Impact of CNS Diseases on Drug Delivery to Brain Extracellular and Intracellular Target Sites in Human: A “WHAT-IF” Simulation Study

The blood–brain barrier (BBB) is equipped with unique physical and functional processes that control central nervous system (CNS) drug transport and the resulting concentration–time profiles (PK). In CNS diseases, the altered BBB and CNS pathophysiology may affect the CNS PK at the drug target sites in the brain extracellular fluid (brainECF) and intracellular fluid (brainICF) that may result in changes in CNS drug effects. Here, we used our human CNS physiologically-based PK model (LeiCNS-PK3.0) to investigate the impact of altered cerebral blood flow (CBF), tight junction paracellular pore radius (pararadius), brainECF volume, and pH of brainECF (pHECF) and of brainICF (pHICF) on brainECF and brainICF PK for 46 small drugs with distinct physicochemical properties. LeiCNS-PK3.0 simulations showed a drug-dependent effect of the pathophysiological changes on the rate and extent of BBB transport and on brainECF and brainICF PK. Altered pararadius, pHECF, and pHICF affected both the rate and extent of BBB drug transport, whereas changes in CBF and brainECF volume modestly affected the rate of BBB drug transport. While the focus is often on BBB paracellular and active transport processes, this study indicates that also changes in pH should be considered for their important implications on brainECF and brainICF target site PK.


Introduction
Both the rate and extent of central nervous system (CNS) unbound drug transport determine CNS concentration-time profiles of the unbound drug (PK) [1]. PK at the CNS target sites in the brain extracellular fluid (brain ECF ) and brain intracellular fluid (brain ICF ) is a function of plasma PK, drug transport across the blood-brain barrier (BBB), and intra-brain distribution. Such PK processes result from the combination of the drug physicochemical properties and the physiological characteristics of the CNS [2,3].
The BBB lies at the brain microvessels, including brain capillaries and their direct surroundings [2]. The BBB has physical properties that reduce passive drug transport across the BBB for hydrophilic and large molecules, i.e., by the presence of the tight junctions between the brain microvascular endothelial cells. In addition, pericytes and astrocyte end feet ensure a complete coverage of the brain microvascular endothelial cells, while the basement membrane surrounds the endothelial cells and pericytes, separating them from each other and from the astrocytes end feet. All together, these cells ensure the physical integrity of the BBB against the foreign plasma molecules. The BBB also has active efflux and influx transporters, pinocytosis, transcytosis, and metabolic enzymes, which are all powered with energy supplied by the large mitochondrial count. The brain tissue composition and active cellular membrane transporters further determine the unbound drug PK in the different brain compartments, while different pH values of the CNS compartments govern, for acids and bases, the extent of ionization [2]. LeiCNS-PK3.0 accounts for the brain and cerebrospinal fluid (CSF) compartments, the presence of the blood-brain barrier (BBB) and blood-CSF barriers, drug transport across the barriers and within the CNS, and physiological process such as non-specific binding and the effect of pH on drug ionization and on its passive transport.

LeiCNS-PK3.0 Model
This simulation study was performed using LeiCNS-PK3.0 ( Figure 1 and Figure S1 in Supplementary Materials) and human CNS physiological parameters (Table 1) [12]. A virtual one-compartment plasma PK model was used as input to the CNS model, with plasma clearance of 297 L/h and a central compartment volume of 108 L. The drug dose was 1 g, which was administered as intravenous infusion over 15 min. The fixed plasma PK model and dosing regimen were used for all investigated drugs, thus solely focusing on the impact of CNS parameters changes on brain ECF and brain ICF PK. More information on the model buildup and the associated equations can be found at [10,12,13].
Active transport across the BBB was described using Kp uu,BBB values ( Table 2 and  Table S1), which were calculated from rat microdialysis plasma and brain ECF drug concentrations [12,[29][30][31]. Then, these were translated to predict human BBB active transport as described in [10], taking into consideration the interspecies difference in protein expression [32][33][34][35][36] of the four main BBB active transporters: P-glycoprotein (p-gp), multi-drug-resistant protein-4 (MRP4), breast cancer resistance protein (BCRP), and organic anionic transporter 3 (OAT3). The protein expression of other relevant transporters at the BBB such as MRP1 was assumed the same in rats and humans, due to the absence of quantitative information on the difference of protein expression in rats and in humans [32][33][34][35][36][37]. Information on drugs affinity to a certain transporter was available from Drugbank [26]. The factors used for the rat-to-human translation are summarized in Table S2. Differences in transporters functionality, which is distinct of expression [38], in rats and humans [39][40][41] were not accounted for. This interspecies difference is not attributed to the transporter per se, but rather to the combination of the drug and the transporter. Given both the scarcity of transporter functionality information in the literature and the goal of the current study, rat-to-human translation was based on differences in expression only. Kp uu,BCSFB values ( Table 2 and Table S1), which represent active transport across the BCSFB, were either available from the literature or assumed the same as Kp uu,BBB .

Selection of Pathophysiological Parameters Values
The CNS parameters investigated in this study were CBF, para radius , Brain ECF volume, pH ECF , and pH ICF . The changes in the parameters values were selected to reflect their values in CNS diseases. Parameters were changed based on literature values as follows: CBF by 70% [42] and 150% [21]; para radius by 50% and 500% [43]; brain ECF volume by 70% and 150% [14,15]; pH ECF to 5 and 8 [23]; and pH ICF to 6 and 7.6 [24,44].
LeiCNS-PK3.0 simulation results were evaluated by comparing the different PK at brain ECF and brain ICF of different parameters values. In addition, heatmaps were generated to reflect the magnitude of change of C max , T max , AUC 0-T , Kp uu,BBB , and Kp uu,cell . AUCs were calculated using the R package PKNCA version 0.9.4.
Kp uu,BBB and Kp uu,cell were calculated as follows [1]: For AUC 0-∞ , the elimination rate constant was calculated from the terminal elimination phase and was used to extrapolate the concentration-time curve to time infinity.
Two-fold change was calculated to reflect the effect of changing one parameter on PK parameters; a value of 1 reflects a two-fold change.
where PK.params ∆=x and PK.params ∆=1 represent the calculated PK parameters (C max , T max , AUC 0-T , Kp uu,BBB , and Kp uu,cell ) at x-fold altered and physiological CNS parameters, respectively.

Results
The simulated impact of pathophysiological changes of CBF, para radius , brain ECF volume, pH ECF , and pH ICF on PK at brain ECF and brain ICF are displayed for selected drugs in Figure 2 and for all drugs in Figure S2. The associated heatmaps, Figure 3 and Figure S3, reflect the changes in the BBB drug transport rate via C max, and T max and extent via AUC 0-T , Kp uu,BBB , and Kp uu,cell . As plasma PK was fixed, any role of plasma in the observed changes is eliminated. The changes of CBF and brain ECF volume affected the rate but not the extent of BBB drug transport, whereas changes in pH ECF , pH ICF , and para radius affected both the rate and extent of BBB drug transport.

Increased Passive Transport via Widened Para radius
Figures 2 and 3 (2nd column) demonstrate that the impact of a changed para radius on BBB drug passive transport varied according to the drug lipophilicity, ionization at physiological pH, and affinity to active transporters. Of interest, a five-fold increase in para radius resulted in a decrease in the extent of BBB transport of risperidone, paliperidone, and omeprazole, as demonstrated by a decrease in AUC 0-T,ECF and in Kp uu,BBB . Figures 2 and 3 (4th and 5th columns) show the influence of pH changes on the rate and extent of drug transport across the BBB and across the brain cell membranes. A pH increase in a given compartment generally resulted in a faster rate and increased the extent of acidic drug transport and a slower rate and decreased the extent of the basic drug transport into that compartment, and vice versa. The rate and extent of drug transport in the adjacent compartment were affected in an inverse fashion. For amphoteric drugs, the effect of pH on their transport rate and extent was relative to the ionization constants of their strongest acidic and basic groups. As expected, pH changes had no effect on drugs that are neutral at the physiological pH range. Figure 3 (1st and 3rd columns) display only a T max increase of <50% associated with a 50% increase of brain ECF volume, while a slight T max decrease of <25% was noticed with a 30% decrease of brain ECF volume. With regard to CBF, a 30%-decrease resulted in a <50%-delay of T max , whereas a 50%-increase resulted in a <25%-earlier T max . These effects were associated with neutral drugs of relatively higher net BBB influx. Figure 2. Simulated concentration-time profiles of selected drugs at physiological and pathophysiological values of CBF, tight junction paracellular pore radius (para radius ), brain ECF volume, pH ECF , and pH ICF . Para radius affected the rate and extent of passive drug transport across the BBB, pH ECF and pH ICF affected the brain ECF and brain ICF unbound drug concentration-time profile (PK), whereas cerebral blood flow and brain ECF volume had a very modest (if any) effect. The fixed plasma PK used excludes the involvement of plasma PK in the observed changes. Heatmaps summarizing the effect of pathophysiological changes of CBF, tight junction paracellular pore radius (para radius ), brain ECF volume, pH ECF , and pH ICF on brain pharmacokinetic parameters: C max , T max , AUC, Kp uu,ECF , and Kp uu,cell . C max and T max define the rate of BBB drug transport, while AUC and Kp uu define the extent of drug transport. Effect of pathophysiological changes remain drug (class) specific. Similar to the concentration-time profiles, para radius , pH ECF , and pH ICF had a profound effect on brain pharmacokinetics compared to the minor effect of cerebral blood flow and brain ECF volume. The fixed plasma PK used excludes the involvement of plasma PK in the observed changes.

Discussion
LeiCNS-PK3.0 simulations have demonstrated the drug-dependent effect of pathophysiological changes of para radius on the rate and extent of BBB passive drug transport, and of pH ECF and pH ICF on the PK of brain ECF and brain ICF .
LeiCNS-PK3.0 allows the prediction of PK in the less accessible brain tissue and the potential PK changes associated with diseased conditions. LeiCNS-PK3.0 predictions are based explicitly on human CNS physiological parameters available from the literature, drug physicochemical parameters available from Drugbank database [26], and translated data from in vitro and preclinical studies. Thus, LeiCNS-PK3.0 overcomes the technical and ethical limitations of experimental approaches, such as the invasiveness of microdialysis, inability to differentiate parent drug and metabolite with imaging techniques, and the inaccurate lumbar CSF surrogacy to brain PK [12,102].
Paracellular passive diffusion across the BBB tight junction pores is especially critical for small, hydrophilic drugs, whose transport across the lipophilic membranes of BBB endothelial cells is limited, although this paracellular route represents about 0.004% of BBB surface area [12]. Increased passive transport via this route has been reported after BBB opening with hyperosmotic mannitol, where the brain exposure of atenolol [43] and methotrexate [103] increased by about 3-and 5-folds, respectively. BBB opening and widening of para raduis after hyperosmotic mannitol were confirmed in the latter study using electron microscopy [103]. In CNS diseases, BBB permeability to drug transport across the paracellular route increases ( Table 3). The impact of increased para radius on passive transport across the BBB is rather dependent on the balance between passive transcellular and passive paracellular drug transport, the difference in pH between the compartments, and the contribution of active transporters to influx or efflux BBB transport ( Table 2 and Table S1 in Supplementary Materials). An increase of passive paracellular transport will generally result in Kp uu,BBB closer to unity [1]. Drugs that are heavily reliant on the transcellular route or on active transport are less sensitive to changes in para radius . Drug physicochemical properties might also play a role, as the three drugs, whose BBB transport extent was affected, were lipophilic bases.
PH changes are relevant for drugs with pk a < 9 and/or pk b > 3, which ionize at the physiological pH range of 5-7.4, as the ionized drug species do not cross the transcellular route or cell membrane as assumed in LeiCNS-PK3.0 and are thus trapped in brain ICF and lysosomes or can escape brain ECF via the paracellular route and with ECF bulk flow [12]. A consequence of the trapping assumption is that the difference in pH across a membrane will result in unequal drug partitioning across the membrane. This phenomena has been overlooked in several studies where changes in brain ECF PK due to traumatic brain injury were attributed to a reduction of active transport [5,10] and increase para radius [5,10,104], but not to pH ECF . The results of our simulation strongly suggest that pH changes in CNS disease might play a bigger role in defining disease brain PK than previously conceived.
The impact on brain PK due to changes in para radius , pH ECF , and pH ICF during traumatic brain injury (TBI), Alzheimer's disease (AD), brain malignancies, cerebral ischemia, and epilepsy has been explored, as guided by LeiCNS-PK3.0 simulations. The pathophysiological changes of the three parameters in these CNS diseases are listed in Table 3. Quantitative information on para radius values in the different diseases are not always reported, and therefore, BBB permeability as an indirect measure of para radius was used.
Microdialysis studies in TBI patients have shown that brain ECF PK is different in the healthy versus injured brain tissue. In two independent studies, morphine PK was higher in the injured than in the healthy brain tissue of adult [104] and pediatric TBI patients [4]. In addition, cyclosporine brain ECF PK might change in TBI patients [105]. In TBI patients, changes occur to pH ECF , pH ECF , and to para radius ; the magnitude of change and time course of these parameters may differ according to trauma type: focal vs. diffuse TBI or close-head vs. open-head injury. In TBI patients, pH ECF and pH ICF decline to 7 [22] and 6.9 [106], respectively. PH measurements in TBI mice suggest a biphasic change of pH, which resolves after two hours, while in TBI patients, pH showed a resolution to normal values after about 10 days [22,106]. PH ICF changes are of minor impact on traumatic brain PK. However, pH ECF changes due to TBI might impact brain PK of drugs with pk a < 8 and pk b > 6, respectively. The BBB opening is another feature of TBI, as evidenced by the decrease in tight junction protein expression mainly claudin-5, occludin, and ZO-1 and an increase in BBB permeability to small and medium (0.1-10 kDa) and large molecules (up to 160 kDa) [107][108][109] in TBI mice. BBB opening and increased permeability resides up to the first 96 and 24 h post-injury for small and large molecules, respectively [107][108][109]. A wide range of CNS-acting medications are used to manage TBI patients including analgesics (e.g., acetaminophen, morphine), anticonvulsants (e.g., gabapentin and carbamazepin), neuroprotective agents (e.g., cyclosporine), etc. LeiCNS-PK3.0 simulations at altered para radius and pH ECF/ICF have shown that the CNS PK of some of these drugs are potentially affected by these changes. An increase in para radius resulted in an increase in brain ECF C max of morphine. Changes in pH ECF/ICF might affect the PK of morphine (pkb = 9.1) and gabapentin (pk a = 4.6, pk b = 9.9). Combining the simulation results and literature findings on TBI pathophysiology and in vivo TBI PK suggests that brain PK may change due to pH and para radius , particularly during the first 48 h after the injury.
Brain PK is potentially altered in epilepsy. Brain PK of phenytoin was lower in epileptic compared to control rats; the difference was accounted for by the increased p-gp expression in epileptic rats [110]. Brain PK of phenytoin increased following a seizure when p-gp expression was suppressed with nimodipine, implying a potential role of the BBB opening in altering phenytoin PK. Postmortem studies in rats and humans have demonstrated an increased BBB permeability to albumin and Evan's blue (Mwt = 69 kDa) following an epileptic seizure [111], which persisted in rats up to 1 week after the seizure [111]. Epileptic seizures result as well in a decrease in pH ECF by 0.5 units, which returns to normal values at a slower rate than pH ICF , which declines by about 0.3 pH units and is corrected within 20 min following seizure [112]. These changes in pH are expected to impact drugs with pk a < 8 and pk b > 6, respectively. Our simulations included antiepileptic drugs such as phenytoin, diazepam, carbamazepine, levetiracetam, and gabapentin. Of these drugs, only levetiracetam was sensitive to changes in para radius , while gabapentin (a zwitterion, pk a = 4.6 and pk b = 9.9) PK in brain ICF was sensitive to changes in pH ECF . Phenytoin PK changes remains interesting, as despite experimental evidence of the importance of the passive transport route [110], LeiCNS-PK3.0 simulations showed no sensitivity to para radius changes. It is worth mentioning that in vitro studies using human-and mouse-derived p-gp have concluded that phenytoin is actively transported in rodents but not in humans [113].
Glioma patients and sarcoma-laden rats showed higher methotrexate brain ECF PK compared to controls [7]. Cyclophosphamide brain ECF PK, on the contrary, was lower in tumor-bearing vs. non-tumor-bearing mice [31]. Brain tumors affect BBB permeability as demonstrated by the 8-fold increase in para radius in rats with a malignant glioma [114], which was measured with gadolinium-labeled nanoparticles of increasing size. In addition, the pH ECF -to-pH ICF ratio is reversed in brain tumors, as pH ECF decreases to 6.7, whereas pH ICF increases to 7.3 [115,116]. This will result in the change in PK and drug partitioning between brain ECF and brain ICF [100], which is indicated by our Kp uu,cell values ( Figure 3 and Supplementary Figure S3), particularly for drugs with acidic and basic groups of pk a and pk b of <8 and >6, respectively. LeiCNS-PK3.0 simulations of the chemotherapeutic drugs, cyclophosphamide and methotrexate, showed a decline of T max due to increased para radius , while only methotrexate (pk a = 3.4) PK at brain ECF and brain ICF PK was sensitive to pH ECF and pH ICF changes. Table 3. Pathophysiological changes of para radius , pH ECF , and pH ICF in multiple CNS diseases.
Disease translation pharmacokinetic modeling is crucial for accurate predictions of drug effect, but it is challenging particularly for CNS diseases that are progressive, with yet unraveled pathophysiology mechanisms and scarce (pre)clinical data for model validation, not mentioning the ethical concerns in this sensitive yet critical research field. Thus, predicting a disease-specific PK at brain target sites requires a holistic approach such as PBPK modeling that accounts for both drug and (patho)physiology. In this manuscript, we applied our CNS PBPK model, LeiCNS-PK3.0, to predict the impact of altering one CNS parameter at a time on brain PK. LeiCNS-PK3.0 can also be used to predict a diseasespecific PK in different regions of the CNS. This will require accounting for all diseasespecific pathophysiological changes such as changes in tissue composition and non-specific binding [120], tissue volumes [121], active transporter expression and functionality [38], pH changes, CSF-related changes [12], etc. and their time course, i.e., deteriorating vs. healing. Such information is not always available from humans, and therefore, translating information on CNS pathophysiology from preclinical species is indispensable. Plasma PK acts as input to LeiCNS-PK3.0, and therefore, having the right plasma model from the disease population of interest is a crucial step to accurate CNS PK predictions. Plasma PK might change in CNS diseases compared to a healthy situation due to drug-drug interactions associated with concomitant drug administrations or due to declining liver and kidney functions as seen in elderly and AD patients.

Conclusions
With LeiCNS-PK3.0 simulations of CNS disease pathophysiology, we demonstrated that the BBB opening might increase the rate and extent of BBB passive transport and that a change of pH ECF and pH ICF can result in altered distribution of unbound drug in brain ECF and brain ICF . The impact of those parameters on CNS PK should not be underestimated. It should be noted that our study conclusions remain limited to small drug molecules and may not extend to other drug classes as biologics.
Supplementary Materials: The following are available online at https://www.mdpi.com/1999-492 3/13/1/95/s1, Figure S1. Detailed mathematical structure of LeiCNS-PK3.0; Figure S2. Simulated concentration-time profiles of all 46 drugs at physiological and pathophysiological values of CBF, para radius , brain ECF volume, pH ECF , and pH ICF ; Figure S3. Heatmaps summarizing the effect of pathophysiological changes of CBF, para radius , brain ECF volume, pH ECF , and pH ICF on brain pharmacokinetics parameters: C max , T max , AUC, Kp uu,ECF , and Kp uu,cell ; Table S1. Physicochemical properties and active transporter affinity of all 46 drugs; Table S2. Mean protein expression levels (in fmol/µg total protein) of relevant transporters at the BBB.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.

Conflicts of Interest:
The authors declare no conflict of interest.