Convective transport of oxygen along vessel segments and diffusion into the surrounding tissue (represented as homogeneous medium) was calculated based on previous estimates for blood flow in the networks, blood O₂ content, tissue diffusion, and consumption of O₂ (35, 56). All O₂ transport parameters are summarized in Table 1.

Inflow of prodrug to the microvascular networks was defined by its unbound plasma level, using area under the concentration-time curve (AUC) as a time-independent exposure variable compatible with Green’s function formalism. Vessel walls were modeled as offering negligible resistance to radial flux by setting the intravascular resistance constant K (56) to a low value (0.1 s/μm). Extravascular transport was calculated using a (pro)drug transport model (Figure 2) assuming that the tissue consists of two homogeneous (extracellular and intracellular) compartments, with activation of prodrug restricted to the intracellular compartment and diffusion confined to the extracellular compartment. Concentrations in the two compartments were calculated as follows: (1)φe∂CeN∂t=DN∇2CeN−φiktNCeN−CiN (2)φi∂CiN∂t=φiktNCeN−CiN−φikmetNCiN+rN

C_e and C_i are the extracellular and intracellular concentrations, respectively, of prodrug or effector (denoted by N = P or E), φ_i and φ_e are the intra- and extracellular volume fractions with φ_e = 1 − φ_i, k_tN are first order rate constants for cell transfer between the extracellular and intracellular compartments, D_N is the effective diffusion coefficient of compound N, ▽² is the Laplacian operator, k_metN is the rate constant for drug metabolism and r is the rate of metabolic production with r_P = 0 and rate of effector production equal to the rate of loss of prodrug: r_E = φ_ik_metPC_iP. The rate constant for prodrug activation is O₂-dependent and is given by: (3)kmetP=KO2KO2+[O2]kmetP,max where k_metP,max and k_metP are the prodrug activation rate constants under anoxia and at the O₂ concentration [O₂], respectively, and KO2 is the O₂ concentration for half-maximum prodrug activation.

Survival probability (SP) at each point of the tumor microregion was calculated using the PK/PD relationship: (4)−logSurvivalProbability(SP)=aAUCiE where AUC_iE is the intracellular exposure (area under the intracellular concentration-time curve) to the effector and a is a proportionality constant (potency) equal to the reciprocal of the effector AUC to produce a SP of 0.1 as measured by clonogenic cell survival.

We distinguish two cases: case 1, where potency a scales with k_metE, broadly representing irreversible inhibitors such as DNA-alkylating agents for which an increase in reactivity has similar effects on reaction with target and non-target nucleophiles (59, 60) and case 2, where a is independent of k_metE (broadly representing reversible inhibitors). Case 1, where cell killing is proportional to the reactivity of the effector is used throughout this study unless noted otherwise.

To estimate cell SP after radiation treatment, the linear-quadratic model was used as previously (35, 54). The SP from both radiation and prodrug at each point of the tumor microregion was calculated from the sum of log (SP) due to drug and radiation alone. Log cell kill was then calculated as (5)logcellkill=−log(AverageSP) where the SP is averaged over the whole tumor microregion. Prodrug-induced cell kill in addition to radiation was calculated as the difference between overall log cell kill by prodrug + radiation and log cell kill by radiation alone.

The SR-PK/PD model calculates the transport of prodrug and effector across the walls of the 582 vessel segments in the FaDu tumor microvascular network. Summing the 582 values for each compound gives the net transport across the tumor-plasma boundary (in picomoles). This was normalized to the volume of the FaDu tumor microregion.

PR-104H (33) and PR-104M (61) were prepared from PR-104A as described and stored in acetonitrile at −80°C. Tetradeuterated internal standards of PR-104H (PR-104H-d4) and PR-104M (PR-104M-d4) were synthesized using the same methods as for the non-deuterated compounds. PR-104H and PR-104H-d4 had a purity of >90% by HPLC while PR-104M and PR-104M-d4 had a purity of 86 and 84%, respectively.

All animal studies were approved by the University of Auckland Animal Ethics Committee. Male NIH-III nude mice (NIH-Lyst^bgFoxn1^nuBtk^xid; 18–20 g body weight), derived from breeding mice purchased from Charles River Laboratories (Wilmington, MA, USA), were dosed i.v. with PR-104H. The dosing solution was prepared fresh for each mouse by dilution of a stock solution of PR-104H in acetonitrile with sterile saline (to <20% acetonitrile) within 3 min of dosing to minimize loss of PR-104H in aqueous solution. At the dose volume of 0.005 ml/g the acetonitrile dose was 755 mg/kg and the vehicle alone did not cause signs of toxicity over the duration of the experiment. Blood was collected by cardiac puncture up to 3 min after cervical dislocation as in (62). Plasma was prepared as described (63) and mixed with three volumes of cold acidified methanol (methanol:ammonium acetate:acetic acid 1000:3.5:0.2, v/w/v) ~6 min after cardiac puncture. Liver tissue was dissected within 3 min of blood sampling, snap-frozen in liquid nitrogen, and stored at −80°C along with plasma samples. Frozen tissue was pulverized at liquid nitrogen temperature using a BioPulverizer™ (BioSpec Products, USA), transferred to tared tubes, weighed, vortex mixed for 30 s with an equal volume of cold phosphate buffered saline and six volumes of cold acidified methanol, and stored at −80°C. For LC-MS/MS analysis [as reported in Ref. (35)], tissue and plasma extracts were centrifuged (13,000 × g, 4°C, 10 min) and supernatants were mixed 1:1 with cold water containing 1 μM PR-104H-d4 and 1 μM PR-104M-d4.

We used a digitized 3D tumor microregion (Figure 3A) that was derived by mapping a region of a subcutaneous FaDu tumor xenograft grown in a mouse dorsal window chamber (57). To assess HAP activation under conditions of physiological hypoxia we also used a 3D region of a rat cremaster muscle (56) as an example of a normal tissue with a well-organized and efficient microvascular network (Figure 3B). While the maximum distance to the nearest blood vessel is 50 μm in the cremaster muscle region, 20% of tissue points in the FaDu tumor region are situated further from blood vessels (50–100 μm; Figure 3C). The FaDu tumor region also showed a higher heterogeneity in vessel diameters (Figure 3D), and a lower median blood flow rate (Figure 3E) at the values chosen for total blood inflow into the regions (Q; Table 1). Q per tissue volume was 2.5-fold lower in the FaDu tumor than in the cremaster muscle microregion, which is realistic for a low-perfused hypoxic tumor area. The value for the tumor microregion falls within the range of mean blood flow values measured in human tumors, which show high variability with values that can be lower, similar, or higher than in the tissue of origin (64, 65). A radiobiological hypoxic fraction (<4 μM O₂) of 43% was achieved in the FaDu tumor microregion (Figure 3F) by using O₂ transport parameters previously chosen to model the hypoxic fraction of tumor xenografts (35) (Table 1). The O₂ transport parameters for the cremaster muscle region were as reported (56), with the oxygen consumption rate adjusted to achieve a radiobiological hypoxic fraction of 7.5% (Figure 3F) that is consistent with moderate hypoxia as measured in some normal human tissues using O₂ electrode histography (45). However, the muscle region lacks the severely hypoxic cells (defined as <0.13 μM O₂, i.e., below the KO2 value for PR-104A) that comprise 5.0% of the FaDu microregion (Figure 3F).

Our previous SR-PK/PD model for Class I HAP showed that high prodrug activation rates limit killing of hypoxic cells by impairing tissue penetration of the prodrug (54). To investigate whether this also applies to HAP with bystander effects and/or activation restricted to more severe hypoxia (low KO2), we modulated the prodrug activation rate constant for anoxia (k_metP,max) under these conditions. For simulations without a bystander effect, k_tE was set to 0, which traps effector within the intracellular compartment.

Increasing k_metP,max resulted in a decrease of prodrug penetration to the most hypoxic regions, an effect that was less pronounced with a low KO2 (Figure 4A) than with a high KO2 value (Figure 4D), as expected. Accordingly, killing in the most hypoxic regions (<0.13 μM O₂) was higher and less affected by an increase in k_metP,max for low-KO2 HAP (Figures 4B,E; without bystander effects). The observed shift of cell killing to higher O₂ concentrations with increasing k_metP,max reflects increased prodrug activation at intermediate O₂ concentrations. In case of low-KO2 HAP this improved complementation of radiation-induced killing (Figure 4B), but in case of high-KO2 HAP it resulted in a loss of hypoxic selectivity at a 100-fold higher k_metP,max (Figure 4E). If the effector was allowed to diffuse through the plasma membrane (i.e., the bystander model), killing was increased across the whole tumor microregion, and killing <0.13 μM was less affected by decreasing prodrug penetration with increasing k_metP,max (Figures 4C,F).

Figures 4C,E illustrate the dependence on prodrug activation rate constant for HAP of Class II (low KO2 + bystander) and Class I (high KO2, no bystander) respectively. It should be noted that in the no-bystander simulations the effector potency, a, was set to a ~fivefold lower value (0.0414 μM⁻¹) than for Class II in Table 2. This was done in order to achieve similar overall (average) killing additional to radiation in the tumor microregion for Class I and II HAP under the default conditions (shown in black). Under these conditions, the Class I HAP provides more killing at intermediate O₂ concentrations (~0.2–10 μM), while the Class II HAP provides much higher cell kill under severe hypoxia (<0.2 μM O₂).

Figures 5A,B show overall HAP-mediated killing, averaged across the whole tumor microregion, for the cases demonstrated in Figure 4. In all cases, monotherapy activity increased with increasing prodrug activation rates over the range examined (k_metP,max = 0.001–1 s⁻¹), although more markedly for low-KO2 compounds (shown in red). This difference was even more pronounced for killing of radiobiologically hypoxic cells (i.e., killing additional to radiation; Figure 5B), in which case activity of high-KO2 compounds (shown in green) decreases at high rates of metabolism reflecting a severe penetration problem (which is not fully offset by allowing bystander diffusion). Class II HAP (dark red) are thus more tolerant of high values of k_metP,max than Class I HAP (light green).

The above analysis suggests that monotherapy activity increases monotonically with k_metP,max up to very high values, but it is important to consider whether this changes selectivity relative to normal tissues. To address this we used the above cremaster muscle microregion (Figure 3), to represent a generic well-perfused normal tissue with mild physiological hypoxia. For the present purpose, we assumed that this “normal tissue” is populated by cells with the same intrinsic sensitivity to effector as cells in the tumor microregion. Cell kill in the normal tissue region showed an even steeper dependence on k_metP,max than the tumor region (Figure 5C). As a consequence, tumor selectivity (assessed using the tumor:normal tissue ratio of log cell kill) fell as rates of bioreductive metabolism increased (Figure 5D). This falling therapeutic ratio reflects the greater compromise to delivery of rapidly metabolized prodrugs in the tumor network because of lower blood flow rates, longer diffusion distances, and more severe hypoxia than in the normal tissue (Figure 3). The model confirmed our expectation that toxicity to physiologically hypoxic normal tissues will be higher for a high-KO2 HAP (Figure 5C).

We next asked whether the activity of class II HAP is sensitive to the diffusibility of the prodrug, as previously shown by the SR-PK/PD model for tirapazamine analogs (54). In the latter study, tissue diffusion was defined by a single parameter, the effective diffusion coefficient as measured by flux through multicellular layer cultures; this represents the weighted averages of the free drug diffusion coefficient within cells, across membranes and in the extracellular matrix, based on treating tissue as homogenous space. In contrast, the present model explicitly considers extra- and intracellular compartments, and overall diffusion is determined by two parameters: the rate constant for transfer between extra- and intracellular compartments, k_tP, and the diffusion coefficient in the extracellular compartment D_P (Figure 2). Since changes in the physicochemical properties of HAP are expected to affect membrane permeability more than paracellular diffusion, k_tP was modulated. The results (Figure 6) show that hypoxic cell killing for Class I HAP is optimal at k_metP,max ~0.1 s⁻¹ [Figure 6A; consistent with the previous SR-PK/PD model for tirapazamine (54)]. Class I HAP also showed an optimum value of k_tP, reflecting the fact that the membrane transfer rate constant controls how much prodrug is available for intracellular activation. In contrast, for Class II HAP killing additional to radiation increased monotonically over the full range of k_metP,max and k_tP (Figure 6B) reflecting the tolerance of high rates of intracellular prodrug activation owing to a low KO2 and because effector diffusion offsets compromised prodrug penetration.

Next, we investigated the dependence of antitumor activity on effector parameters for Class II HAP. Since tissue transport of the effector is dependent on its membrane transfer (k_tE), paracellular diffusion (D_E) and its stability (k_metE), these parameters were modulated ~10-fold relative to the base model. In order to see an impact of a change in the paracellular diffusion coefficient D_E, k_tE had to be increased 10-fold to 0.1s⁻¹, indicating that effector transport is otherwise limited by membrane transfer. An increase in diffusion coefficient, D_E (Figure 7A) caused increased diffusion of the effector away from the hypoxic regions where it is formed, which decreased killing in hypoxic regions and increased killing in aerobic regions. As a consequence, overall killing in addition to radiation decreased and monotherapy activity increased (Figures 7B,C). A similar effect could be observed when increasing the membrane transfer rate constants k_tE (Figures 7D,E). However, the effect of increased diffusibility (higher D_E or k_tE) on single-agent activity was only minor because the effector was defined to freely permeate the blood vessel walls, and thus lost into the vasculature. The protective effect of this washout was confirmed by simulations with zero vessel permeability to the effector, which showed a much larger increase in HAP monotherapy activity with increasing k_tE (Figures 7G,H). Notably, an increase in effector diffusibility in the presence of vessel permeability elevated the tumor:normal tissue ratio of killing (Figures 7C,F), reflecting that washout of effector into the circulation is more protective in normal tissue (with lower distances to nearest vessel; Figure 3) than in tumor tissue.

The effect of increasing the rate constant for effector reaction k_metE was investigated using the default case where cell killing scales with effector reactivity (case 1) and alternatively where cell killing is independent of reactivity (case 2). The proportionality constant a was set to the values given in Table 2 to achieve equivalent killing of the two effector types at the default k_metE of 0.01 s⁻¹. In case 1, an increase in k_metE produces a proportional increase in the rate of formation of cytotoxic lesions and resulted in higher killing in hypoxic regions (Figure 8A). Killing in aerobic regions (>4 μM O₂) was decreased at high values of k_metE due to associated low effector penetration, and this limited overall activity (Figure 8B). Tumor selectivity decreased with increasing k_metE (Figure 8C) due largely to increasing cell killing in normal tissue.

In case 2 (where cytotoxic lesion production is independent of effector reactivity) decreasing k_metE resulted in higher killing across the whole tumor microregion (Figure 8D), with a large increase in HAP activity, both as a single agent and in addition to radiation, with increasing effector stability (Figure 8E). Killing in the normal tissue microregion was affected to a similar extent, so that tumor selectivity was comparable for different values of k_metE (Figure 8F).

The above analysis demonstrated that washout of effector by blood flow can, under some conditions, significantly protect perivascular cells from cytotoxicity. This raises the question whether effector washout might have pharmacodynamic effects in downstream tumor regions (redistribution of effector through the tumor vasculature), or might result in significant systemic exposure to the effector. To test the sensitivity of effector washout on different parameters, we used the Class II HAP model to calculate net transport of effector across the tumor/plasma boundary in each vessel segment of the tumor microregion. This showed high sensitivity to the rate constant of effector production (k_metP,max) and effector stability (k_metE) but only moderate sensitivity to effector diffusibility (k_tE and D_E) (Figure 9), because the former parameters substantially affect overall effector concentrations.

The impact on systemic exposure will depend on the distribution volume (V _D) and clearance (CL) of the effector. To evaluate a specific case, we returned to the SR-PK/PD model for PR-104 (35) because the plasma AUC of its active metabolites (PR-104H and PR-104M) after dosing PR-104 has been determined in three strains of mice (35, 52, 61). To facilitate this analysis, we measured the pharmacokinetics of PR-104H and PR-104M in plasma and liver following i.v. dosing of NIH-III nude mice with synthetic PR-104H (Figure 10). This showed a very short half-life (2.6 min) for PR-104H in plasma, and high PR-104M concentrations in plasma and liver, indicating rapid conversion of PR-104H to PR-104M. The half-lives of PR-104M in plasma and liver (~7 min) were similar to the half-life of PR-104M in culture medium at 37°C [6.6 min (35)], suggesting that CL of PR-104M is mainly due to its chemical instability.

Since washout was most sensitive to k_metP,max (Figure 9), we performed PR-104 SR-PK/PD model simulations using two different values of this parameter, corresponding to rates measured in vitro for HCT116/WT and a cell line with 20-fold higher k_metP,max (HCT116/sPOR#6) (35). This confirmed that washout of metabolites produced in hypoxic regions can increase plasma levels in nearby vessels, an effect that was more pronounced at the higher k_metP,max (white arrows in Figure 11). Using V _D and CL estimates from measured plasma PK following administration of PR-104 or PR-104H (Table 3), we calculated that washout would elevate the free plasma AUC of PR-104H+M in NIH-III nude mice [estimated from the measured PK after i.p. administration of 562 μmol/kg PR-104 (35)] by only 0.8% in case of HCT116/WT tumors, and 3.3% in case of HCT116/sPOR#6 tumors (Table 3). This was calculated assuming all PR-104H+M was released at once and hence represents a maximum addition to the circulating metabolites. This is consistent with published data showing similar plasma concentrations of reduced metabolites in NIH-III nude mice with HCT116/WT and HCT116/sPOR#6 tumors 30 min after i.p. administration of 562 μmol/kg PR-104 (35).

It should be noted that all simulations in this study were performed at blood flows where prodrug delivery and effector extraction were not highly perfusion limited. To demonstrate this (and the effect of blood flow on increasing effector washout into the systemic circulation) we increased the blood flow rate, Q, 2.5-fold, while decreasing inflow pO₂, to maintain a similar hypoxic fraction (Figures S1A,B in Supplementary Material). Under conditions of high prodrug metabolism (k_metP,max of 1 s⁻¹), this increased prodrug extraction from the plasma 1.5-fold and effector washout into the plasma twofold (Figure S1C in Supplementary Material) but overall killing in the microregion increased by only 26% (Figures S1D,E in Supplementary Material) reflecting little increase in perivascular effector concentrations.

A novel feature of the present study is the comparison of predictions for a tumor and normal tissue network, the latter based on a mapped microvascular network in a rat cremaster muscle (56) with oxygen consumption rate adjusted to simulate mild hypoxia (Figure 3). This comparison is important because the utility of HAP is likely to be constrained by the requirement that prodrug activation at intermediate O₂ does not cause toxicity in tissues with physiological hypoxia, such as liver (43–45), retina (66), and possibly bone marrow (49). The low tumor:normal tissue ratios of killing determined in our study (Figures 5, 7, and 8) point to limitations on achieving tumor selectivity with HAP. However, it is important to note that our model makes the assumption that intrinsic cellular sensitivity to the released effector (potency parameter a) is the same for cells in the tumor and normal tissue networks. Most effectors of HAP in clinical development are DNA-reactive cytotoxins (13) that provide some tumor-specificity due to the cytokinetics and DNA repair abnormalities (67) of tumor cells relative to normal cells. In addition, release of HAP effectors that target oncogenic pathways in tumor cells has potential for conferring additional tumor selectivity (68). Normal tissue models will need to be revisited when more quantitative information about oxygenation and drug targets in potentially dose-limiting normal tissues is available. Nevertheless, the present results emphasize the importance of using HAP strategies to augment selectivity of effectors that already provide some level of tumor selectivity, rather than as the sole mechanism of tumor targeting.

In addition, normal tissue toxicity due to washout of effectors has been a concern in the development of targeted anticancer prodrugs (69, 70) although to our knowledge no clear link between toxicity and increased effector levels has been established. In the current study systemic toxicity of HAP as a result of release of active metabolites from the tumor appears unlikely; our model suggests that a significant contribution to toxicity would require a combination of extreme assumptions (high tumor burden, intra-tumor activation rates, effector stability, tumor blood flow rates, as well as low systemic CL of effector). However, toxicity in normal tissue sharing a microcirculatory system with the tumor remains a possibility.

This study compared an idealized Class I HAP (high KO2 with no-bystander effect, illustrated by tirapazamine and SN30000) and a Class II HAP (low KO2 with bystander effect, e.g., PR-104A and TH-302) to assess which of these HAP strategies is better suited for complementation of radiotherapy. Our previous tirapazamine SR-PK/PD model showed that Class I HAP exhibit an optimum k_metP,max, above which hypoxic cell killing decreases because increasing consumption of the prodrug limits its penetration to hypoxic regions (54). This finding could be replicated using the present model, in which intra- and extracellular compartments are made explicit (Figure 5). In contrast, activity of Class II HAP was predicted to increase monotonically with increasing k_metP,max in the investigated range of 0.001–1 s⁻¹; we consider this range to be physiologically and pharmacologically relevant based on measured rate constants (32, 35, 54, 60). In addition, the potential to further increase k_metP,max by drug design would be limited by membrane transport and by the concurrent decrease in tumor selectivity (Figure 5D).

The superiority of Class II over Class I HAP at high k_metP,max can be explained by two factors. Firstly, the lower KO2 value minimizes metabolic loss during diffusion into hypoxic target regions (compare Figures 4A,D). Secondly, bystander effects alleviate the impact of poor prodrug penetration due to redistribution of effector between regions of different prodrug exposure. Both of these factors also explain the lower sensitivity of antitumor activity to prodrug diffusibility of class II relative to class I HAP (Figure 6).

Spatially resolved pharmacokinetic/pharmacodynamic modeling represents a valuable tool for the rational design of improved HAP, as has been demonstrated by our previous SR-PK/PD model for Class I HAP (54). The insight that there is an optimum for combinations of D_P and k_metP that can accommodate the competing requirements of efficient prodrug activation and tissue penetration prompted the SR-PK/PD model-guided screening of tirapazamine analogs (71) that identified SN30000 as a prodrug with superior tissue penetration and antitumor activity in combination with radiation (32). The model-based design of class II HAP presents a greater challenge as it requires the specific consideration of the transport parameters of the effector in addition to those of the prodrug. In this study SR-PK/PD modeling was used to identify reaction-diffusion parameters of Class II HAPs that could be optimized. The outcome is summarized in Table 4, which shows that antitumor activity of class II HAP could be enhanced by increasing k_metP,max, although this would need to be balanced against the need to maintain sufficient tumor selectivity.

When looking at the impact of a change in effector metabolism (k_metE) we distinguished two types of effectors: an effector that needs to react irreversibly with its target to elicit cytotoxicity, meaning that cell killing is a function of this chemical reactivity as for alkylating agents (Case 1), and an inhibitor where chemical transformation of the effector (whether spontaneously or by metabolism) gives rise to non-toxic products (Case 2). Modeling showed that effector reactivity should be increased in Case I but decreased in Case 2, in order to improve antitumor activity. In Case 1 the increase in overall killing when increasing reactivity by drug design needs to be balanced against a predicted decrease in tumor selectivity.

The model revealed that bystander effects are limited not only by diffusion and reaction of the effector, but also by effector washout, unless this washout targets downstream regions via a blood-borne bystander effect. The blood vessels act as a sink for effector, a problem that has previously been flagged in the context of drug diffusion into peritoneal tumors from the peritoneal cavity (72). Therefore, the choice of optimal effector diffusibility (defined by k_tE and D_E) depends on the therapeutic context, with low diffusibility generally better for combination with radiation, and high diffusibility preferred for monotherapy activity (Figures 7B,E).

Notably, a greater increase of bystander killing with increasing effector diffusibility has previously been suggested by the finding that bystander effects of dinitrobenzamide mustard prodrugs in multicellular layer co-cultures of NfsB-overexpressing and WT cells correlated with effector lipophilicity (73, 74). This may partially be due to the intimate mixture of activator and target cells in these co-cultures, so that effector washout at the multicellular layer boundaries affects both cell types to the same extent. In contrast, blood vessels in the virtual tumor microregion that act as a sink for effector are generally more distant from hypoxic prodrug-activating regions than from bystander target zones. Therefore, multicellular layer co-cultures have may limited use in assessing antitumor activity for HAP, although they are useful to rank HAP according to the diffusion range of their effectors.

Although an increase in the effector diffusion range provided only a moderate increase in single-agent activity it was found to have a surprisingly large effect in protecting cells in normal tissues where the HAP is activated (Figures 7C,F). Increasing effector diffusibility and prodrug activation rate simultaneously (the latter to compensate for washout) may therefore be a good strategy to improve monotherapy activity.

The suggested HAP model parameters could be modulated in drug design by changing the physicochemical properties that determined these parameters; e.g., one-electron reduction potential in controlling k_metP,max (9, 75, 76) or lipophilicity, pK_a, molecular weight, and number of H-bond donors and acceptors in controlling diffusibility (77). In most cases any change will affect several model parameters, but the value of the SR-PK/PD model lies in part in its ability to accommodate all such changes.

The high prodrug diffusibility and low effector diffusibility that would be ideal for combination with radiotherapy according to the model predictions may not be achievable in all chemical classes of HAP. In case of dinitrobenzamide mustards (PR-104 analogs), the physicochemical properties of prodrug and effector (other than mustard reactivity) will be similar since their structures only differ in one aromatic substituent. The use of fragmenting prodrugs of aliphatic mustards such as TH-302 relaxes this constraint, providing a higher scope for independent optimization of prodrug and effector diffusion properties.

The present SR-PK/PD model has two key limitations. Firstly, the model uses a small tumor region (0.12 mm³) that cannot be expected to fully capture the heterogeneity in vascular density and perfusion in tumors (78). This heterogeneity results in macroregional variations in oxygenation and prodrug delivery that may decrease the overall relevance of bystander effects of Class II HAP. For example, macroscopic, well-perfused, and oxygenated areas [observed in some tumor xenografts (35, 79, 80)] would be beyond the reach of the hypoxia-driven bystander effects studied here, unless there is redistribution of diffusible effectors between differently oxygenated tumor regions via the bloodstream (blood-borne bystander effect). Mapped tumor regions of a larger scale are not yet available but could be used to investigate these macroregional effects in the future. Secondly, our steady-state model does not account for time-dependent processes such as cycling hypoxia (81–83) and the kinetics of reoxygenation, cell proliferation, and cell death. Cycling hypoxia is thought to arise from variations in blood flow (84–86), which would affect not only delivery of oxygen but also that of the HAP. Since cycling hypoxia has a dominant periodicity of two to three cycles per hour (82), it may be relevant even for HAP with a residence time in the circulation of few hours and critically important for HAP with long residence times in tumors as is reoxygenation for effectors with long residence times such as AQ4N (87). The implications of variable blood flow and cycling hypoxia should be incorporated in future SR-PK/PD models.