Drug transport kinetics of intravascular triggered drug delivery systems

Intravascular triggered drug delivery systems (IV-DDS) for local drug delivery include various stimuli-responsive nanoparticles that release the associated agent in response to internal (e.g., pH, enzymes) or external stimuli (e.g., temperature, light, ultrasound, electromagnetic fields, X-rays). We developed a computational model to simulate IV-DDS drug delivery, for which we quantified all model parameters in vivo in rodent tumors. The model was validated via quantitative intravital microscopy studies with unencapsulated fluorescent dye, and with two formulations of temperature-sensitive liposomes (slow, and fast release) encapsulating a fluorescent dye as example IV-DDS. Tumor intra- and extravascular dye concentration dynamics were extracted from the intravital microscopy data by quantitative image processing, and were compared to computer model results. Via this computer model we explain IV-DDS delivery kinetics and identify parameters of IV-DDS, of drug, and of target tissue for optimal delivery. Two parameter ratios were identified that exclusively dictate how much drug can be delivered with IV-DDS, indicating the importance of IV-DDS with fast drug release (~sec) and choice of a drug with rapid tissue uptake (i.e., high first-pass extraction fraction). The computational model thus enables engineering of improved future IV-DDS based on tissue parameters that can be quantified by imaging.

. In vivo fluorescence linearity. Intravascular fluorescence was compared to plasma concentration quantified from blood samples at various time points after administration of unencapsulated dye (data in Fig. S5).   We normalized the plasma concentration data (Fig. S5) for each dose relative to the first time point at 2 min (Fig. S6). Subsequently, a bi-exponential fit (Equ. 7) was made (Fig. S7) from which the distribution and clearance rate constants were calculated (Equ. 8).   Table 3 and Table S2 for parameter and variable descriptions).

Global sensitivity analysis
We performed global sensitivity analyses based on the computer model parameter variability indicated in Table S4, both for unencapsulated drug and for thermosensitive liposomes (fTSL). We calculated (1) main effects, which indicate the contribution of an individual parameter on output variance, and (2) total effects, which indicate both the individual contribution of a parameter and it's interactions with other parameters on output variance. As output we considered the root-mean-square error (RMSE) of the tumor interstitial (EES) concentration calculated over 20 min, in comparison to the reference EES concentration based on the parameter means (Equ. 19).
The results for unencapsulated drug suggest that the variability in tumor drug uptake is primarily dependent on pharmacokinetic parameter variation, i.e. mainly affected by systemic distribution and elimination (Fig. S13). In contrast, for TSL the pharmacokinetic parameters have little impact. Tumor drug uptake variability for TSL (i.e. IV-DDS) is primarily dependent on the variability of tumor transport parameters (transit time (TT), permeability-surface area product (PS)), and on TSL release time (trel)) (Fig. S14). These three parameters are also present in the two indices (release index (R.I.), permeability index (P.I.)) that have been identified as dictating tumor drug uptake, providing additional evidence for the relevance of these indices. 0.80 ± 0.30 *10 -3 Elimination rate constant Serial blood sampling * For the parameters indicated, no experimental data was available to estimate variability and we assumed a standard deviation equal to 10% of the mean. ** These parameters can be derived from other parameters in this table, and were therefore not explicitly included in the sensitivity analysis.

Computer model considering varying release times due to recirculation of IV-DDS
We created an extended computer model where we implemented the consideration of multiple IV-DDS populations, depending on whether IV-DDS had already passed through the tumor. However, this extended model is only applicable for the simplified case of IV-DDS having a constant release time (e.g. assuming a constant temperature throughout triggered release if thermosensitive liposomes (TSL) are used). The issue of multiple passes is relevant for IV-DDS that do not conform perfectly to 0 th order release kinetics under certain conditions, such as the fTSL and sTSL employed here (see Fig. S10). In such a case, if an IV-DDS passes the tumor a second time, the release time will be different from the first time. We assumed the specific release kinetics of our example IV-DDS (fTSL and sTSL), and as mentioned assumed a simplified case where release times and temperature are constant during the release duration. This assumption considerably simplifies the model, since then each IV-DDS population that passed through the tumor a certain number of times has the same release time assigned -i.e. resulting in a very limited number of IV-DDS populations that need to be considered, rather than an infinite number of populations as would be required for a generalized model. This approach takes advantage of the fact that all IV-DDS that passed through the tumor once release the same amount of drug; the same is true for IV-DDS passing through the tumor a second and third time. IV-DDS with more than three passes were ignored, as they represent <<0.01% of all IV-DDS based on our model results. Each of these three IV-DDS populations was assigned a specific release time based on our experimental data, where we measured release time of fast releasing (fTSL) and slow releasing thermosensitive liposomes (sTSL) at 42ºC. We determined the release time as described above, but now measured three release times, for liposomes that had passed through the tumor zero, once, or twice, respectively. Accordingly, we made a linear fit to the TSL release data (1) during the first 5 s (=tumor transit time, i.e. the time a liposomes would spend in the tumor during a single pass), (2) from 5-10 s, (3) and from 10-15 s (Table S7). We added the following equations, where we represent IV-DDS populations individually that passed the tumor already zero, one, or two times (as mentioned, IV-DDS entering with >2 prior passes represent <<0.01% of all IV-DDS, and were ignored): As mentioned, for IV-DDS release, each IV-DDS population was considered with it's specific release time, and Equ. 9 and Equ. 10 were modified accordingly to consider all three IV-DDS populations from Equ. S1-S3. We performed a simulation where we assumed that the tumor was instantaneously heated to 42ºC, and remained at 42ºC for 6.6 min. This scenario represents a worst case relative to our experimental conditions, where temperature slowly approached 42ºC (where release is fastest), and remained between 41-42ºC for only 6.6 min (Fig. 4a). Note that below 41ºC, release is very slow (Fig.  S11), and no significant tumor drug accumulation occurs until tumor temperature reaches 41ºC (Fig.  4a,c). Figure S15 shows the results for the standard model compared to the model considering multiple passes. The reduced release from fTSL that pass through the tumor a 2 nd or 3 rd time manifests as lower concentrations in tumor plasma (cp T ) and tumor interstitium (ce T ) (Fig. S15b). The error due to neglecting multiple passes was however small, with 2.7% mean error for fTSL, and with 0.9% mean error for sTSL (Table S8).
The volume ratio of tumor plasma (where drug release from IV-DDS occurs) to systemic plasma (which serves as reservoir of IV-DDS-encapsulated drug) in the model was ~700:1, which is based off a mouse tumor with a volume of 10 μL. For comparison, to achieve this same ratio in a human patient would require a human tumor of >6 cm diameter. I.e. the consideration of the varying release time due to recirculation of IV-DDS can be neglected not only here, but also for most human tumors since the plasma volume where drug release from IV-DDS is triggered is very small compared to the systemic plasma volume.