom available from the hyperthermia system is the water bolus temperature.Although this temperature is currently not included as a variable in the optimisation, we analysed the effect of increasing the water bolus temperature through a simulation with its temperature set at 37 °C.

Robustness evaluation
Besides effective focusing to the target, the robustness of heating was also evaluated.To this end, the impact of the following uncertainties was investigated: • Mouse misalignment; • Respiratory induced motion; • Changes in stomach and intestine filling; • Uncertainties in tissue property and perfusion values.
Extreme-case scenarios were considered to examine the impact of mouse misalignment, respiratory induced motion, and variations in the gastrointestinal tract filling (stomach and intestine).The impact of mouse misalignment was evaluated by simulating cranial-caudal shifts of +5 and −5 mm.Given that the mouse is fully enclosed by the water bolus, the pressure of the water bolus from all sides centres the animal during treatment.Misalignments in the proximal-distal direction were therefore considered minimal and neglected in this study.
To investigate the impact of respiratory motion, the fully exhaled state was compared to the fully inhaled state.Similarly, the impact of possible air in the stomach and intestinal lumen was evaluated by comparing stomach and intestines lumen filled with a muscle-equivalent tissue and a scenario where they contained air.The baseline model was composed out of a centred anatomy, in fully inhaled state and with filled stomach and intestines.The baseline antenna settings were optimised using the T ratio objective function.All scenarios were simulated using the baseline-optimised antenna settings and subsequently power-scaled until the centre of the tumour was 43 °C to mimic thermometry-guided treatment.
Quantification of the impact of uncertainties in tissue property and perfusion values was more challenging.First, the differences between minimum and maximum values reported for the properties in the IT'IS database do not adequately represent the impact of the tissue property and perfusion uncertainties.Secondly, the high- dimensional, reciprocal interactions of the tissue property and perfusion values are not intuitive, often showing the largest effects under contrasting conditions.For instance, certain conditions, such as the combination of a highly perfused liver and under-perfused muscle tissue, may lead to hot spots that are otherwise absent in a temperature plan.Due to these complexities, issues of this nature are typically addressed using a Monte Carlo approach.However, given the considerable number of uncertainties ( ) 126 and the consequently large number of simulations required for a Monte Carlo evaluation, this approach is impractical, mainly due to FDTD calculation times-∼170 min per simulation on an Intel i7-10700 CPU with Nvidia Quadro RTX 400 GPU -.
Instead, we employed a polynomial chaos expansion (PCE) evaluation.PCE is achieved using a series expansion with an orthonormal polynomial basis that is orthogonal to a given uncertainty distribution.This basis is then used to establish a surrogate model that expresses the variability of a signal with respect to the original uncertainty distribution-the tissue property and perfusion value uncertainties for our case.The resulting model can then be employed to obtain, among others, statistics about the impact of the uncertainties.Notably, PCE models require only a fraction of the simulations necessary for Monte Carlo simulations, making them considerably more efficient in cases where each simulation is time-consuming, such as with high resolution FDTD simulations.PCE therewith provides an efficient method for assessing the individual and combined impact of all relevant uncertainty factors in hyperthermia as was recently demonstrated for humans (Groen et al 2023).PCE models have been widely applied in other areas such as in engineering mechanics (Ghanem and Spanos 2003), fluid flow (Le Matre et al 2001), aerodynamics (Witteveen et al 2007) and in radiotherapy treatment planning (Perkó et al 2014(Perkó et al , 2016)).
The investigated uncertainties were assumed to be normally distributed, of which the mean and standard deviation were obtained from the IT'IS database (Hasgall et al 2018).PCE was implemented using Chaospy library version 4.3.1 (Feinberg and Langtangen 2015).Smolyak sparse-grid was used for sampling.Tissue property and perfusion uncertainties that had an individual impact larger than 0.1 °C were considered for analysis (standard deviation of the temperature variation exceeds 0.1 °C).In total, we conducted 924 simulations to assess the influence of pertinent uncertainties in tissue properties and perfusion, including 468 unique FDTD simulations.

Simulations in phantom models
Simulations conducted in phantom models revealed an ellipsoidal focus measuring approximately 9 by 20 mm.This focus could be shifted to any desired target location within the phantom as shown in figure 3, indicating flexible focusing abilities of the 1.66 GHz microwave array.

Simulation in a realistic mouse model
Simulations performed using the realistic mouse model demonstrated that adequate focusing on targets located in both the head and tail of the pancreas is feasible.Well focused heating was obtained with all objective functions.

Comparison of optimisation strategies
Antenna settings consistently achieved satisfactory temperature focusing with all optimisation strategies.The highest target temperature was attained using the T 90 optimisation.When the plans were scaled to mimic treatment conditions-where the target is heated until a thermometry probe located at the centre of the tumour records 43 °C-the T 90 and T 50 of all plans exceeded 41.29 °C and 42.24 °C respectively.Table 2 summarises the individual target parameters for both the scaled and unscaled scenarios.Almost all optimisation objectives resulted in focussed temperature distributions with minimal healthy tissue heating.The focus volume, the volume with temperatures exceeding 41 °C, varied between 0.32 and 1.07 ml (0.95%-3.16% of the mouse volume).Only for the temperature homogeneity objective function, the optimiser compromised healthy tissue temperatures slightly (up to 43 °C) at locations further away from the target region.In general, the highest temperature was located at the centre of the target, with a strong temperature gradient towards the periphery.Temperature-volume histograms of the target volumes are depicted in figure 4.These histograms reveal that the SAR ratio optimisation method is the least effective when compared to the temperature-based optimisation strategies.From the temperature predictions in figure 5 it can be observed that, although the SAR focus has its maximum at the centre of the target, the temperature focus is slightly beyond the target centre.Similarly, the plans that were generated using temperature-based optimisation, namely T ratio , T 90 , and homogeneity objective functions, resulted in a more accurate temperature focus, but did not always yield a central SAR focus.The T ratio -optimised plan exhibited the most confined target focus and was accurate on both the SAR and the temperature distribution.This more confined focus is also reflected in the relatively low total power needed, which is 45%-55% of the power required with T90 or homogeneity optimisation.Furthermore, the T ratio optimisation strategy demonstrated great flexibility to focus at different treatment locations, as illustrated by a target in the pancreas tail (T 90 of 40.7 °C, T 50 of 41.9 °C, T 10 of 42.69 °C, homogeneity coefficient of 0.52 and a focus size of 0.24 ml, 0.70%).SAR and temperature distributions for treatment of a tumour in the pancreas tail are visualised in figure 6.
In terms of target temperature homogeneity, the T ratio , and even more so the SAR ratio plans, were substantially less homogeneous compared to the plans optimised using T 90 and homogeneity objective functions.However, it was found that the homogeneity of a T ratio plan could be improved when the water bolus temperature was set to 37 °C.This also resulted in an expanded focus size, comparable to the T 90 plan.Visualisations of the treatment plans obtained from all optimisation methods are displayed in figure 5.

Robustness evaluation
The simulations demonstrated strong robustness under both respiratory motion and fluctuations in intestine and stomach filling (∆  T 0.14 90 °C).Target heating was somewhat more sensitive to mouse positioning errors with an impact on T90 up to 0.23 °C and a decrease in homogeneity from 0.26 to 0.34.In the case of a −5 mm lateral shift, a hot spot was visible in the lungs (up to 44.9 °C).Temperature-volume histograms of the target volume are depicted for all considered circumstances in figure 7. The corresponding SAR and temperature distributions are shown in figure 8.
The uncertainties of tissue property and perfusion values had the largest impact on predicted temperatures.From the individual impact analyses, it was found that uncertainties on thermal conductivity and specific heat capacity had negligible impact (<5 × 10 −12 °C).Uncertainty in density resulted in a small impact (<0.1 °C).Uncertainty in permittivity and perfusion resulted in an impact smaller than 0.36 °C.Electrical conductivity Figure 3. Specific absorption rate (SAR) distributions achieved with the 1.66 GHz microwave-array system in a homogeneous phantom.The SAR is focussed on a target at the centre of the phantom (left), a target 10 mm away from the centre (top right) and on a target at position (X, Y) = (10, 5) mm from the centre (bottom right).In each case, the system is able to accurately focus on the desired target location.The focus size (full-width half-maximum) is a spheroid with diameters 9 mm (radially) and 20 mm (axially).
Table 2. Target temperature metrics for optimised treatment plans.Total power, T 90 , T 50 , the homogeneity coefficient (T 10 -T 90 )/(T 90 − 37) and focus size are shown for treatment plans generated using varying optimisation strategies.
Results are given for both unscaled plans (the plan as end result of optimisation) and scaled plans (the total power was scaled until a central target temperature of 43 °C was achieved to mimic treatment control using a thermometry probe in the centre of the tumour).The focus size is the volume in the mouse that experiences temperatures larger than 41 °C.

Total deposited power
[W] uncertainties had the largest impact of which the uncertainties of the target, liver and lungs resulted in the largest variation (max SD of 0.46 °C, 0.45 °C and 0.44 °C) respectively.Especially uncertainties of liver property-values were impactful across all properties.The individual impact of all tissues for each property is visualised in figure 9. Uncertainty analyses of the combined impact (21 properties) showed that the average treatment plan given all uncertainties had a similar focus but with slightly lower temperatures compared to the treatment plan generated using mean property values (T 90 of 40.95 °C for the average plan versus 41.59 °C for the plan using mean values).The expected variation (represented by the Standard Deviation) to the average plan went up to 0.56 °C.Most variation could be found in the liver and around the target volume.The variation in T 90 was found to be 0.32 °C (1 SD).The combined impact is visualised in figure 10.

Discussion
The simulations in this paper showed that the novel small-animal hyperthermia system represents an advanced and promising device for future preclinical hyperthermia research.We assessed its efficacy through simulations in both a uniform phantom and a mouse model, examining its focusing precision, the benefits of different optimisation approaches for treatment planning, and the effects of physiological uncertainties.Our analysis reveals that miniature high frequency antenna-array systems such as the ALBA Micro8 are suitable for generating robust and confined target heating at deep-seated tumour locations, analogous to clinical deep hyperthermia, and without inducing treatment-limiting hot spots in healthy tissue.

Limitations
In line with current hyperthermia treatment planning practices, the tissue property values used in this study were sourced from the IT'IS database (Williams and Leggett 1989, Duck 1990, McIntosh and Anderson 2010, Peyman and Gabriel 2012, Hasgall et al 2018).This choice was based on to the unavailability of mouse-specific properties for all tissues included in the Moby digital mouse model, leaving the IT'IS database as the only complete and established database for the property values for all required tissues.Gathering and/or measuring mouse-specific tissue properties for all tissues was beyond the scope of this study.However, properties like perfusion may differ in mice compared to larger animals, including humans.These differences could extend beyond the uncertainties factored into our PCE analysis.In particular, anaesthesia is known to affect blood perfusion, metabolic heat production and the core body temperature (Seyde et al 1985, Johnson et al 1976, O'Connor et al 1982).The latter is important to prevent hypothermia and achieve study results that better resemble human clinical treatment, where anaesthesia is rarely used.Future research needs to evaluate the impact of anaesthesia and determine the appropriate water bolus temperature to maintain a stable core temperature.Since it is expected that some forms of anaesthesia would decrease tissue perfusion, the resulting effect on our treatment plans would be an overall increase in temperatures for the same SAR distribution.As result, the balancing point between water bolus cooling and antenna heating would shift slightly.In other words, either the water bolus temperature should be adjusted to lower temperatures (to counter the increased temperature), or the total power should be decreased, having a similar effect as increasing water bolus temperature.We have already investigated the effect of changing water .Temperature-volume histograms of optimised treatment plans for the 1.66 GHz microwave-array system.Target temperatures shown for treatment plans generated using varying optimisation strategies.Results are given for both unscaled plans (the temperature distribution as end result of the optimisation strategy) and scaled plans (the total power was scaled until a central target temperature of 43 °C was achieved to mimic treatment control using a thermometry probe in the centre of the tumour).WB37 refers to the situation with a 37 °C water bolus.For all other cases the water bolus was 30 °C.
bolus temperature on treatment plans.Increasing the temperature results in a less confined, more homogeneous heating of the target (visible in figure 5, T ratio(WB37) ) and likewise, decreasing the water bolus temperature would increase the confinement.Moreover, given the strong focussing ability of the system-observed both in SAR and temperature-, it is unlikely that reduced perfusion, and therewith the impact of anaesthesia, will result in radically different treatment plans or unexpected healthy-tissue hot spots.If anything, reduced perfusion is more likely to reduce the risk of hot spots as the contrast in maximum temperature between normally well perfused and ill perfused tissues will decrease if perfusion differences decrease.The overall conclusion of the study, i.e. the ability to realize adequate and robust locoregional heating of deep-seated target regions in mice, is likely to remain valid.
The Moby digital mouse model is an averaged model based on a collection of mice CT and MRI scans, which is therefore a good representation for the average mouse.Future studies should however investigate the impact of anatomical inter-mouse variation on hyperthermia treatment plans.Nonetheless, the strong robustness found in this study makes it likely that the heating will also be robust under inter-mouse variations.The use of a generalised treatment plan for treating multiple mice might therefore be sufficiently accurate, which would be beneficial for the work flow in preclinical hyperthermia applications.This is part of ongoing research.Phase-amplitude settings were optimised for the baseline (blue), and tested for the impact of patient positioning errors (orange, green), respiratory motion (red) and changes in stomach and intestine air (purple).The total power was scaled such that a central target temperature of 43 °C was achieved to mimic treatment control using a thermometry probe in the centre of the tumour.

Optimisation strategies
All of the investigated optimisation strategies were able to accurately focus heating in the target.Only small differences were seen in T 90 and T 10 performance.The T ratio objective function creates the most confined temperature focus.However, the high focussing ability of the 1.66 GHz microwave-array system intrinsically results in steeper temperature gradients and highly heterogeneous temperature distributions within the target, as can be seen in the temperature-volume histograms and the homogeneity coefficients in figures 4 and 7.This is Figure 8. SAR and temperatures for different scenarios.Phase-amplitude settings were optimised for the baseline model and tested for the impact of patient positioning errors, respiratory motion and changes in stomach and intestine air.The total power was scaled such that a central target temperature of 43 °C was achieved to mimic treatment control using a thermometry probe in the centre of the tumour.
not always desired, e.g. when investigating the temperature-dependency of specific hyperthermia mechanisms.In such cases, homogeneous tumour temperatures might be preferred.Improved homogeneity can be achieved by utilising other objective functions such as T 90 or by optimising directly on homogeneity.In addition, increasing the water bolus temperature will also result in less sharp temperature-gradients and thereby lead to improved target homogeneity.Finally, enlarging the effective target volume during optimisation beyond the true tumour size might also help to avoid large thermal gradients at the real tumour periphery.In any case, increasing temperature homogeneity within the tumour can only be achieved by defocussing and increasing the size of the focus, thus (mildly) increasing heating of the surrounding healthy tissue.Whether a strong (heterogeneous) focus or a less strong but more homogeneous target heating is preferable will be determined by  the study goals of the research in which this device is used.In either case, the 1.66 GHz antenna array is suitable for delivering target temperature distributions that are customised to the user's preference.Ongoing research focuses on experimental validation of the heating characteristics of the antenna-array system and comparison of measured and predicted heating patterns.

Heating robustness
Our simulations demonstrated substantial robustness under respiratory motion and changes in intestine and stomach filling.Mouse positioning errors can result in somewhat less optimal temperature distributions.This was seen by the larger impact on target temperatures and decreased target homogeneity.Furthermore, a hot spot in the lungs was observed for the case with a −5 mm displacement.Although high SAR values occurred in the lungs for all cases, this did generally not result into hot spots due to the low density of lung tissue and the efficient cooling by the nearby arterial blood flow.Even when lung tissue would heat up in the simulation, such as is the case with a −5 mm displacement, the lung temperatures will likely be lower in reality, since the highly effective lung cooling due to breathing was not considered in our simulations.The notable decline in the quality of target heating should nevertheless be taken into consideration.We found that re-optimising phases and amplitudes did not significantly improve treatment plans (data not shown).Therefore, accurate positioning of the mouse is important to ensure treatment quality when using a 1.66 GHz phased-array system.Markers in combination with laser guidance could ensure accurate positioning in a similar way as done for clinical treatments.
Uncertainties in tissue property and perfusion values are associated with significant variability in the predicted temperatures.The impact was however notably smaller (about 10 times) compared to the uncertainties found in humans (Groen et al 2023).Where the impact of the uncertainties in humans was found to be spread throughout the body, for mice it seems to be focussed around the target region.Nevertheless, tissue property and perfusion uncertainties are in relative terms the most impactful of all evaluated errors and will likely negatively impact tumour temperatures and its homogeneity.This negative impact will be reduced in practice when treatments are guided based on a target thermometry probe, thereby also ensuring a level of robustness.The impact is relatively small, but if desired, it might be possible to further improve robustness under tissue property and perfusion uncertainties with dedicated optimisation.For example, margins can be used, possibly informed by the surrogate model that was created using PCE analysis.Future research could implement a PCE-based robust optimisation method that minimises tumour-temperature uncertainty in addition to tumour and healthy tissue temperatures.

Mouse treatment planning
Clear differences can be seen when comparing treatment plans created in this study with treatment plans generated for human patients.The strong, distinct temperature focus and the lack of healthy tissue hot spots in our mouse plans are in strong contrast with temperature predictions observed for human patients (Groen et al 2023).There are a few factors that could explain this.
First of all, it seems that because of the relatively small body size and relatively long water bolus, the cooling effect of the water bolus is far more substantial and affects deeper tissues in the mouse compared to humans.In humans, the water bolus cooling was measured to reach 1-2 cm deep, in mice this distance covers the entire mouse.The resulting extra power deposition that is required to compensate for the cooling and achieve goal temperatures is therefore also much higher.Good focusing abilities are also better achieved because of the relatively small wavelength and larger number of independent antennas used by the 1.66 GHz antenna array, compared to locoregional heating systems used for human treatments, operating at 60-120 MHz.Furthermore, the MOBY mouse model, like mice in general, does not contain fat, and fat-muscle interfaces are notorious for treatment limiting hot spots in human patients because of the high contrast in dielectric properties and perfusion.All these effects combined seem to suppress the influence of tissue properties and perfusion, which also explains why the impact of the corresponding uncertainties is about 10 times lower than those found for human plans.
Because of the incidence of treatment limiting hot spots in human patients, hot spots should be taken into account during clinical treatment planning.This requires objective functions like the hot-spot-target ratio (HTQ) or temperature-based optimisation including normal tissue temperature constraints (Canters et al 2009, Kok andCrezee 2022).In mice, with absence of hot spots, a relatively simple SAR optimisation strategy as SAR ratio already provides adequate results.This strategy aims to minimise energy deposition in healthy tissue, and because of the absence of hot spots there is a good correlation between SAR and temperature.Nevertheless, similar to treatment planning in humans, temperature-based strategies accounting for thermal influences of the water bolus and blood flow overall yield better results, which can clearly be observed in the case of heating a target in the pancreatic tail (figure 6).In this case, bolus cooling has a significant influence on target heating and therefore the SAR and temperature focus do not coincide.Again, because of the absence of normal tissue hot spots, a relatively simple T ratio objective already provides good results.Target temperatures and homogeneity could be further improved using more sophisticated objective functions as the T 90 and homogeneity objective functions, albeit at the cost of less confined heating, since these objectives do not penalise moderate energy absorption or temperature rise in normal tissue.
Another important difference between pre-clinical and clinical hyperthermia treatments is the partial reliance on patient feedback.In a clinical setting, when a patient feels discomfort, this is communicated to the operator, who can then adjust the power or phase settings accordingly.However, a mouse cannot provide verbal feedback, making pre-clinical hyperthermia treatments solely dependent on temperature measurement.The inability to give this type of feedback is perhaps a less urgent issue as our simulations demonstrate that robust plans can be generated and that the predicted temperature distributions in the mouse are significantly less heterogenic with no clear potential hot spot locations compared to human anatomies during hyperthermia.Furthermore, the ALBA Micro8 device provides a number of 4 thermometry probes, which can be positioned at specific locations, also in normal tissue.This way, treatment quality and safety in pre-clinical hyperthermia can be ensured, regardless of 'patient' feedback.This could also open up opportunities for automated treatment through real-time feedback, if desired.By strategically placing a few temperature probes in the tumour and healthy tissue areas, the location and potentially the size of the temperature focus could be estimated.By employing an online feedback system, accurate heating could be established that corrects for any remaining irregularities and ensures reliable treatment.

Impact of water bolus temperature
Whether a confined (heterogeneous) focus or a less confined but more homogeneous target heating is preferable depends on the study goals when using this device.It should be noted though that homogeneity can be improved in several ways as stated before.One of these ways is by increasing the water bolus temperature.As illustrated by the treatment plan with a water bolus temperature of 37 °C in figure 5, increasing this temperature indeed results in a more homogeneous, but also less confined, focus volume.Higher water bolus temperatures would however imply that the tissue properties and perfusion uncertainties become relatively more influential, which could negatively influence robustness.
Aside from improving homogeneity, there could also be other reasons to increase the water bolus temperature.For example, due to the concern for hypothermia.Since the water bolus has such a strong cooling effect even relatively deep in the body, the core temperature of the mouse could drop, which possibly leads to hypothermia.Although additional strategies could be applied to maintain body temperatures or vascular temperatures, future research will need to further identify the impact of this type of hyperthermia treatment on the core temperature of a mouse.

Orthotopic animal models
In order to perform pre-clinical research that translates well to clinical results, both the heating method and the tumour model needs to be representative for clinical situations.Hyperthermia on small animals is currently often performed using either full-body hyperthermia or localised limb heat treatment.Localised limb treatments are technically feasible, but this tumour location involves a need for xenograft tumours implanted into hind limbs of immune deficient rats or mice, after which the limb is heated to hyperthermic temperatures using hot water baths or capacitive systems.Localised limb treatment negates the importance of a realistic tumour biological microenvironment, rendering the study of normal tissue effects unfeasible, such as impacts on neighbouring critical organs or the local immune response.
Genetic mouse models offer a more accurate approximation of in vivo tumour biology and include a functional immune system.This combination of features enhances the reliable translation of pre-clinical results into clinical applications.An example of this is the KPC mouse model, that mimics human pancreatic ductal adenocarcinoma (PDAC) (Hingorani et al 2005), capturing its genetic and microenvironmental complexities.

Novelty and comparison with existing systems
Most preclinical animal model research traditionally used tumours implanted at practical locations in immunedeficient animals, but results from these models are less reliable in translation to the clinical situation.The use of orthotopic models, such as the KPC model, do necessitate the adoption of dedicated preclinical hyperthermia systems capable of targeted heating of the relevant tumour site, which may be more deep-seated.Unfortunately, existing pre-clinical microwave systems are not capable of targeting deep-seated tumour locations like PDAC.These systems are either for superficial use (Curto et al 2018, Raaijmakers et al 2018), or specifically aimed on heating the bladder (Salahi et al 2012).These systems therewith do not reflect the localised heating procedures applied in clinical practice.Though arguably still suitable for studying tumour control, these systems do not provide the means required for investigating the specific effects of localised hyperthermia on tumour biology, the surrounding microenvironment, and the local immune response.This limits translatability to the clinical situation.
As mentioned before, other heating techniques such as focussed ultrasound can in principle provide the desired localised heating, but are presently under development and still missing the robustness required for reproducible pre-clinical hyperthermia of deep targets, specifically in the abdomen and pelvic area.
The results of this study indicate that, in contrast to existing pre-clinical systems, high frequency miniature phased-array systems are better suited for robust, localised deep heating, as required for orthotopic tumour targets.This system will therefore more likely enable pre-clinical studies to perform representative, reproducible experiments that translate better to the clinic.

Conclusion
This study analysed the heat-focussing capabilities, compared optimisation strategies and investigated heating robustness under realistic physiological circumstances for pre-clinical hyperthermia treatments using the newly developed locoregional ALBA micro8 system.Our simulations indicate that this phased-array system can effectively heat targeted, deep-seated regions in mice without causing hot spots in healthy tissue.Furthermore, the heating is robust under respiratory-induced motion and changes in stomach and intestine filling (ΔT 90 0.14 °C).Mouse positioning errors appear to have slightly more impact on tumour heating (ΔT 90 0.23 °C) and should be minimised during application.Uncertainties on tissue properties and perfusion resulted in a T 90 variation of 0.32 °C (1 SD).Treatment plans for hyperthermia in mice were therewith found to be significantly more robust and focussed compared to human plans.
Using phase-amplitude optimisation, robust treatment plans can be generated for pre-clinical hyperthermia research.Plans can be constructed to the users demands, ranging from a confined focus at the target centre to homogeneous target heating.
Integrating orthotopic tumour models with dedicated phased-array hyperthermia systems provides a beneficial enhancement to the efficacy and clinical relevance of preclinical hyperthermia studies, potentially leading to more effective and personalised treatment strategies in clinical oncology.

••Figure 1 .
Figure 1.Phantom model setup for simulations with the ALBA micro8 small-animal hyperthermia device.The system consists of eight waveguide antennas operating at 1.66 GHz.A water bolus couples the electromagnetic energy to the phantom.The phantom model is a homogeneous, muscle-like phantom.Target volumes are visualised at the centre of the phantom (left) and 10 mm away from the centre of the phantom (right).

Figure 2 .
Figure 2. The baseline model for evaluating heating robustness of the 1.66 GHz microwave array.The model is based on the MOBY digital mouse model in exhaled state and filled stomach and intestines.To mimic an orthotopic KPC mouse model, a spherical tumour with a diameter of 10 mm is added in the pancreatic head, delineated in red.The water bolus (blue) is in direct contact between the antennas and the mouse's skin, ensures efficient coupling of electromagnetic waves to the animal while also providing skin cooling to prevent overheating.

Figure 4
Figure4.Temperature-volume histograms of optimised treatment plans for the 1.66 GHz microwave-array system.Target temperatures shown for treatment plans generated using varying optimisation strategies.Results are given for both unscaled plans (the temperature distribution as end result of the optimisation strategy) and scaled plans (the total power was scaled until a central target temperature of 43 °C was achieved to mimic treatment control using a thermometry probe in the centre of the tumour).WB37 refers to the situation with a 37 °C water bolus.For all other cases the water bolus was 30 °C.

Figure 5 .
Figure 5. Objective function comparison for treatment plan optimisation using the 1.66 GHz microwave-array system.Specific absorption rate (SAR) and temperature distributions of optimised treatment plans.Optimisations were performed for treating a pancreatic head target in the MOBY digital mouse model.

Figure 6 .
Figure6.Treatment plan optimisation for heating a pancreatic tail tumour.Specific absorption rate (SAR) and temperature distribution of a hyperthermia treatment plan optimised using T ratio for treatment of a pancreatic tail tumour in the MOBY digital mouse model using the 1.66 GHz microwave-array system.

Figure 7 .
Figure7.Temperature-volume histograms for different scenarios.Phase-amplitude settings were optimised for the baseline (blue), and tested for the impact of patient positioning errors (orange, green), respiratory motion (red) and changes in stomach and intestine air (purple).The total power was scaled such that a central target temperature of 43 °C was achieved to mimic treatment control using a thermometry probe in the centre of the tumour.

Figure 9 .
Figure 9. Impact of uncertainties in electrical conductivity values, permittivity and perfusion values on the predicted temperature distribution for treatment of a pancreatic head tumour in a mouse.The values represent the variation in temperature as result of the uncertainty at the location of its maximum impact.

Figure 10 .
Figure 10.Average treatment plans and variation due to tissue property uncertainties.Transversal and coronal slices are visualised of the average treatment plan and the corresponding plan variation as result of the tissue property uncertainties.Plan variation goes up to 0.56 °C.

Table 1 .
Tissue property and perfusion values and uncertainties (standard deviations) for all tissues included in the treatment plans for a pancreatic target in the MOBY digital mouse model.* SD replaced by a fraction similar to muscle.