Examining the efficacy of localised gemcitabine therapy for the treatment of pancreatic cancer using a hybrid agent-based model

The prognosis for pancreatic ductal adenocarcinoma (PDAC) patients has not significantly improved in the past 3 decades, highlighting the need for more effective treatment approaches. Poor patient outcomes and lack of response to therapy can be attributed, in part, to the dense, fibrotic nature of PDAC tumours, which impedes the uptake of systemically administered drugs. Wet-spun alginate fibres loaded with the chemotherapeutic agent gemcitabine have been developed as a potential tool for overcoming the physical and biological barriers presented by the PDAC tumour microenvironment and deliver high concentrations of drug to the tumour directly over an extended period of time. While exciting, the practicality, safety, and effectiveness of these devices in a clinical setting requires further investigation. Furthermore, an in-depth assessment of the drug-release rate from these devices needs to be undertaken to determine whether an optimal release profile exists. Using a hybrid computational model (agent-based model and partial differential equation system), we developed a simulation of pancreatic tumour growth and response to treatment with gemcitabine loaded alginate fibres. The model was calibrated using in vitro and in vivo data and simulated using a finite volume method discretization. We then used the model to compare different intratumoural implantation protocols and gemcitabine-release rates. In our model, the primary driver of pancreatic tumour growth was the rate of tumour cell division and degree of extracellular matrix deposition. We were able to demonstrate that intratumoural placement of gemcitabine loaded fibres was more effective than peritumoural placement. Additionally, we found that an exponential gemcitabine release rate would improve the tumour response to fibres placed peritumourally. Altogether, the model developed here is a tool that can be used to investigate other drug delivery devices to improve the arsenal of treatments available for PDAC and other difficult-to-treat cancers in the future. Author Summary Pancreatic cancer has a dismal prognosis with a median survival of 3-5 months for untreated disease. The treatment of pancreatic cancer is challenging due to the dense nature of pancreatic tumours which impedes retention of drug at the tumour site. As such, systemic administration of chemotherapies, such as gemcitabine, has a limited efficacy. To overcome this, sustained-release devices have been proposed. These devices are injected locally and release drug slowly over time, providing a concentrated local, sustained drug concentration. To investigate the possible efficacy of these devices, we developed a mathematical model that would allow us to probe treatment perturbations in silico. We modelled the individual cancer cells and their growth and death from gemcitabine loaded into the sustained delivery devices. Our platform allows future investigations for these devices to be run in silico so that we may better understand the forms of the drug release-profile that are necessary for optimal treatment.


Introduction 43
Inoperable pancreatic ductal adenocarcinoma (PDAC) has a dismal prognosis, with a median survival of 3−5 months 44 for untreated disease [1]. Treatment of PDAC with the chemotherapeutic agent gemcitabine can achieve clinical 45 benefit and symptom improvement in 20−30% of patients [1,2], although PDAC is still regarded as a chemotherapy-46 resistant tumour [3,4]. Gemcitabine is designed to target and kill cancer cells by incorporating into the DNA strand of a PDAC cell allowing only one deoxynucleotide to be incorporated, which prevents strand elongation [5,6], Figure 1 Motivation for sustained-delivery implants for treatment of PDAC. Sustained-delivery implants are a promising treatment size distribution on diffusional drug release from sustained-delivery systems using a system of partial differential volume measurements began when tumours reached a volume of 200 3 using 135 = ℎ × ℎ 2 2 136 where is the longest tumour measurement and is the tumour measurement along a perpendicular axis. Tumour 137 volume was measured daily for a duration of approximately 33 days. Full details for this experiment can be found in 138 Wade et al. [13]. All animal experiments were conducted in accordance with the NHMRC Australian Code for the 139 Care and Use of Animals for Scientific Purposes, which requires 3R compliance (replacement, reduction, and

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We model the diffusion and movement of drug inside the fibre assuming radial symmetry. We assumed that diffusion 173 in the radial direction is significantly faster than along the fibre since the radius of the fibre is significantly less 174 than the length of the fibre ( Figure TS1 and Figure TS2). This gives where ( ) is the time-dependent diffusion of drug inside the fibre. We imposed the continuity condition 176 ( , , ) = ( , , ), so that the diffusion of drug out of the fibre at the line source will depend on the location ( , ) and local exterior 179 This term is derived by converting the flux out of the radial fibre into the flux represented by the line source in Eq.

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(1) and converting to a concentration per surface area where ℎ is the depth of the rectangular region (presumed thing, 181 see Figure TS1). Both Eq. (3) and Eq. (4) are necessary boundary conditions for Eq. (1) and Eq. (2). In this way, we 182 assume the concentration is continuous and the flux of the fibre is equal to the flux into the TME, equivalent to a 183 conservation of mass.

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The diffusivity of the drug, ( ), is modeled by the function where controls the decay rate to the constant decay rate from the fibre (i.e. how quickly the fibre swells), is 186 the constant decay rate from the fibre and is a tuning constant to provide a finite initial diffusion coefficient, i.e.

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. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted April 19, 2022. ; https://doi.org/10. 1101/2022 where ⃗ is the outward unit normal on the boundary ( Figure TS5). In the case of a fibre implantation, all drug in 214 the domain is initially situated in the fibre:

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We solved Eqs. (1)-(4) numerically using a Finite Volume approximation. In particular, the diffusion of drug 220 within the fibre, Eq. (6), was solved through discretising the cross section of a fibre into annuli (see Figure 2B and  was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted April 19, 2022. ; https://doi.org/10.1101/2022.04.18.488716 doi: bioRxiv preprint cells could proliferate, die from gemcitabine, or form MCCs. Once formed, these pancreatic stem cells then move and 250 proliferate until they die. Healthy cells are assumed to be able to move or become MCCs. (defined by a Delaunay triangulations). Consider cell , the displacement of this point in time Δ is given by where (

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promoting the movement of cells in the environment ( Figure 2D).

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Tumour cell proliferation was assumed to be a function of the cell's distance, , to the nutrient source 260 (tumour periphery, i.e. nearest healthy cell centre, see Figure S3). The maximum radial distance for nutrient-261 dependent cell proliferation is . Cells that are a further distance from the nutrients than enter a quiescent

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(non-proliferative state), forming what is commonly known as a necrotic core. The probability of a cell dividing in time step Δ is given by

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Gemcitabine-loaded fibres were placed in a solution bath and the resulting cumulative concentration of gemcitabine 324 measured ( Figure 3A). To obtain a model describing the release rate of the drug from the fibre, we fitted parameters 325 from Eq. (1)-(4) to these in vitro measurements for the release of gemcitabine from 3% alginate 15% PCL fibres [14].

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Fitting the release curve parameters , , 0 and gave the fit in Figure 3B and parameter values in Table   327 S1. Overall, the model was able to obtain the fit to the data and followed the trend which showed a rapid initial release = + 50 , where is the exponential proliferation rate of cancer cells in vitro, is the death rate of cancer cells by gemcitabine,  Table S2.

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. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted April 19, 2022. ;https://doi.org/10.1101https://doi.org/10. /2022

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To analyse the drivers of pancreatic tumour growth dynamics in our model, we conducted a detailed 371 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted April 19, 2022. ; https://doi.org/10.1101/2022.04.18.488716 doi: bioRxiv preprint  was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted April 19, 2022. ;https://doi.org/10.1101https://doi.org/10. /2022 volume. Large concentrations of gemcitabine loaded into the fibre positioned at = 3.5 mm or = 4.3 mm from 444 the tumour centre were unable to stabilise or eradicate the tumour, also known as tumour arrest (Figure 6B-C and 445 Figure S10). Once the fibre was positioned closer to the tumour centre (≤ 1.7 mm) lower concentrations of drug were tumour growth to the different protocols, suggesting that tumour stabilisation or arrest might be achievable for some 449 tumours whereas others might experience tumour growth even in the presence of drug-loaded fibre.

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To then analyse the effects of changes to the drug release profile on the tumour growth, we investigated four 451 different release profiles: constant release, exponential release, sigmoidal Emax/Imax release profiles [82][83][84] (See

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the Technical Supplementary Information, Section TS3). Each of these release profiles were parameterised by a 453 release rate and for the Emax and Imax curves a half-effect term . The different release profiles were tested with ( Figure 6E). The four different release profiles (constant, exponential, sigmoid emax, sigmoid imax) were tested with 456 8 different release rates. For each parameter value,10 simulations were run over 33 days, with an initial amount of 500 457 of gemcitabine.

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For fibres positioned in the centre (Figure 6D), it is possible to eradicate the tumour with all release profiles 459 considered given a small enough value of . In comparison, none of the drug release profiles resulted in tumour 460 eradication when positioned peripherally ( Figure 6E). However, interestingly an exponential release profile with a 461 release rate of = 10 −4 results in the greatest decrease in tumour volume. This ideal release rate is likely because it 462 allows the drug concentration to remain in the therapeutic range and kill newly developed pancreatic cancer cells  was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made