Temperature sensitive liposomes combined with thermal ablation: Effects of duration and timing of heating in mathematical models and in vivo

Background Temperature sensitive liposomes (TSL) are nanoparticles that rapidly release the contained drug at hyperthermic temperatures, typically above ~40°C. TSL have been combined with various heating modalities, but there is no consensus on required hyperthermia duration or ideal timing of heating relative to TSL administration. The goal of this study was to determine changes in drug uptake when heating duration and timing are varied when combining TSL with radiofrequency ablation (RF) heating. Methods We used computer models to simulate both RF tissue heating and TSL drug delivery, to calculate spatial drug concentration maps. We simulated heating for 5, 12 and 30 min for a single RF electrode, as well as three sequential 12 min ablations for 3 electrodes placed in a triangular array. To support simulation results, we performed porcine in vivo studies in normal liver, where TSL filled with doxorubicin (TSL-Dox) at a dose of 30 mg was infused over 30 min. Following infusion, RF heating was performed in separate liver locations for either 5 min (n = 2) or 12 min (n = 2). After ablation, the animal was euthanized, and liver extracted and frozen. Liver samples were cut orthogonal to the electrode axis, and fluorescence imaging was used to visualize tissue doxorubicin distribution. Results Both in vivo studies and computer models demonstrate a ring-shaped drug deposition within ~1 cm of the visibly coagulated tissue. Drug uptake directly correlated with heating duration. In computer simulations, drug concentration increased by a factor of 2.2x and 4.3x when heating duration was extended from 5 to either 12, or 30 minutes, respectively. In vivo, drug concentration was by a factor of 2.4x higher at 12 vs 5 min heating duration (7.1 μg/g to 3.0 μg/g). The computer models suggest that heating should be timed to maximize area under the curve of systemic plasma concentration of encapsulated drug. Conclusions Both computer models and in vivo study demonstrate that tissue drug uptake directly correlates with heating duration for TSL based delivery. Computational models were able to predict the spatial drug delivery profile, and may serve as a valuable tool in understanding and optimizing drug delivery systems.

20 ρ is the density (kg·m -3 ), c is the specific heat (J·kg -1 ·K -1 ), k is the thermal conductivity 21 (W·m -1 ·K -1 ), Q rf (W·m -3 ) is the heat generated by RF current, and Q P (W·m -3 ), is the heat 22 loss due to blood perfusion. The energy generated by the metabolic processes is 23 neglected since it is orders of magnitude lower than Q P . 24 25 26 T bl is the temperature of the blood (commonly assumed to be 37 °C), ρ bl is the blood 27 density (kg·m -1 ), c bl is the specific heat of human blood (J·kg -1 ·K -1 ), and w bl is the blood 28 perfusion (s -1 ). The temperature dependence of the blood perfusion term w bl was 29 implemented as described in a prior publication [7], with an initial increase in perfusion 30 followed by vascular stasis (Fig. S1). This temperature dependence was implemented 31 based on a first-order kinetic Arrhenius model. A variable "degree of stasis" (DS) was 32 modeled according to following equation with A as the frequency factor (1.98 x 10 106 s -33 1 ), and ΔE is the activation energy (6.67 x 10 5 J·mole -1 ) [7]: 34 35 (3) 36 37 Based on DS, perfusion was varied according to Figure S1. For RF heating at frequencies between 300 kHz and 1 MHz, tissue can be considered 47 as purely resistive as the as the displacement currents are negligible. Thus heating 48 around the active electrode due to dissipating electrical power Q h (Joule loss) can be 49 modeled via quasi-static approach: 50 51 where σ is the electrical conductivity and V is the electric potential (Volts). 58 59

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The tissue temperature and perfusion were fed into the drug delivery model to calculate 73 intravascular release from TSL-Dox, transport from plasma into tissue interstitium 74 (extracellular-extravascular space (EES)), and uptake by liver cells (Fig. S2

Dox concentration in systemic tissue
Dox concentration in liver plasma 118 119 120 121

Dox concentration in liver cells (bound)
129 130 Within the EES, spatial diffusion was considered based on diffusion coefficients 131 experimentally measured in liver tissue [21]. 132 133 135 Release rate calculation 136 The in vitro measured TSL release data in Fig. S3 was modeled by a bi-exponential fit 137 (represented by solid lines). The drug fraction released from TSL depends on both local 138 temperature, and on the time the plasma requires to pass through the heated tissue 139 volume (=transit time, t T ) -i.e. the time TSL are exposed to heat. This transit time (t T ) 140 depends on plasma perfusion as follows: 141 The release rate is then calculated as follows, where rf(T,t T ) is the release fraction, i.e. 143 fraction of drug released at a particular temperature (T), after time (t T ), corresponding to 144 the data plotted in Fig. S3: 145 For a specific temperature, the release rate was interpolated between the temperatures 147 where data was measured (see Fig. S3), by using linear interpolation of rf(T,t T ) between 148 neighboring temperatures. The data for Fig. S3   Release at body temperature (37 ºC) was treated differently than described above. This 171 was necessary since TSL are exposed to 37 ºC continuously after administration rather 172 than just for a few seconds (i.e. transit time, t T ) as is the case for hyperthermic 173 temperatures. Based on the derivative of the release curve for 37 ºC from Fig. S3, a  174 temporally varying release rate R R37 (t) was devised for equations (5)  Convergence tests were performed to ensure adequate mesh size. The temporal 213 resolution for the models was 0.3-2 s. 214

Initial and boundary conditions 215
An initial temperature of 37 ºC was assumed throughout the model domain. Cooling of 216 the needle electrode was simulated by setting electrode temperature constant to 20 ºC. 217 Electric ground potential was assigned to the boundaries of the model domain, and V cc 218 was assigned to the active electrode tip. The voltage V cc was varied throughout the 219 simulation based on proportional-integral (PI) control algorithm to keep maximum tissue 220 temperature at 100 ºC. 221 222

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Calibration curve for conversion of fluorescence to doxorubicin concentration 224 Figure S5 shows the calibration curve used to convert fluorescence to tissue drug 225 concentration. Since at very low concentrations the relationship between concentration 226 and fluorescence is linear, we likely introduce an error at low concentrations (<~2 μg/g). 227 228 229 230