Anne Rodallec

Sébastien Benzekry

Bruno Lacarelle

Joseph Ciccolini

Sebastien Benzekry

Dr Raphaelle Fanciullino
email: raphaelle.fanciullino@univ-amu.fr.

PHARMACOKINETICS VARIABILITY: WHY NANOPARTICLES ARE NOT MAGIC-BULLET IN ONCOLOGY

Keywords:

Abstract

Developing nanoparticles to improve the specificity of anticancer agents towards tumor tissues and to better control drug delivery is a rising strategy in oncology. An increasing number of forms (e.g., conjugated nanoparticles, liposomes, immunoliposomes…) are now made available on the shelves and numerous other scaffolds (e.g., dendrimeres, nanospheres, squalenes…) are currently at various stages of development. However, the attrition rate when developing nanoparticles is particularly high and several promising forms showing excellent behavior and efficacy in preclinical studies failed to succeed in subsequent first-in-man studies or later in phase-II trials. The issue of pharmacokinetic variability is a major, yet largely underestimated issue with nanoparticles. A wide variety of causes (e.g; tumor type and disease staging, comorbidities, patient's immune system) can explain this variability, which can in return impact negatively on pharmacodynamic endpoints such as lack of efficacy or severe toxicities. This review aims at covering the main causes for erratic pharmacokinetics observed with most nanoparticles. Should the main causes of such variability be identified, specific studies in non-clinical or clinical development stages could be undertaken using dedicated models (i.e., mechanistic or semi-mechanistic mathematical models such as PBPK approaches) to better describe nanoparticles pharmacokinetics and decipher PK/PD relationships. In addition, identifying relevant biomarkers or parameters likely to impact on nanoparticles pharmacokinetics would allow either modifying their characteristics to reduce the influence of the expected variability during development phases, or developing biomarker-based adaptive dosing strategies to

Introduction:

In oncology, achieving and ensuring an optimal efficacy/toxicity balance is still a challenging issue. The narrow therapeutics margins of standard cytotoxics and the issue of low intratumor diffusion have triggered huge expectations from the development of nanoparticles [1]. Thus, if much kind of nanoparticles have been developed over the last decades, relatively few have been actually approved over the last years. However, a rising number of new entities are making their way from bench to bedside application (Table 1), displaying now a wide variety of forms and indications (Figure 1). Despite increasing efforts and resources in developing nanocarriers, little is known about their actual pharmacokinetics. Paradoxically, the expected higher therapeutic efficacy is mostly based upon improved pharmacokinetics (i.e., reduced clearance, higher specificity towards target organs) [1]. However, the few data made available regarding nanoparticles (i.e., liposomes) pharmacokinetics have reported higher interpatient variability as compared with standard drugs [START_REF] Schell | Meta-analysis of inter-patient pharmacokinetic variability of liposomal and non-liposomal anticancer agents[END_REF], as if behavior of nanoparticles in the body could be both more targeted and less predictable. Of note, interpatient variability in drugs exposures is a major cause for treatment failure in oncology, owing to the narrow therapeutic window of most anticancer agents [START_REF] Mathijssen | Determining the optimal dose in the development of anticancer agents[END_REF]. To what extent this variability accounts for the particularly elevated attrition rates when developing nanoparticles remains to be fully elucidated. Here, this review will not exclusively but preferentially address the issue of liposomes pharmacokinetics in oncology, since most nanoparticles developed in cancer are liposomal drugs [4].

I.

Expected improvements in pharmacokinetics with nanoparticles.

1. Achieving longer exposure through decreased clearance.

In vivo elimination of conventional liposomes and other nanoparticles has been extensively studied and reported before [START_REF] Zamboni | Liposomal, Nanoparticle, and Conjugated Formulations of Anticancer Agents[END_REF]. Briefly, it depends on upstream interactions with specific proteins in plasma then activity of the Mononuclear Phagocyte System (MPS) [START_REF] Zamboni | Liposomal, Nanoparticle, and Conjugated Formulations of Anticancer Agents[END_REF]. Macrophages play indeed a major role, as 80% to 90% of nanoparticles will get engulfed in the liver or the spleen to get degraded. Although this process occurs rapidly, liposomes shows longer stay in the body as compared with free drugs [START_REF] Gabizon | Pharmacokinetics and Tissue Distribution of Doxorubicin Encapsulated in Stable Liposomes With Long Circulation Times[END_REF]. Even if first-generation nanoparticles displayed reduced clearance as compared with standard drugs, different strategies have been further developed next to limit organ uptake and immune system-related clearance. The most common strategy consists in masking the nanoparticle through surface pegylation, thus generating stealth, or second-generation nanoparticles [1]. Second-generation nanoparticles are less likely to be recognized by MPS and accumulate in the spleen and the liver [START_REF] Allen | Pharmacokinetics of stealth versus conventional liposomes: effect of dose[END_REF], enabling the drug to stay longer in the blood stream, as demonstrated for instance for stealth liposomal doxorubicine [START_REF] Gabizon | Prolonged circulation time and enhanced accumulation in malignant exudates of doxorubicin encapsulated in polyethylene-glycol coated liposomes[END_REF].

Reducing toxicity via higher tumor specificity

Passive tumor targeting: the EPR effect

Solids tumors present a leaky vasculature originally allowing nutrient supply, necessary for sustained tumor growth. This anarchical organization has been defined by Maeda as enabling the Enhanced Permeability and Retention (EPR) effect [START_REF] Maeda | The enhanced permeability and retention (EPR) effect in tumor vasculature: the key role of tumor-selective macromolecular drug targeting[END_REF]. Nanoparticles could passively target the tumor by going through the vasculature gaps (i.e., 200 nm [START_REF] Sawant | Challenges in Development of Targeted Liposomal Therapeutics[END_REF]) to be retained near the tumor because of deficient lymphatic drain (Figure 2).

Radiotherapy has been sometimes used to enlarge these gaps by depleting the pericytes, so as to further enhance permeation [START_REF] Kobayashi | Improving Conventional Enhanced Permeability and Retention (EPR) Effects; What Is the Appropriate Target?[END_REF] and thus tumor accumulation [START_REF] Lammers | Image-guided and passively tumourtargeted polymeric nanomedicines for radiochemotherapy[END_REF].

Developing stealth agents (e.g. PEG, see above) are other strategies to increase the EPR effect since the longer nanoparticles stay in the blood, the more they will pass through the vasculature gaps to target tumor tissues. This could explain why some nanoparticles display both decreased clearance and higher volume of distribution (Vd), with a limited drug accumulation in healthy tissues [1].

Active tumor targeting

In spite of a more specific delivery to the tumor, the EPR effect alone usually achieves less than a 2-fold increase [START_REF] Nakamura | Nanodrug Delivery: Is the Enhanced Permeability and Retention Effect Sufficient for Curing Cancer?[END_REF] of tumor accumulation. Efforts have thus been made for developing third generation nanoparticles that display more active targeting. This is mostly achieved by grafting on the surface of the carrier an agent that will recognize specifically cancer cells (Figure 3). Many moieties (e.g., small-molecule ligands, peptides and monoclonal antibodies) have been used over the last years to actively target cancer cells through different strategies, including targeting EGFR [START_REF] Xu | Biodistribution and Pharmacokinetics of EGFR-Targeted Thiolated Gelatin Nanoparticles Following Systemic Administration in Pancreatic Tumor-Bearing Mice[END_REF], folate and transferrin receptors, tumor antigens [START_REF] Deshpande | Current trends in the use of liposomes for tumor targeting[END_REF] and neo-antigens showing on the surface of irradiated tumor cells [START_REF] Lowery | Tumor-targeted delivery of liposome-encapsulated doxorubicin by use of a peptide that selectively binds to irradiated tumors[END_REF]. Bioengineered-albumin can also be used as a targeting agent, by generating albumin-bound nanoparticles. So far, albumin-bound paclitaxel is the only example of such scaffold (nab-paclitaxel, ABI-007) that showed better performances in terms of tumor tissue/healthy tissue balance as compared with free paclitaxel [START_REF] Desai | Increased antitumor activity, intratumor paclitaxel concentrations, and endothelial cell transport of cremophor-free, albumin-bound paclitaxel, ABI-007, compared with cremophor-based paclitaxel[END_REF]. Such targeting is achieved because nano-albumin has a higher affinity for SPARC glycoproteins that is found overexpressed in many cancer types such as breast or pancreatic cancers. Folic acid can also be used as a targeting agent, because it is recognized by folate receptors which are overexpressed in many cancer cells, thus ensuring eventually a better trafficking into tumors [START_REF] Wang | Folate-targeted docetaxel-lipid-basednanosuspensions for active-targeted cancer therapy[END_REF].

II.

Predicting nanocarrier pharmacokinetics: an ongoing challenge.

How to anticipate Carrier-driven Pharmacokinetics

1.1 Size.

As discussed since 1999 [START_REF] Nagayasu | The size of liposomes: a factor which affects their targeting efficiency to tumors and therapeutic activity of liposomal antitumor drugs[END_REF], size is a major factor not only for the residence time of nanoparticles in blood but also for further tumor targeting performances. The smaller is a nanoparticle the less it will be recognized by the MPS and eliminated from the body [START_REF] Liu | Role of liposome size and RES blockade in controlling biodistribution and tumor uptake of GM1-containing liposomes[END_REF]. However it has been demonstrated that nanoparticles <8 nm are mostly eliminated by the kidneys [START_REF] Choi | Renal Clearance of Nanoparticles[END_REF], not to mention loss of stability in plasma and therefore quicker clearance below a given size. Being too big (i.e., > 200 nm) is also a major drawback, since it prevents nanoparticles to benefit from the EPR Effect. Several studies have shown how size can affect the distribution phase within the tumor tissues and does matter indeed for tumor accumulation. When testing three different batches of stealth liposomes of 5-FU varying in size (i.e., 70 to 250 nm) in mice bearing resistant breast tumor, data showed that the smaller the liposomes, the greater the tumor uptake [START_REF] Fanciullino | Biodistribution, Tumor Uptake and Efficacy of 5-FU-Loaded Liposomes: Why Size Matters[END_REF].

Consequently, better efficacy and longer survival were achieved in animals treated with smaller liposomes, thus demonstrating how size can impact on tumor tissue distribution and efficacy endpoints eventually. Similar results were found by Charrois et al. who studied the influence of liposomes diameter on tumor distribution in mice bearing mammary carcinoma [START_REF] Charrois | Rate of biodistribution of STEALTH® liposomes to tumor and skin: influence of liposome diameter and implications for toxicity and therapeutic activity[END_REF]. Statistically significant lower accumulation and reduced efficacy were evidenced for bigger liposomes. Overall, those experimental results confirmed older studies reporting that the optimal size for nanoparticles has to be in the 100-200 nm range, much probably because of the EPR effect [START_REF] Mayer | Influence of Vesicle Size, Lipid Composition, and Drug-to-Lipid Ratio on the Biological Activity of Liposomal Doxorubicin in Mice[END_REF].

Composition

The use of stealth or targeting agent deeply modifies the drug pharmacokinetics. In addition, the choice of components is a key factor too since it will modulate the stability of the nanoparticle in the systemic circulation by affecting the RES recognition and subsequently the drug release. Unstable nanoparticles will display increased plasma clearance and reduced circulating times, as compared with stable nanoparticles. The Gregoriadis group extensively studied the major role of the composition in phospholipids and cholesterol in the early 1980's [START_REF] Senior | Stability of small unilamellar liposomes in serum and clearance from the circulation: the effect of the phospholipid and cholesterol components[END_REF]; subsequent studies have further addressed the issue of lipids and cholesterol ratios required to achieve the most stable liposomes with optimal controlled release, especially the critical role cholesterol plays [START_REF] Briuglia | Influence of cholesterol on liposome stability and on in vitro drug release[END_REF]. Indeed, cholesterol's inclusion in the lipids bilayer of a liposome stabilizes its structure and decreases drug leakage and risk of opsonisation, thus extending circulation time [START_REF] Ait-Oudhia | Application of Pharmacokinetic and Pharmacodynamic Analysis to the Development of Liposomal Formulations for Oncology[END_REF].

Electric Charge

The zeta potential of nanoparticles is another major factor influencing stability and pharmacokinetics. Of note, this potential depends all on the components used to synthesize the nanoparticle. Geng S et al. studied the impact of cholesterol on a doxorubicin PEGylated liposome stability, but this time focusing on electric charge [START_REF] Geng | Two cholesterol derivative-based PEGylated liposomes as drug delivery system, study on pharmacokinetics and drug delivery to retina[END_REF].

Using two cholesterol derivatives (i.e., positively charged VS. neutral), pharmacokinetic studies in rats showed that neutral cholesterol liposomes achieved higher stability than positively charged ones. Gabizon et al. tested in mice the impact of negatively charged lipids on liposomes clearance and found that it depended on their composition [START_REF] Gabizon | The role of surface charge and hydrophilic groups on liposome clearance in vivo[END_REF].

Similarly, the Torchillin group evaluated in mice the clearance of liposomes displaying different surface properties [START_REF] Levchenko | Liposome clearance in mice: the effect of a separate and combined presence of surface charge and polymer coating[END_REF]. Different charged lipids were tested, with or without surface pegylation. Charged liposomes showed higher clearance, especially the negatively charged one (i.e., with PA or PS) which were preferentially found in the liver.

Adding PEG-750 helped counter-balancing the higher clearance of positively (i.e. with SA) charged liposome but no that of negatively charged ones. Conversely, PEG-5000 partly reduced negatively charged liposome clearance, thus highlighting how complicated can be the combined impacts of electric charge and pegylation on subsequent nanoparticles pharmacokinetics. Recent studies have confirmed the deleterious impact of the negative charge on liposome clearance, and showed how pegylation can help improving their pharmacokinetics [START_REF] Zhang | The influence of different long-circulating materials on the pharmacokinetics of liposomal vincristine sulfate[END_REF]. Additionally, other studies focused on the impact of positively charged nanoparticles on tumor uptake. For instance, Campbell and al. have studied the biodistribution of cationic liposomes in human colon cancer bearing mice [START_REF] Campbell | Cationic Charge Determines the Distribution of Liposomes between the Vascular and Extravascular Compartments of Tumors[END_REF]. The impact of cationic lipid ratio on distribution was investigated: increasing cationic lipid by 10% decreased spleen uptake, whereas further increase did not reduce anymore liposome accumulation in spleen. Regarding tumor uptake, although differences in the total tumor accumulation were not statistically significant, intravital microscopy revealed that cationic charges specifically target tumor vasculature. Increasing the charge content led to doubling the neo-vessels uptake, suggesting its impact on the tumor distribution and the benefit of using charged lipids for further increasing tumor specificity. Indeed, as compared with neutral liposomes, the cationic ones display a higher tumor uptake that can be hindered when pegylated.

Positive charge and pegylation are then two opposite characteristics that can modulate tumor specificity. Both can be combined to achieve adequate targeting. For instance, Li and al. evaluated the quantitative relationship between these parameters on pancreatic cancer cells [START_REF] Li | Relationships between Liposome Properties, Cell Membrane Binding, Intracellular Processing, and Intracellular Bioavailability[END_REF], using liposomes with alterable zeta potential and using a methoxyanalog of PEG-DSPE to reduce the electric charge. Data showed that each mol % of PEG could be compensated with a 4 mV increase, thus suggesting the existence of a balance between those two parameters to maximize the stealth property while ensuring tumor internalization of cationic liposomes. Once again, this highlights the complexity of how carrier composition must be finely tuned to optimize its pharmacokinetics eventually, especially at the tumor level.

Shape

Although most of the developed carriers are spherical, other shaped nanoparticles showed interesting properties [START_REF] Truong | The importance of nanoparticle shape in cancer drug delivery[END_REF]. Shape is another major parameter indeed related to macrophages uptake and subsequent nanodrug biodistribution [START_REF] Toy | Shaping cancer nanomedicine: The effect of particle shape on the in vivo journey of nanoparticles[END_REF]. Macrophageinduced phagocytosis and therefore clearance not only depends on the size but also the geometry of the particle. Champion et al. described the behavior of macrophages against six nanoparticles shaped differently [START_REF] Champion | Role of target geometry in phagocytosis[END_REF]. Spheres, oblate ellipsoids, prolate ellipsoids, elliptical disks, rectangular disks, and UFOs shapes were studied. It was observed that the initial angle contact between the macrophages and the nanoparticles influences its phagocytosis and therefore its clearance. For instance, phagocytosis of elliptical disks could be 20 fold longer if macrophages attached along their minor axis, thus illustrating how shape is critical to reduce recognition by macrophages. Similarly, Barua et al., evaluated the impact of particle shape on its tumor internalization [START_REF] Barua | Particle shape enhances specificity of antibody-displaying nanoparticles[END_REF].

They studied tumor uptake of spherical, rod-and disk-shaped particles in different breast cancer models. When uncoated, spheroid nanoparticles showed higher tumor specificity. However, those results were different when adding trastuzumab as targeting agent. Indeed, when coated, tumor internalization of rod-shaped, and to a lesser extent disk-shaped particles, were higher than with the spherical ones.

Protein corona

When in biological fluids, the nanoparticle surface attracts proteins and biomolecules which will form around the liposome a dynamic layer, exchanging continuously with the environment. This rapidly shaped layer is usually called protein corona. Its composition depends on the surface properties of the nanoparticle, the nature of the environment, the time of exposure and the tumor type [START_REF] Colapicchioni | Personalized liposome-protein corona in the blood of breast, gastric and pancreatic cancer patients[END_REF]. The protein corona can affect liposome specificity by modifying its surface properties (i.e., charge, size) or by hampering targeting agents [START_REF] Salvati | Transferrin-functionalized nanoparticles lose their targeting capabilities when a biomolecule corona adsorbs on the surface[END_REF]. However, the presence of specific proteins in the corona can also improve tumor uptake. Corbo and al. demonstrated that the presence of apolipoproteins and immunoglobulins in the corona increased liposome uptake in breast cancer cells [START_REF] Corbo | Effects of the protein corona on liposome-liposome and liposome-cell interactions[END_REF]. They found however a similar increase in macrophages uptake, modifying the drug release rate from the carrier. When engulfed by the MPS, the encapsulated drug is quickly released indeed and stops benefiting from advantages such as a longer half-life and a more specific biodistribution towards tumor tissues. Thus, efficacy/toxicity balance can be affected [START_REF] Charrois | Drug release rate influences the pharmacokinetics, biodistribution, therapeutic activity, and toxicity of pegylated liposomal doxorubicin formulations in murine breast cancer[END_REF], because the nanoparticle pharmacokinetics becomes quickly similar to that of the free drug.

Separating the free drug from the carried one: an ongoing challenge.

The lack of comprehensive pharmacokinetic studies with nanoparticles can be partly explained by the fact that it remains difficult to discriminate carried drugs from free drugs in the blood stream. Depending on the nanoparticle stability and its pharmacokinetics, part of the payload can be released early from the carrier.

Consequently, both carried drug and free form are found together in plasma, but most standard bioanalytical techniques used when performing PK studies will fail in discriminating them. Direct methods usually used to differentiate non-protein-bound drugs to bound-ones, like solid-phase micro extraction could be adapted to measure the amount of drug remaining inside the liposome [START_REF] Sullivan | Rapid Method for Determination of Residual tert-Butanol in Liposomes Using Solid-Phase Microextraction and Gas Chromatography[END_REF]. For instance, Hempel's group developed an analytical method based on solid-phase extraction followed by capillary electrophoresis with fluorescence detection, to quantify drug concentration of free and encapsulated daunorubicin in plasma [START_REF] Griese | Determination of free and liposome-associated daunorubicin and daunorubicinol in plasma by capillary electrophoresis[END_REF]. Another promising technique is based upon microdialysis probes applied to nanomedicine. Microdialysis technique relies indeed on the passive uptake of free, unbound drug only. If the cut-off of the semi-permeable membrane is smaller the nanoparticle diameter, then only the free released drug will cross the membrane to be further analyzed. Parallel blood sampling will allow measuring the whole drug, thus enabling to discriminate encapsulated and non-encapsulated drug. Of note, only the free-fraction of the released drug will be measured; however, by knowing the protein binding of the drug it is possible to calculate the whole concentration eventually. In those conditions, Zamboni's group was able to measure in vivo the percentage of encapsulated and released platinum and topotecan [START_REF] Zamboni | Relationship between tumor extracellular fluid exposure to topotecan and tumor response in human neuroblastoma xenograft and cell lines[END_REF]. The released drug displays theoretically the same pharmacokinetic parameters than the standard, non-encapsulated form. However, because its own release rate is closely related to the pharmacokinetics of the carrier, its ADME profile depends eventually on the upstream behavior of the carrier in the body, thus generating an erratic behavior because its Ka is likely to be impacted by the pharmacokinetics of the carrier. Indeed, the absorption rate Ka of the released drug directly depends on the Ke elimination rate of the nanoparticle, which itself is related to the stability of the carrier (see above). Drug release varies therefore upon the nanoparticle composition, the fabrication process and the drug properties (Figure 4). Nounou et al. used compared in vitro the release rates from a liposomal hydrophobic drug (i.e., dibucaine base) and a more hydrophilic drug (i.e., 5-fluorouracil) [START_REF] Nounou | In vitro release of hydrophilic and hydrophobic drugs from liposomal dispersions and gels[END_REF]. Results showed major differences between the two drugs. Whereas liposomal dibucaine was stable, 5-fluorouracil nanoparticles showed a burst effect, with a fast and early leakage followed by a constant release phase. Studying drug release keeps being improved with the recent development of numerical deconvolutions that can evaluate the drug release directly from the nanoparticle, and no longer from the receiver compartment [START_REF] Zhou | A New Method for Evaluating Actual Drug Release Kinetics of Nanoparticles inside Dialysis Devices via Numerical Deconvolution[END_REF].

How tumor characteristics can affect nanoparticle pharmacokinetics?

3.1. confirmed in breast cancer bearing mice that vascular density was a key-factor impacting on the extent of the tumor uptake of stealth liposomal 5-FU uptake measured at different cancer stages [START_REF] Fanciullino | Biodistribution, Tumor Uptake and Efficacy of 5-FU-Loaded Liposomes: Why Size Matters[END_REF]. A strong correlation was evidenced between tumor size, vascular density and the accumulation of liposomes, suggesting a lower accumulation in metastasis. Although only experimental, such data provided clues for better understanding the negative impact anti-angiogenics drug could have when combined with nanoparticles as reported in phase II trial combining bevacizumab and nabpaclitaxel [START_REF] Heist | Improved tumor vascularization after anti-VEGF therapy with carboplatin and nab-paclitaxel associates with survival in lung cancer[END_REF]. It is however suggested that bevacizumab induces a transitory vascular normalizing effect on tumor neo-vessels [START_REF] Jain | Antiangiogenic therapy for cancer: current and emerging concepts[END_REF], and that during this phase of normalization the amount of associated cytotoxic reaching the tumor would be greater [START_REF] Mollard | Model driven optimization of antiangiogenics + cytotoxics combination: application to breast cancer mice treated with bevacizumab + paclitaxel doublet leads to reduced tumor growth and fewer metastasis[END_REF]. Therefore, sequential administration of antiangiogenics followed by nanoparticles could improve the efficacy of the combination. In this context, mathematical models could be used to predict the vasculature normalization [START_REF] Benzekry | A new mathematical model for optimizing the combination between antiangiogenic and cytotoxic drugs in oncology[END_REF] so as to determine the best time-window to optimize the distribution of nanoparticles when combined to anti VEGF agents.

Tumor Microenvironment

The tumor microenvironment including all the non-neoplastic cells such as fibroblasts, immune cells, stem cells, and endothelial cells [START_REF] Adjei | Modulation of the tumor microenvironment for cancer treatment: a biomaterials approach[END_REF] could modulate the EPR effect [START_REF] Zhao | Molecular targeting of liposomal nanoparticles to tumor microenvironment[END_REF].

Zamboni's group studied in mice bearing melanoma and ovarian xenografts the relationships between tumor accumulation of pegylated-liposomal drug and MPS [START_REF] Zamboni | Tumor disposition of pegylated liposomal CKD-602 and the reticuloendothelial system in preclinical tumor models[END_REF].

The greater presence of macrophages and dendritic cells in the tumor extracellular fluid of ovarian model was related to increased tumor delivery of pegylated liposome when compared to melanoma model. These results suggest the close relationship between nanoparticle delivery and the MPS. More recently, the same group confirmed the importance of tumor microenvironment heterogeneity depending on tumor type, by profiling the MPS in mice bearing ovarian, breast, and endometrial xenografts [START_REF] Lucas | Profiling the relationship between tumorassociated macrophages and pharmacokinetics of liposomal agents in preclinical murine models[END_REF].

Macrophages were quantified in the liver, the spleen and the tumor and marked differences were found between the tumor types. Significantly more macrophages were found in both liver and spleen in animals with endometrial cancer than those with breast and ovarian cancers. Similarly, differences in tumors infiltrating macrophages depending on cancer types were observed. Significantly more macrophages were found in breast cancer models as compared with ovarian and endometrial tumors. This macrophage disparity in the liver, the spleen and the tumor was also reported for various cell lines within a same tumor type. Because macrophages play an important role in the clearance of nanoparticles, such variability can impact their pharmacokinetics at the tumor level, thus explaining why and how tumor type could affect nanoparticles pharmacokinetics. In addition, because tumor microenvironment can be considered as a target related to tumor growth and to drug delivery, several studies have focused on strategies to affect its barrier. Chen and al. oxygenated the tumor microenvironment to decrease head-and-neck cancer resistance to radiations and chemotherapies [START_REF] Chen | Oxygen microenvironment affects the uptake of nanoparticles in head and neck tumor cells[END_REF] whereas Hingorani and al. proved that pegylated hyaluronidase (PEGPH20) can be useful to enhance the efficacy of nanoparticles. Hyaluronic acid halos in the tumor micro-environment matrix reduce tumor perfusion and therefore limit the access of nanoparticles. In a recent phase-II trial, PEGPH20 was associated to nab-paclitaxel plus gemcitabine in pancreatic cancer. Both responses and survival were improved using this strategy [START_REF] Hingorani | Interim results of a randomized phase II study of PEGPH20 added to nab-paclitaxel/gemcitabine in patients with stage IV previously untreated pancreatic cancer[END_REF]. Finally, triggered drug delivery systems are a promising option to release the drug from the nanocarrier in tumor surroundings only. It can be functionalized with heat, ultrasound, light, enzymes or pH [START_REF] Bregoli | Nanomedicine applied to translational oncology: A future perspective on cancer treatment[END_REF]. Ph-triggered nanoparticles such as liposomes and micelles can specifically release their bioactive content in the tumor microenvironment, because of the acidic tumor surroundings [START_REF] Lindner | Factors affecting drug release from liposomes[END_REF],

highlighting how tumor specificities can be used as a Trojan horse to target cancer tissues.

III. Main Causes for NPs pharmacokinetic variability 1. Age

Because nanoparticles, especially the stealth ones, are expected to bypass liver uptake and to avoid renal elimination, age which affects usually those organs should theoretically not be a factor of variation (Fig. 5). However, because age affects the MPS, it can in some respect change nanoparticles pharmacokinetics [START_REF] Plowden | Innate immunity in aging: impact on macrophage function[END_REF]. For instance, pharmacokinetics of doxorubicin encapsulated in PEGylated liposomes was studied in 35 elderly patients. Doxorubicin plasma levels, leukocyte DNA breaks and monocytes count variations were measured as PK and PD endpoints. Results showed a 30% increase in mean T1/2 with two-fold increase in drug plasma levels for patients > 77 years old. Older patients (i.e., > 80 years) showed even more extended half-life [START_REF] Gusella | Age affects pegylated liposomal doxorubicin elimination and tolerability in patients over 70 years old[END_REF]. In addition, age can also be associated with increased toxicities upon nanoparticles administration. Wu and al. also related age-effect with irinotecan PEGylated liposome (IHL-305) in patients with advanced solid tumors [START_REF] Wu | Factors affecting the pharmacokinetics and pharmacodynamics of PEGylated liposomal irinotecan (IHL-305) in patients with advanced solid tumors[END_REF]. Neutrophils and monocytes decrease were found lower in younger patients (i.e., <60 years old), with an inverse correlation between monocytes decrease and clearance of total irinotecan.

Consequently, it seems that nanoparticles may display reduced clearance and subsequent increased exposure and pharmacodynamic effects (efficacy, toxicity) in the elderly, thus advocating for adaptive dosing strategies in older patients.

Body mass

Body mass is usually best described through BMI or body surface area (BSA). It can affect drug pharmacokinetics because the Vd depends partly on hydrophilic or lipophilic profile (i.e., lipophilic drugs tend to accumulate in fat tissues). Considering the more specific distribution achieved with nanoparticles, limited impact is expected from changes in body mass. However it has been suggested that body weight could modulate the clearance of nanoparticles via changes in the MPS [START_REF] Zamboni | Factors affecting the pharmacokinetics of pegylated liposomal doxorubicin in patients[END_REF]. In a clinical study, LaBeck and al. evaluated factors that affect pharmacokinetics of PEGylated liposomal doxorubicin as part of phase I/II studies in 70 patients with either solid tumors or Kaposi's sarcoma. BSA and BMI were both evaluated as potential covariates in the clearance values. BSA, but not BMI, contributed to a non-significant reduction in the clearance variability, thus suggesting that its impact was only marginal. However, Wu and. al showed that clearance of pegylated liposomal irinotecan (IHL-305) was dependent on a composite marker between body mass and age [START_REF] Wu | Factors affecting the pharmacokinetics and pharmacodynamics of PEGylated liposomal irinotecan (IHL-305) in patients with advanced solid tumors[END_REF]. The relationship between the ratio of total body weight to ideal body weight (TBW/IBW) and age with IHL-305 pharmacokinetics was evaluated, and showed that old patients plus TBW/IBW higher than the median displayed higher levels of free circulating irinotecan, thus suggesting a loss of stability of the nanoparticle in elderly patients with overweight.

Increased proteinemia in overweight people could explain this difference, and suggest that specific populations (e.g., obese patients) should have their dosing tailored.

Gender

It is well established that gender is a factor affecting a drug pharmacokinetics, distribution and clearance because of sex differences in body mass distribution, enzymes activities, to name but a few [START_REF] Harris | Gender effects in pharmacokinetics and pharmacodynamics[END_REF]. La Beck and colleagues evaluated using non-compartmental methods the impact of gender on the clearance of three PEGylated liposomes. For each nanocarrier, female patients displayed lower clearances as compared with males, a finding consistent with previous reports regarding gender difference in drug pharmacokinetics [START_REF] Wu | The evaluation of gender on the pharmacokinetics (PK) of pegylated liposomal anticancer agents[END_REF]. With nanoparticles, the most significant results

were found for doxorubicin PEGylated liposome because female patients showed a 58% reduction in clearance as compared with men [START_REF] Wu | The evaluation of gender on the pharmacokinetics (PK) of pegylated liposomal anticancer agents[END_REF].

Drug-drug interactions

Only few studies have reported drug-drug interactions with nanoparticles. Because of reduced liver uptake and the fact that nanoparticles are not substrate of efflux transporters, there are less likely to be affected by inhibiting/inducting drugs. However, liposomal doxorubicin (Doxil®) showed higher AUC and decreased clearance when coadministrated with paclitaxel or docetaxel [START_REF] Briasoulis | Interaction pharmacokinetics of pegylated liposomal doxorubicin (Caelyx) on coadministration with paclitaxel or docetaxel[END_REF]. Inversely when given after Cisplatin, the clearance of Doxil® was increased, although no clear underlying mechanisms has been identified yet [START_REF] Petschauer | The effects of nanoparticle drug loading on the pharmacokinetics of anticancer agents[END_REF]. Other clinical data suggested possible interaction of liposomal doxorubicin with bevacizumab. When given as a combination for treating locally recurrent or metastatic breast cancer, they triggered more toxicities than expected, suggesting overexposure [START_REF] Petschauer | The effects of nanoparticle drug loading on the pharmacokinetics of anticancer agents[END_REF]. As related earlier, bevacizumab and to a broader extent anti-angiogenics are also suspected to decrease nanoparticles efficacy through a diminished EPR effect, although no experimental data have demonstrated this point [START_REF] Heist | Improved tumor vascularization after anti-VEGF therapy with carboplatin and nab-paclitaxel associates with survival in lung cancer[END_REF].

Immunity

Nanoparticle clearance being partly controlled by the immune system and more specifically the MPS, evaluating its activity and possible causes for variations is critical [START_REF] Song | Nanoparticles and the Mononuclear Phagocyte System: Pharmacokinetics and Applications for Inflammatory Diseases[END_REF]. A preclinical study demonstrated the influence of the tumor type on the MPS and resulting impact on nanoparticles clearance [START_REF] Kai | Tumor Presence Induces Global Immune Changes and Enhances Nanoparticle Clearance[END_REF]. The modification in immune cells population near the tumor is indeed well established [START_REF] Marigo | Tumor-induced tolerance and immune suppression by myeloid derived suppressor cells[END_REF], and can affect the MPS global activity. Decreased circulation time of the nanoparticle was observed in tumor-bearing mice as compared with healthy mice and among the different xenografted cancer models. Such discrepancy was explained by an increase in M2-like macrophages activity, demonstrating the importance of tumor type on the variability of the MPS activity. Prior treatment, especially with cytotoxics, is another major factor explaining variability in MPS activity. Most cytotoxics will indeed affect the MPS and subsequently the nanoparticles clearance. For instance, in a phase-I study of liposomal camptothecin analog, deep and equal decrease in both monocytes and neutrophils was first found with standard CKD-602 [START_REF] Zamboni | Bidirectional pharmacodynamic interaction between pegylated liposomal CKD-602 (S-CKD602) and monocytes in patients with refractory solid tumors[END_REF]. Conversely with liposomal S-CKD602, decrease in monocytes was deeper than in neutrophils. This discrepancy could be explained by the fact that liposomes are likely to be engulfed in monocytes. Gusella and al. also demonstrated the major effect of previous treatment on doxorubicin pegylated liposomes administrated in patients above 70 years old [START_REF] Gusella | Age affects pegylated liposomal doxorubicin elimination and tolerability in patients over 70 years old[END_REF]. They found a reduction in nanoparticle clearance throughout cycles, related to monocyte count, suggesting that treatment-related impact on the MPS will, in return, modify the pharmacokinetics.

Genetic polymorphism

Germinal polymorphisms affecting genes coding for proteins implicated into ADME (liver enzymes, membrane transporters) can be major causes for pharmacokinetic variability with anticancer agents. For instance, genotyping of UGT1A1 (UDP glucoronosyltransferase 1A1) allelic variants (i.e., UGT1A1*28) is recommended when giving irinotecan to colorectal cancer patients [START_REF] Innocenti | Dose-Finding and Pharmacokinetic Study to Optimize the Dosing of Irinotecan According to the UGT1A1 Genotype of Patients With Cancer[END_REF]. UGT1A1 being involved in active showed that patients with the homozygous UGT1A1*28 variant could be safely administered with the nanoparticle provided that 50% reduction in dosing was performed [START_REF] Infante | Phase I and pharmacokinetic study of IHL-305 (PEGylated liposomal irinotecan) in patients with advanced solid tumors[END_REF]. Similarly, when developing liposomal irinotecan MM-398 (Onyvide®), starting with half-dose for the first course was recommended in UGT1A1*28 patients, then switching to standard dose next if the first administration was well tolerated. More recently, a phase-1 study of liposomal SN-38 also demonstrated a good safety profile, regardless of the UGT1A1 genotypes [START_REF] Kraut | Final results of a phase I study of liposome encapsulated SN-38 (LE-SN38): Safety, pharmacogenomics, pharmacokinetics, and tumor response[END_REF]. Similarly, DPYD genetic polymorphism leading to DPD deficiency syndrome strongly impact on the PK and safety of standard 5-FU, one of the most widely prescribed anticancer agent. In a non-clinical study in rodents, it has been demonstrated that stealth liposomal 5-FU was only moderately affected by the DPD status (i.e., DPD deficiency) in terms of pharmacokinetics and toxicities, whereas standard 5-FU administered to DPD-deficient rats led to sharp plasma overexposure and subsequent severe neutropenia [START_REF] Fanciullino | In Vitro and In Vivo Evaluation of Lipofufol, a New Triple Stealth Liposomal Formulation of Modulated 5-Fu: Impact on Efficacy and Toxicity[END_REF]. This illustrates how developing stealth nanoparticles to bypass at least partly liver uptake and metabolic clearance could help reducing the deleterious impact of genetic polymorphisms affecting liver enzymes. Finally, the role of genetic factors on doxorubicin PEGylated liposome was recently studied in mice. Results showed a correlation between nanoparticles clearance with a variation within a genomic region encoding for Gulp 1, a protein necessary for the engulfment of apoptotic cells by phagocytes. This suggests new genetic variants potentially involved in inter-patient variability observed with nanoparticles [START_REF] Song | Gulp1 is associated with the pharmacokinetics of PEGylated liposomal doxorubicin (PLD) in inbred mouse strains[END_REF].

IV.

Mathematical models: a tool for a better understanding of nanoparticles pharmacokinetics?

Mechanistic models of nanodrugs distribution

the scale of a tumor and its associated vasculature, mathematical models can be derived for the intra-tumor drug transport and have relevance to address important questions for the design of nanoparticles. First, static differences in the fractal organization of the vasculature between tumor and healthy tissue have been evidenced

and characterized by mathematical constructs [START_REF] Gazit | Fractal characteristics of tumor vascular architecture during tumor growth and regression[END_REF]. Going further, biophysical models attached to the description of interstitial tumor drug transport have been developed [START_REF] Jain | Transport of molecules in the tumor interstitium: a review[END_REF].

These are based on established biophysical laws such as Starling law for flow across semi-permeable membranes, Darcy's law for flow through porous media or Poiseuille's equation for fluid velocity profiles [START_REF] Zamboni | Bidirectional pharmacodynamic interaction between pegylated liposomal CKD-602 (S-CKD602) and monocytes in patients with refractory solid tumors[END_REF]. Therefore, they rely on biophysically meaningful and measurable parameters which in turn allows to make quantitative predictions. Liu et al. reviewed computational techniques for modeling of nanomedicine, including continuum and stochastic-based methods [START_REF] Liu | Computational Modeling of Nanoparticle Targeted Drug Delivery[END_REF]. The interest of such techniques lies in their ability to predict (and thus, optimize) the outcome on tumor cell kill of specific characteristics of nano-carriers such as their size, drug release rate or binding affinity.

They rely on the derivation of equations that allow the computation of quantities of fundamental importance for drug transport such as the blood vessels velocity profile, the interstitial fluid pressure and the encapsulated or free drug concentrations in the tissues.

Comparative effects of diffusive and convective transport can then be computed, leading to quantitative predictions of the amount of drug effectively reaching the tumor cells and ultimately killing them, as a function of the nanocarrier properties (such as its size, weight, shape, drug load or drug release rate). For instance, the impact of multistage release of nested nanoparticles has been computationally investigated in where simulations were used to tune drug release kinetics and binding affinities in order to improve the drug delivery, and favored smaller nanoparticles. Similar investigation of multi-stage gold nanoparticles was also performed in [START_REF] Curtis | An interdisciplinary computational/experimental approach to evaluate drug-loaded gold nanoparticle tumor cytotoxicity[END_REF]. In another study from the same group, modeling was employed to investigate the impact of post-angiogenesis inhibition vascular normalization [START_REF] Jain | Normalization of tumor vasculature: an emerging concept in antiangiogenic therapy[END_REF] on the delivery of nanoparticles and demonstrated that drug delivery was improved but only for small (i.e., 12 nm diameter) nanoparticles [START_REF] Chauhan | Normalization of tumour blood vessels improves the delivery of nanomedicines in a size-dependent manner[END_REF]. One level of complexity higher, other groups have developed models still based on the principles of continuum mechanics that integrate two additional components:

tumor cells (possibly composed of several phases) and angiogenesis. Indeed, the 1990's have witnessed extensive mathematical modeling research for description of spatially distributed tumor growth, with various levels of complexity and phenomena taken into account at the tumor scale (e.g., avascular versus vascular tumor growth, hypoxia, necrosis, invasion and interactions with the extra-cellular matrix) [START_REF] Byrne | Dissecting cancer through mathematics: from the cell to the animal model[END_REF]. A dynamic interplay exists between tumor growth and the development of the surrounding vasculature (necessary to grow beyond the diffusion limit of nutrients, i.e. a few millimeters in diameter), which motivated mathematicians to develop even more complex models of vascular tumor growth [START_REF] Anderson | Continuous and discrete mathematical models of tumor-induced angiogenesis[END_REF]. These have relevance in the context of nanoparticles delivery. Indeed, when coupled with hydrostatic laws of network fluid distributions, the models can predict perfusion features of the tumor vasculature and associated heterogeneity [START_REF] Curtis | An interdisciplinary computational/experimental approach to evaluate drug-loaded gold nanoparticle tumor cytotoxicity[END_REF]. However, due to the technical difficulty to obtain morphological data of blood networks formation and blood flow in vivo, it is very challenging to validate them against experimental data [START_REF] Stéphanou | How tumour-induced vascular changes alter angiogenesis: Insights from a computational model[END_REF]. Building on a model that incorporates the above-mentioned features [START_REF] Zheng | Nonlinear simulation of tumor necrosis, neovascularization and tissue invasion via an adaptive finite-element/level-set method[END_REF], the first model integrating tumor growth with delivery of nanoparticles compared the delivery of a cytotoxic drug either via free drug administration or via 100 nm nanocarriers [START_REF] Sinek | Two-dimensional chemotherapy simulations demonstrate fundamental transport and tumor response limitations involving nanoparticles[END_REF]. They found that drug transport limitations were severe, with important areas of the tumor where the drug concentration did not reach adequate levels. In a subsequent study, quantitative data from intravital microscopy was combined to computational simulations to determine how much drug per particle and how many particles need to be released in the vasculature to ensure tumor decay [START_REF] Van De Ven | Integrated intravital microscopy and mathematical modeling to optimize nanotherapeutics delivery to tumors[END_REF]. covariate, as seen above (see also [START_REF] Wu | Population Pharmacokinetics of Pegylated Liposomal CKD-602 (S-CKD602) in Patients With Advanced Malignancies[END_REF] for a similar study with another anticancer liposomal-encapsulated drug). For determination of the initial dose in Phase-I clinical trials, it is essential to be able to predict PK disposition in humans from animal data.

Pharmacokinetics (PK

Classical approaches for PK interspecies extrapolation consist mainly in allometric scaling laws (with body weight or other physiologically relevant variable). A study of the applicability of allometry was performed to determine the clearance in humans of several pegylated liposomal and nanoparticle anticancer agents [START_REF] Caron | Allometric scaling of pegylated liposomal anticancer drugs[END_REF]. Due to the particularity of the elimination process for these molecules (through the mononuclear phagocytic system rather than kidney and/or liver, see above), the authors integrated to their analysis variables potentially related to this process such as the spleen weight or the total monocyte count. Nevertheless, an important discrepancy between the clearance predictions and observations from a Phase-I clinical trial was obtained, possibly because of the influence of tumor type. To perform interspecies scaling in more details, PBPK models have recently been developed for the PK of nanoparticles (Figure 6) [START_REF] Li | Physiologically based pharmacokinetic modeling of nanoparticles[END_REF]. These are based on a more realistic and intricate description of the vascular system and organs vascular distribution than with mere aggregated compartments. Lin et al. used a PBPK model for gold nanoparticles first developed in mice [START_REF] Lin | A physiologically based pharmacokinetic model for polyethylene glycol-coated gold nanoparticles of different sizes in adult mice[END_REF] and further extended to other species including human [START_REF] Lin | A computational framework for interspecies pharmacokinetics, exposure and toxicity assessment of gold nanoparticles[END_REF]. Based on a common structure for all species and species-specific adaptation of physiological parameters (thus determined a priori), they obtained good predictions of concentrations independently measured in humans. Together, mathematical modeling offers a powerful comprehensive framework for interpretation/analysis of experimental data at various scales which provides quantitative information and predictions useful for the optimal design of the nanoparticle itself (tumor-scale models) and determination of improved scheduling strategies (dosing and timing) both for clinical trials and personalized clinical routine (organism-scale PK models).

Conclusion & Perspectives: nanoparticles are not magic bullets!

Far from being the universal "magic bullet" once expected, the nanoparticles show a wide range of different parameters possibly impacting on their pharmacokinetics, and therefore their efficacy/toxicity balance. When studying the pharmacokinetics of nanocarriers, one must consider three distinct pharmacokinetic profiles: the systemic one, the tumor microenvironment one and the tumor one. In addition, discriminating free released drug and drug encapsulated or conjugated to its carrier is critical. This singularity plus the wide variety of factors possibly impacting on the ADME process may contribute to the greater pharmacokinetic variability described with liposomes by [START_REF] Costa | Evaluation of Nanoparticle Uptake in Co-culture Cancer Models[END_REF]. Another emerging model with nanoparticles is working with 3-dimentional (3D) tumor spheroids [START_REF] Perche | Cancer cell spheroids as a model to evaluate chemotherapy protocols[END_REF] as the issue of tumor uptake cannot be properly described in standard 2D monolayer models [START_REF] Sinek | Two-dimensional chemotherapy simulations demonstrate fundamental transport and tumor response limitations involving nanoparticles[END_REF].

More sophisticated models are now developed, such as those combining co-culture with 3D model [START_REF] Jyoti | An in vitro assessment of liposomal topotecan simulating metronomic chemotherapy in combination with radiation in tumor-endothelial spheroids[END_REF] or developing patients-derived organoids, all being even closer to the in vivo representation of liposomal accumulation and drug release in the tumor. Similarly, in vivo techniques are being improved, with the development of genetically engineered cancer models that can address better than canonical xenograft models, tumor heterogeneity to correctly predict the pharmacokinetic parameters [START_REF] Combest | Genetically Engineered Cancer Models, But Not Xenografts, Faithfully Predict Anticancer Drug Exposure in Melanoma Tumors[END_REF]. Of note, with regard to the important role played by the immune system on nanoparticle pharmacokinetics, switching from immune-compromised mice to syngeneic models could probably help to better picture the actual PK profile of nanocarriers during nonclinical development phases. Finally, owing to the complexity in picturing the whole pharmacokinetics of most nanoparticles, developing and using sophisticated models derived from applied mathematics is a critical, yet largely underestimated tool. Although limited, when available model-driven studies (i.e., using PB-PK approaches) seem to perform better than trial-and-error studies, thus possibly reducing the high attrition rates observed when developing nanoparticles and bridging the gap between bench and bedside.

  SN38 elimination, poor-metabolizer (PM) patients bearing the UGT1A1*28 variant could experience severe hematological toxicities. Reduced hepatic clearance for liposomal drugs may lower the role of the liver and the relevance of UGT1A1 genotyping when liposomal irinotecan or SN-38 are administered. However, a phase-I pharmacokinetics study on IHL-305 liposomal irinotecan in advanced solid tumor patients was performed with pharmacogenetic support. Two subsets were evaluated: patients with wild-type (wt) allele of UGT1A1 gene and patients with the UGT1A1*28 homozygous variant. Results

  ) / Pharmacodynamic (PD) and Physiologically-based pharmacokinetics models to better understand nanoparticles pharmacokinetics.PK models are usually divided into compartmental versus non-compartmental approaches. The compartmental approach consists in an abstract representation of the body as divided into compartments. Mass balance laws for transfers of the drugs between the compartments are then applied and formalized as ordinary differential equations. Non-compartmental approaches on the other hand directly describe the drug concentration as a function of time, without deriving this expression from any representation of the processes at play. Both approaches are attached to the characterization of the kinetics and exposure of the drug, as a function of fundamental parameters such as the clearance. A particularly interesting and useful tool is the population approach in which, using nonlinear statistical mixed-effects models, description of the inter-patient variability of the model parameters and associated quantities of interest can be quantified. Moreover, covariate analysis allows identifying meaningful subgroups that respond differently as a function of their sex, age or any other clinical feature such as genetic polymorphism or data regarding MPS status in cancer patients. While widely spread in the area of small drug pharmacokinetics, such modeling remains limited for nanodrugs. In[START_REF] Wu | Population pharmacokinetics of PEGylated liposomal CPT-11 (IHL-305) in patients with advanced solid tumors[END_REF], Wu et al. used such a population approach to characterize the pharmacokinetics of a PEGylated liposomal formulation of irinotecan and considered the distribution of the encapsulated, released and metabolized forms of the drug. Their results emphasized gender as an important

39 NSCLCFig. 1 :Fig. 2 :

 3912 Figures:

Fig. 3 :

 3 Fig.3: Schematic representation of active tumor cells targeting for immunoliposomes.

Fig. 4 :

 4 Fig.4: Schematic representation of pharmacokinetic differences between free,

Fig. 5 :

 5 Fig.5: Schematic representation of patient factors affecting nanoparticle

Fig. 6 :

 6 Fig.6: Schematic representation of the different pharmacokinetics to study for antitumor

  1 Size and Vasculature of the tumor It has to be underlined that the disease can affect nanoparticle pharmacokinetics, for instance by varying in neo-vessels density depending on tumor burden or cancer type.To evaluate the impact of the tumor itself on the EPR effect,Hirsjärvi and al. studied in

	vivo the biodistribution of a 50 nm nanocarrier on four different tumor types (i.e.,
	glioblastoma, breast cancer and two liver cancer models) [48]. Results showed a similar
	distribution profile in healthy tissues (i.e., heart, lung, brain, skin, muscle, kidney,
	bladder, intestine, spleen, pancreas, fat, stomach, liver and lymph node) but a marked

heterogeneity regarding tumor delivery, depending on the cancer type. Accumulation was much higher indeed for glioblastoma and breast cancer cells. Therefore, the two liver cancer models were classified as "weak EPR effect" tumors, illustrating how tumor characteristics should be a new parameter to consider for understanding and predicting the pharmacokinetics of nanoparticles at the tumor level. This heterogeneity in EPR effect found by

Hirsjärvi and al.

between tumors can be related to the variability in tumor growth. Liver cancer models showed indeed a slower growth than glioblastoma and breast cancer models, as a result of reduced neo-vascularization

[START_REF] Hirsjärvi | Influence of size, surface coating and fine chemical composition on the in vitro reactivity and in vivo biodistribution of lipid nanocapsules versus lipid nanoemulsions in cancer models[END_REF]

.

Fanciullino et al.

  Schell and colleagues[START_REF] Schell | Meta-analysis of inter-patient pharmacokinetic variability of liposomal and non-liposomal anticancer agents[END_REF]. Of note as previously mentioned, carried drugs are expected to stay in the body much longer than standard drugs and sampling plan to perform PK studies with nanoparticles should probably be adapted to this new profile, rather than being based on standard sampling times that could be less informative. Moreover,

	patients involved in most Phase-1 studies generally present a wide range of different
	solid tumors. As discussed previously, characteristics inherent to tumor-type (i.e. size,
	vascular density, tumor micro-environment) are likely to change the pharmacokinetics of
	nanoparticles, thus adding again to the global inter-patient variability. Overall, a better
	and more comprehensive understanding of the specificities in nanoparticles
	pharmacokinetics could help selecting tumors the more likely to benefit from a
	nanocarrier. To achieve this goal, in vitro techniques more representative of tumor
	structure and tumor microenvironment, are currently being developed. For instance, co-
	culture models emerged by adding fibroblasts and other cell types, thus better
	mimicking components of the tumor microenvironment

Table : Table 1 :

 :1 Examples of clinically approved nanomedicines

	Product name	Manufacturer	Description	Targeted cancer	Approval details
	Oncaspar	Sigma tau	PEGasparaginase	Accute lymphoblastic	1994
		pharmaceuticals Inc.		leukemia
	Doxil	Centocor Ortho	PEGylated	Recurrent ovarian	1995; EMA for
		Biotech, J&J	Doxorubicin liposomes	cancer,	metastatic breast
				AIDS-related Kaposi	cancer (Caelyx)
				sarcoma,
				Multiple myeloma
	DaunoXome	Galen, Ltd.	Daunorubicin	HIV-associated	1996
			liposomes	Kaposi Sarcoma
	DepoCyt	Sigma-Tau	Cytarabine liposomes	Lymphomatous	1999
		Pharmaceutical, Inc.		meningitis
	Myocet	Sopherion	Doxorubicin liposomes Metastatic breast	2000 in Canada and
		Therapeutics, LLC		cancer	Europe
		and Cephalon, Inc.
	Neulasta	Amgen, Inc.	PEGfilgrastim	Chemotherapy-	2002
				associated
				neutropenia
	Abraxane	Celgene	Albumin bound -	Metastatic breast	2005, 2012, 2013
			paclitaxel	cancer, advanced

generous grant from the Ligue Contre le Cancer.


Kangli Li

Gabin Gbabode

Gérard Coquerel

René Céolin

Ivo B Rietveld

On the Dimorphism and the Pressure-Temperature State Diagram of Racemic m-Nisoldipine, a Dihydropyridine Calcium Ion Antagonist

Keywords: Racemic m-nisoldipine, crystalline polymorphism, topological P-T diagram, thermodynamic stability m-nisoldipine racémique, polymorphisme cristallin, diagramme P-T topologique, stabilité thermodynamique

The pressure-temperature phase diagram of the dimorphism of racemic m-nisoldipine is constructed using temperatures and enthalpies of fusion of forms A and B. At ordinary pressure, the transition from form B to form A is found to occur around 192 K, which indicates that these polymorphs are enantiotropically related and that form A is stable at room temperature. Nevertheless, the phase relationship turns to be monotropic when pressures become greater than about 100 MPa, which indicates that form B becomes the sole stable phase.

Résumé

Le diagramme pression-température du composé racémique m-nisoldipine est construit en utilisant les températures et les enthalpies de fusion des formes A et B. À pression ordinaire, la température de la transition de la forme B en forme A est déterminée à environ 192 K, ce qui indique que ces polymorphes sont en relation énantiotropique, la

forme A étant la forme stable à température ambiant. Néanmoins, la relation entre ces phases devient monotropique quand les pressions deviennent supérieures à environ 100 MPa, indiquant ainsi que la forme B devient la seule forme stable.

Introduction

Racemic m-nisoldipine, of which the chemical structure is given in Figure 1, is a Ca 2+ channel antagonist by blocking the current through these potential dependent channels [START_REF] Fleckenstein | Specific pharmacology of calcium in myocardium, cardiac pacemakers, and vascular smooth muscle[END_REF][START_REF] Janis | New developments in calcium ion channel antagonists[END_REF]. In the solid state, it exhibits crystalline dimorphism and the calorimetric and crystallographic aspects have recently been investigated by Yang et al. [START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF][START_REF] Yang | Thermodynamic stability analysis of mnisoldipine polymorphs[END_REF]. It was concluded that "Forms A and B have an enantiotropic relationship with a conversion temperature of 47 °C and form A is the thermodynamically stable form below this temperature" [START_REF] Yang | Thermodynamic stability analysis of mnisoldipine polymorphs[END_REF]. This conclusion was obtained through solubility data at saturation and the intersection of the respective Van't Hoff plots [START_REF] Yang | Thermodynamic stability analysis of mnisoldipine polymorphs[END_REF], because no direct experimental transition was observed by differential scanning calorimetry or by X-ray diffraction as a function of temperature.

In the present paper, it will be shown that on thermodynamic grounds this conclusion should be modified. Moreover, through the approach presented here it can be deduced how the relative stabilities of the polymorphs depend on the pressure.

Available data from the literature

The first crystal structure of m-nisoldipine was resolved by Fossheim et al. (compound III in ref [START_REF] Fossheim | Crystal structures and pharmacologic activities of 1,4-dihydropyridine calcium channel antagonists of the isobutyl methyl 2,6-dimethyl-4-(substituted phenyl)-1,4-dihydropyridine-3,5dicarboxylate (nisoldipine) series[END_REF]), who obtained crystal data at 123 K (Cambridge Structural Database (CSD) code: FULPAD). They reported that the compound had a monoclinic unit cell, setting P21/n, and a melting point of 127-129°C. A similar monoclinic cell was reported by Kapor et al. obtained at 293 K (CSD code: FULPAD01) [START_REF] Kapor | Crystal and molecular structure of a photodegradation product of nisoldipine[END_REF] and later also by Yang et al. (at 298 K, no CSD entries) [START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF], although the latter group used the setting P21/c. The structure was ascribed to polymorph A, however, form A was reported to melt at 135.8 °C (Tmax) by Yang et al. with a melting enthalpy ΔA → LH of 82.3 J g -1 [START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF]. The second polymorph, form B, was found to be triclinic with a melting point of TB → L = 129.2 °C (Tmax) and the associated enthalpy ΔB → LH = 88.3 J g -1 [START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF]. New slightly modified calorimetric data were published one year later by the same group even if the inequalities (i.e. TB → L < TA → L and ΔA → LH < ΔB → LH) remained the same [START_REF] Yang | Thermodynamic stability analysis of mnisoldipine polymorphs[END_REF]. In addition to the adjustments in the melting data, solubility experiments had been reported in the second article [START_REF] Yang | Thermodynamic stability analysis of mnisoldipine polymorphs[END_REF]. These experiments on the two polymorphs in water at temperatures ranging from 25 to 49 °C led to the enthalpies of solution using ln(S) versus 1/T plots in which S stands for saturation concentration (solubility). The data from the four abovementioned references have been compiled in Table 1.

Data analysis

In the approach presented in this paper, the most important aspect is the inequality between the properties of the two polymorphs, such as ∆v, ∆H, and ∆T, and in particular their sign, because it defines the global phase behavior of the system and thus which type of pressure-temperature phase diagram the system exhibits. Once these inequalities have been determined correctly, accurate data will simply allow constructing a more accurate phase diagram in relation to the coordinates of the phase equilibria. Thus the inequalities had best be determined from data obtained on the same equipment, as any constant calibration error will be minimal. This would not be the case for different equipment with different calibrations. Therefore for the inequality of the specific volume between the two polymorphs, only the data obtained by Yang et al. will be taken into account [START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF].

Table 1. Crystallographic and calorimetric data from the literature for forms A and B of racemic m-nisoldipine

Données cristallographiques et calorimétriques pour le composé racémique mnisoldipine trouvées dans la littérature

Form A Form B Reference Crystal system, Space group, formula units per unit cell Monoclinic, P21/n, Z = 4 P21/c, Z = 4 [START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF]. However, instead of the Tmax temperatures reported by those authors, in the present paper, the onset temperatures have been determined from the previously reported graphs (see Figure 2) [START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF]. It is the onset temperature, which will in principle be closer to the thermodynamic temperature of transition, in particular for fusion. Analysis of the aforementioned melting peaks (Figure 2) has led to the temperatures of fusion of TA → L = 133.1°C (or 406.2 K) for form A and TB → L = 126.2°C (399.3 K) for form B. The melting enthalpies for the two polymorphs as reported by Yang et al. and here reproduced in Table 1 differ significantly between the two papers [START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF][START_REF] Yang | Thermodynamic stability analysis of mnisoldipine polymorphs[END_REF]. However, in both cases ΔA → LH is smaller than ΔB → LH. The difference between the two papers is due to the integration over the melting peak of form A in the first paper [START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF], which led to an underestimated value. It can be seen in Figure 2 S3 of the electronic supplementary information associated to reference [START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF]. Underestimation of the melting enthalpy of form A: Baseline a-c is to be used instead of baseline a-b. The underestimation is shown by the area in violet: by weighing the area of peak A and comparing those for baselines a-b and a-c, a value for the melting enthalpy of A close to that of peak B is obtained. Moreover, the large difference between the start of the peak (the start of the upward curvature) and the extrapolated onset temperature may be indicative for the presence of impurities in the m-nisoldipine samples.

Détermination des températures de fusion commençante des formes A et B du composé racémique m-nisoldipine, d'après les courbes DSC de la Figure S3 de l'information électronique supplémentaire associée à la référence [3]. Sous-estimation de l'enthalpie de fusion de la forme A : la ligne de base ac doit être utilisée au lieu de la ligne a-b. La sous-estimation est visualisée par la surface violette : en pesant la surface du pic A au-dessus des lignes de bases a-b et a-c, on obtient une valeur très proche de celle du pic B. De plus, la grande différence entre le début du pic (le début de la courbure vers le haut) et la température de début extrapolée peut indiquer la présence d'impuretés dans les échantillons de m-nisoldipine.

The calorimetric data provided in the second paper [START_REF] Yang | Thermodynamic stability analysis of mnisoldipine polymorphs[END_REF] seems to be an average over four DSC runs at various heating rates. Thus, the enthalpy of fusion values reported in [START_REF] Yang | Thermodynamic stability analysis of mnisoldipine polymorphs[END_REF], which seem overall more reliable, will be used in the approach that follows below. However, the melting temperatures obtained through the onset of the peaks from reference [START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF] will be used by lack of anything better (It is not clear, whether in reference [START_REF] Yang | Thermodynamic stability analysis of mnisoldipine polymorphs[END_REF] the melting temperatures are given as Tmax or Tonset). It can be concluded that forms A and B have melting enthalpies that are very close to each other with form A a slightly lower one than form B leading to a transition enthalpy between the two solids of ΔB → AH = 1.4 J g -1 .

Considering the foregoing, the heats of solution from the Van't Hoff plots of the saturated solutions [START_REF] Yang | Thermodynamic stability analysis of mnisoldipine polymorphs[END_REF] for forms A and B are very surprising. First of all, the heat of solution of form A is larger than that of form B contrary to the melting data and secondly the difference is extremely large. Fusion and dissolution are similar processes, and although in the case of fusion the system is unary, whereas in the case of dissolution, the system is binary, which may affect phase equilibria, the large change observed here is rather improbable and thus the dissolution data must be unreliable. This is illustrated in figure 3, where the fusion and dissolution processes have been drawn in the form of a cycle (Hess law). These cycles should lead to similar values for the heat of transition from form B to form A, whereas in this case for the heats of solution, they lead to the relatively large value of -91.55 J g -1 similar to its heat of fusion, instead of the +1.4 J g -1 obtained from the fusion data and much more common for heat differences between polymorphs (1 to 20 J g -1 ). It can be seen that the sign of the transition changes too classifying the same transition simultaneously endothermic (cycle I, DSC data) or exothermic (cycle II, solubility data).

Chaleur de la transition de la forme B du composé racémique m-nisoldipine en forme A, déterminée soit à partir des chaleurs de fusion (cycle I), soit à partir des chaleurs de dissolution (cycle II).

As the solubility data appear to be unreliable, it is likely that the transition temperature between forms A and B of 47°C obtained through these data may not be correct either. A different way to estimate the transition temperature is by using a thermodynamic equation, which has been thoroughly tested in a paper by Yu [START_REF] Yu | Inferring Thermodynamic Stability Relationship of Polymorphs from Melting Data[END_REF]. It uses the heats and temperatures of fusion of the two polymorphs, although in the present form it neglects the variation of the heat capacities with temperature between the solids and between the liquid and the solid:

T B→ A = Δ A→L H -Δ B→L H Δ A→L H T A→L - Δ B→L H T B→L = Δ A→L H -Δ B→L H Δ A→L S -Δ B→L S ≈ Δ B→ A H Δ B→ A S (1)
In this equation TB → A is the temperature of transition of form B to form A, and Ti → L and Δi → LH, the temperature and enthalpy of fusion of form i (i = A or B) respectively. Using ΔA → LH = +88.88 J g -1 , ΔB → LH = +90.28 J g -1 , TA → L = 406.2 K and TB → L = 399.3 K, TA → B is found to be 192.12 K (-81 °C), i.e. far below the value of 47 °C reported by Yang et al. [START_REF] Yang | Thermodynamic stability analysis of mnisoldipine polymorphs[END_REF]. It implies that forms A and B are enantiotropically related as was already concluded by Yang et al., however form B, stable below 192 K, endothermically transforms into form A at 192 K as ΔB → AH is positive (+1.4 J g -1 ).

To investigate whether the inequality in the heat of transition was determined correctly, because the melting enthalpies were rather close to each other, those melting enthalpies can be interchanged in the calculation using eq. ( 1). Keeping the melting temperatures as obtained, as they can generally be measured with a relatively high precision, a negative transition temperature is found for the solid phase B into the solid phase A. This result is simply impossible, because firstly negative temperatures do not physically exist and secondly this result is thermodynamically impossible, because B would have the lowest melting enthalpy and form B would therefore necessarily be the "high-temperature" form. As form A has the highest melting point and is thus the most stable phase just below its melting point, the only option for a "virtual" A-B transition temperature would be above the melting point of form A as a metastable solid-solid transition. Obviously, the requirement of a solid-solid transition temperature above the melting point of form A together with the calculated result of a negative transition temperature cannot be true simultaneously.

Finally, it can be argued that the melting enthalpies as determined by DSC possess experimental uncertainties. As in both papers by Yang et al. [START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF][START_REF] Yang | Thermodynamic stability analysis of mnisoldipine polymorphs[END_REF], the melting enthalpy of form A is smaller than that of form B, the enthalpy difference between the two forms and obtained through the melting enthalpies, 1.4 J g -1 can be varied from 0.4 to 2.4 J g -1 , thus implying an experimental error of ±1 J g -1 . Maintaining the melting temperatures for which the relative error is much smaller, one finds with eq. ( 1) for an enthalpy of 0.4 J g -1 a transition temperature between A and B of 83 K and for an enthalpy of 2.4 J g -1 , one finds 246 K. It can be seen that the range of transition temperatures is rather large, but with a reasonable estimate of the transition enthalpy between forms A and B obtained through the DSC data, the transition temperature appears to be far below 47°C (320 K).

Building on the conclusions that the system is enantiotropic and that form A is the stable form at room temperature and up to its melting point, the influence of pressure on the equilibria can be examined by means of the Clapeyron equation, leading to a topological pressure-temperature (P-T) phase diagram for m-nisoldipine, as shown below.

Topological P-T phase diagram involving forms A and B

The general procedure for the construction of topological P-T phase diagrams, which has been described in a recent paper [START_REF] Céolin | The topological phase diagram of cimetidine: A case of overall monotropy[END_REF], has been frequently applied to other cases and validated against experimental results (see references in [START_REF] Céolin | The topological phase diagram of cimetidine: A case of overall monotropy[END_REF] and [START_REF] Ceolin | Pitfalls and feedback when constructing topological pressure-temperature phase diagrams[END_REF]). The method can be divided up in three steps: 1) Specific volume-temperature (v-T) phase diagrams, in particular of the solids and if possible of the liquids are measured or estimated to calculate (or estimate) the volume changes at the phase transition temperatures.

2) The two-phase equilibrium curves in the P-T diagram are assumed to be straight lines whose dP/dT slopes are determined by the Clapeyron equation using volumetric and calorimetric data. Because the chance that these lines are parallel is basically zero, the two-phase equilibrium curves must intersect at their respective triple points providing the boundary for the different stable-phase regions.

3) The resulting P-T phase diagram can be compared with the four possible cases of dimorphism described by Bakhuis-Roozeboom [START_REF] Roozeboom | Die heterogenen Gleichgewichte vom Standpunkte der Phasenlehre. Erstes Heft: Die Phasenlehre -Systeme aus einer Komponente[END_REF][START_REF] Céolin | X-ray crystallography, an essential tool for the determination of thermodynamic relationships between crystalline polymorphs[END_REF].

Following the data in Table 1 and the reasoning in the text above, the difference between the specific volumes of forms A and B at 298 K is equal to vA -vB = 0.77821 -0.75643 = 0.02178 cm 3 g -1 . Using the data in Table 1, the linear expansivity of form A can be estimated, because the crystal structure has been determined at 123 K by Fossheim et al. [START_REF] Fossheim | Crystal structures and pharmacologic activities of 1,4-dihydropyridine calcium channel antagonists of the isobutyl methyl 2,6-dimethyl-4-(substituted phenyl)-1,4-dihydropyridine-3,5dicarboxylate (nisoldipine) series[END_REF] and at 298 K by Yang et al. [START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF]. In addition, the unit-cell volume obtained by Kapor et al. at 293 K [START_REF] Kapor | Crystal and molecular structure of a photodegradation product of nisoldipine[END_REF] can be used to determine an average unit-cell volume valid at 295.5 K of 2006.52 Å 3 . This leads to a specific volume for form A of 0.7625 cm 3 g -1 at 231 K and of 0.7777 cm 3 g -1 at 295.5 K. Using a linear approach, the expansivity α can be calculated as follows: vA = v0,A + aT = v0,A(1+αT), leading to a value of 1.17×10 -4 K -1 , near the average expansivity of 2.21× 10 -4 K -1 for solids consisting of small pharmaceutical molecules [START_REF] Céolin | The topological phase diagram of cimetidine: A case of overall monotropy[END_REF][START_REF] Rietveld | Phenomenology of crystalline polymorphism: overal monotropic behavior of the cardiotonic agent FK664 forms A and B[END_REF][START_REF] Céolin | The topological pressure-temperature phase diagram of ritonavir, an extraordinary case of crystalline dimorphism[END_REF]. The expansivity of 1.17 ×10 -4 K -1 can be used for form A and in approximation for form B to calculate the specific volumes of both forms at their respective melting points. Now, considering that the mean volume change on melting of the highest melting form, form A, is such that vL/vA = 1.11 [START_REF] Céolin | The topological phase diagram of cimetidine: A case of overall monotropy[END_REF][START_REF] Rietveld | Phenomenology of crystalline polymorphism: overal monotropic behavior of the cardiotonic agent FK664 forms A and B[END_REF][START_REF] Céolin | The topological pressure-temperature phase diagram of ritonavir, an extraordinary case of crystalline dimorphism[END_REF], the specific volume of the melt at TA → L can be estimated to equal 0.87440 cm 3 g -1 . Thus the volume change on melting of form A equals vL -vA =0.08665 cm 3 g -1 . Inserting the latter value with TA → L = 406.2 K and ΔA → LH = +88.88 J g -1 into the Clapeyron equation:

dP dT = Δ A→L H T A→L Δ A→L V (2),
the value of the slope of the melting equilibrium of form A is found to be 2.53 MPa K -1 .

Taking the expansivity of the liquid as 1.19× 10 -3 K -1 , which is the average liquid expansivity found for molecular pharmaceutical compounds [START_REF] Céolin | The topological phase diagram of cimetidine: A case of overall monotropy[END_REF][START_REF] Rietveld | Phenomenology of crystalline polymorphism: overal monotropic behavior of the cardiotonic agent FK664 forms A and B[END_REF][START_REF] Céolin | The topological pressure-temperature phase diagram of ritonavir, an extraordinary case of crystalline dimorphism[END_REF], the specific volume of the melt at the melting point of form B, TB → L = 399.3 K is 0.86956 cm 3 g -1 . It results in a volume change on melting for form B of vL-vB = 0.10445 cm 3 g -1 . Using the latter value in the Clapeyron equation for the equilibrium curve between form B and the liquid gives dP/dTB-L = 90.28/(399.3 × 0.10445) = 2.16 MPa K -1 .

The two melting equilibria can be approximated by straight lines determined through the respective melting temperatures and their slopes. The vapor pressure of nisoldipine is neglected in this approach, but considering the steepness of the slope, this is in most cases fully acceptable. Thus with the melting temperatures 406.2 K for form A and 399.3 K for form B and the vapor pressure taken as 0 MPa (these two melting points represent therefore two triple points: A-L-Vap and B-L-Vap), the expressions for the two phase equilibria become:

A-L: P/MPa = 2.53 T/K -1026 (3)
B-L:

P/MPa = 2.16 T/K -864 (4)
The intersection between the two equilibria is a triple point, where form A, form B, and the liquid are stable. Its coordinates can be calculated by equating eqs. 2 and 3 leading to TA-B-L = 448 K and PA-B-L = 105 MPa.

Equilibria between two different crystalline polymorphs are in most cases straight lines in P-T diagrams ( [START_REF] Ceolin | Pitfalls and feedback when constructing topological pressure-temperature phase diagrams[END_REF] and references therein). The equilibrium line A-B will intersect triple point A-B-L, which was just obtained above and triple point A-B-Vap. The latter triple point has been obtained through eq. 1 resulting in an equilibrium temperature of 192 K, while taking the vapor pressure as 0 MPa, which at such temperatures is hardly an approximation. Fitting a line through the two triple points results in the expression:

A-B: P/MPa= 0.41 T/K -79 [START_REF] Fossheim | Crystal structures and pharmacologic activities of 1,4-dihydropyridine calcium channel antagonists of the isobutyl methyl 2,6-dimethyl-4-(substituted phenyl)-1,4-dihydropyridine-3,5dicarboxylate (nisoldipine) series[END_REF] The enthalpy change of the solid-solid equilibrium can be obtained by multiplying the slope of eq. 5 by the equilibrium temperature of 192 K and by the volume change between the two solid phases at 192 K of Δ Β→Α v = vA-vB = 0.02105 cm 3 g -1 . This leads to the enthalpy of transition ∆B → AH = +1.7 J g -1 , close to the value of +1.4 J g -1 obtained by subtracting the heat of fusion of form A from that of form B (see cycle (I) in Figure 3).

With these results, it can be inferred that the topological P-T diagram accounting for the phase relationships involving the two polymorphs of racemic m-nisoldipine is of the same type as the state diagram of sulfur, i.e. triple point A-B-L is found at positive pressure as shown in Figure 4 [START_REF] Céolin | X-ray crystallography, an essential tool for the determination of thermodynamic relationships between crystalline polymorphs[END_REF]. As is shown in the Figure 4, the intersection of line A-L and line B-L (triple point A-B-L) is above the temperature axis. That means that the pressure at the intersection is positive and that the triple point is stable. Below the intersection, the system is enantiotropic and form A is more stable than form B at room temperature and under atmospheric conditions. Above triple point A-B-L, the system becomes monotropic and form B is the only stable form. This trend is consistent with the Le Chatelier principle. According to the data in Table 1, the specific volume of form A is larger than that of form B at 298 K. In other words, form B is denser than form A and thus form B will become more stable on increasing the pressure.

Table 2. Two-phase equilibrium equations for alternative volume change on melting form A, and P-T coordinates for triple point A-B-L.

Equations décrivant les equilibres à deux phases pour différentes valeurs du changement de volume lors de la fusion de la forme A et valeurs correspondantes des coordonnées P et T du point triple A-B-L. vliq/vA A-L B-L A-B

The linear expression for the A-B equilibrium has been calculated based on the triple point A-B-Vap and the triple point A-B-L. Triple point A-B-L has been determined through the equilibria A-L and B-L. Thus, the slopes of these two equilibria affect the position of triple point A-B-L and thus of equilibrium A-B. The two slopes of the melting equilibria have been obtained through the Clapeyron equation (eq. 2). The largest uncertainty in this slope is the volume change on melting, which was obtained from statistical information. The spread in the statistical data for the volume change on melting is vliq/vA = 1.11 ± 0.04 [START_REF] Céolin | The topological phase diagram of cimetidine: A case of overall monotropy[END_REF][START_REF] Rietveld | Phenomenology of crystalline polymorphism: overal monotropic behavior of the cardiotonic agent FK664 forms A and B[END_REF][START_REF] Céolin | The topological pressure-temperature phase diagram of ritonavir, an extraordinary case of crystalline dimorphism[END_REF] and therefore volume change on melting can be considered by comparing vliq/vA = 1.07, 1.11, and 1.15. For all three values, the slope of the A-B equilibrium line has been calculated and the result has been compiled in Table 2. It can be concluded that the temperature and pressure of triple point A-B-L increases with an increase in vliq/vA, but the expression for the solid-solid equilibrium A -B remains virtually the same.

Concluding remarks

Contradictory information in the literature can sometimes be solved by investigating the consistency between the data and by making use of the thermodynamic requirements of the system. Previously, this has been shown in the case of the polymorphism of piracetam [START_REF] Ceolin | Pitfalls and feedback when constructing topological pressure-temperature phase diagrams[END_REF].

In the present case, the data provided by two papers of the same authors has allowed to validate some of the data (in particular the melting enthalpies mentioned in ref [START_REF] Yang | Thermodynamic stability analysis of mnisoldipine polymorphs[END_REF]) and to eliminate other data, because they are inconsistent with thermodynamic and calorimetric notions for small organic molecules such as the heat of a solid-solid transition, which must be considerably smaller than a melting enthalpy.

For the phase behavior of racemic m-nisoldipine, the present work confirms that forms A and B are enantiotropically related at ordinary pressure, turning to a monotropic relation as pressure reaches about 100 MPa. It also demonstrates that form A, the "high-temperature" form, is most likely the stable form at room temperature since

Figure 1 .

 1 Figure 1. Racemic m-nisoldipine: 1,4-dihydro-2,6-dimethyl-4-(3-nitrophenyl)-3,5-pyridinedicarboxylic acid methyl 2-methylpropyl ester, C 20 H 24 N 2 O 6 , M = 388.41 g mol -1 . An asterisk indicates the stereogenic center. Atom identification: black = C, pink = H, blue = N, red = O. Molécule de m-nisoldipine racémique. 1,4-dihydro-2,6-dimethyl-4-(3-nitrophenyl)-3,5pyridinedicarboxylic acide méthyl 2-methylpropyl ester, C 20 H 24 N 2 O 6 , M = 388.41 g mol -1 . L'atome de carbone asymétrique est identifié par une étoile (*). Identification des atomes : noir = C, rose = H, bleu = N, rouge = O.

  that point b of segment a-b is located on the DSC curve before the melting peak of form A reaches the baseline, which is not the case for point b' of segment a'-b' under the melting peak of form B. If the heat of fusion of form A is determined by integrating the peak above the alternative and more correctly placed baseline a-c, a value very close to the heat of fusion of form B is obtained complicating the interpretation of the ∆H inequality.

Figure 2 .

 2 Figure 2. Determination of the onset temperatures of fusion for racemic m-nisoldipine forms A and B using the DSC curves in FigureS3of the electronic supplementary information associated to reference[START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF]. Underestimation of the melting enthalpy of form A: Baseline a-c is to be used instead of baseline a-b. The underestimation is shown by the area in violet: by weighing the area of peak A and comparing those for baselines a-b and a-c, a value for the melting enthalpy of A close to that of peak B is obtained. Moreover, the large difference between the start of the peak (the start of the upward curvature) and the extrapolated onset temperature may be indicative for the presence of impurities in the m-nisoldipine samples.Détermination des températures de fusion commençante des formes A et B du composé racémique m-nisoldipine, d'après les courbes DSC de la FigureS3de l'information électronique supplémentaire associée à la référence[START_REF] Yang | Structure and characterization of mnisoldipine polymorphs[END_REF]. Sous-estimation de l'enthalpie de fusion de la forme A : la ligne de base ac doit être utilisée au lieu de la ligne a-b. La sous-estimation est visualisée par la surface violette : en pesant la surface du pic A au-dessus des lignes de bases a-b et a-c, on obtient une valeur très proche de celle du pic B. De plus, la grande différence entre le début du pic (le début de la courbure vers le haut) et la température de début extrapolée peut indiquer la présence d'impuretés dans les échantillons de m-nisoldipine.

Figure 3 .

 3 Figure 3. Heat of transition from racemic m-nisoldipine form B to form A, determined using either the heats of fusion (cycle I) or the heats of solution (cycle II).Chaleur de la transition de la forme B du composé racémique m-nisoldipine en forme A, déterminée soit à partir des chaleurs de fusion (cycle I), soit à partir des chaleurs de dissolution (cycle II).

Figure 4 .

 4 Figure 4. Topological pressure-temperature phase diagram for the dimorphism of racemic mnisoldipine. The diagram corresponds to Bakhuis Roozeboom's type I [10-11], with a relatively limited P-T domain for the stability of form A, which becomes metastable at higher pressures. Triple points: 1 = A-liq-vap, 2 = B-liq-vap, 3 = A-B-liq, 4 = A-B-vap. Two-phase equilibrium lines: 1-2 = liq-vap, 1-3 = Aliq, 2-3 = B-liq, 3-4 = A-B, 1-4 = A-vap, 2-4 = B-vap (liq = liquid, vap = vapor). Diagramme topologique pression-température du dimorphisme du composé racémique m-nisoldipine. Le diagramme correspond au type I de Bakhuis Roozeboom [10-11], avec un domaine limité en pression et température pour la stabilité de la forme A, qui devient métastable aux pressions élevées. Points triples : 1 = A-liq-vap, 2 = B-liq-vap, 3 = A-B-liq, 4 = A-B-vap. Lignes d'équilibres à deux phases : 1-2 = liq-vap, 1-3 = A-liq, 2-3 = B-liq, 3-4 = A-B, 1-4 = A-vap, 2-4 = B-vap (liq = liquid, vap = vapor).

Specific volume/ cm 3 g -1 0.76254

			Triclinic,
				[5],[6]
			P-1, Z = 2	[3]
	Vcell/ Å 3	1967.32*	-	[5]
		2005.68**	-	[6]
		2007.36***	975.89***	[3]
		*	-	[5]
		0.77741**	-	[6]
		0.77821***	0.75643***	[3]
	Tfus/K	400-402	-	[5]
		408.95****	402.4****	[3]
		410.94****	403.31****	[4]

Heat of fusion ΔfusH/J g -1 82

  Yang et al. reported DSC curves in the supplementary materials of the CrystEngComm paper

	same equipment.
		.3	88.3	[3]
		88.88±1.55	90.28±1.09	[4]
	Heat of solution /J g -1	139.94	48.39	[4]

the temperature of the transition from form B to form A should occur around 192 K, i.e. far below room temperature. Moreover, the use of statistical data for the change in density on melting barely affects the A-B equilibrium line, which depends in this analysis on the position of the A-B-L triple point.

= T max given by the authors (see text), valeurs de T peak = T max données par les auteurs (voir texte)

Disclosure of Interest

The authors declare that they have no competing interests.