A complex study of the pharmacokinetics and compartmentalization of lithium ascorbate in 11 biosubstrates

Abstract

For lithium ascorbate in a dose of 1000 mg/kg, pharmacokinetic curves were obtained for whole blood and tissue homogenates of 11 various biosubstrates (brain, frontal lobe of the brain, heart, aorta, lungs, liver, kidneys, spleen, adrenal glands, femur, urine). As part of the chamber-free analysis of the dynamics of concentrations in whole blood, the following values of pharmacokinetic parameters of lithium ascorbate were obtained: Cmax=50.59 μg/l, tmax=1.50 h, Clast=33.7 μg/l, AUCt=1750 μg/l*h, MRTt=22.9 h, Lz=0.005 1/h, T1/2=141 h, CL=0.029 l/h, Vd=5.9 L. Lithium concentrations in whole blood and in the frontal lobe of the brain remained stable for at least 40... 45 hours after passing the peak of concentration. Multichamber pharmacokinetic analysis showed that the stabilization of lithium levels in the blood and brain is maintained by a special lithium depot, probably consisting of the adrenal glands, aorta, femur, and brain. The comparison of the experimentally obtained and calculated data showed acceptable values of the developed three-chamber model (standard deviation of lithium concentrations in blood - 3.4 μg, correlation coefficient between theoretical and experimental values of lithium concentrations - r=0.92).

Keywords: lithium ascorbate, chamber-free model, multi-chamber modeling, pharmacokinetics, biosubstrates

Introduction

Lithium ion is characterized by normothymic action. The most well-known pharmacological form of lithium is lithium carbonate, which is used in psychiatry for the treatment of bipolar disorders [1], manic syndrome, gambling addiction [2], etc. However, lithium carbonate-based drugs have significant drawbacks. 

Firstly, for the effective and safe administration of these drugs, it is necessary to measure regularly lithium concentration in the blood, which leads to additional invasive procedures [3]. Secondly, lithium carbonate is characterized by a narrow therapeutic range of lithium concentrations in plasma - 0.6-1.2 mmol/L. Li+ concentrations of 1.5-2.5 mmol/L are associated with low toxicity, 2.5-3.5 mmol/L - with severe poisoning, and exceeding the threshold of 3.5 mmol/L can be life-threatening [4]. Thirdly, in order to achieve the desired therapeutic effect in psychiatry, it is necessary to use significant doses of lithium carbonate (1... 3 g/day, in the acute period – up to 9 g/day), which, due to the high toxicity of lithium carbonate, reduces the attractiveness of this lithium salt to be administered by physicians [5].

Therefore, the effects of other lithium salts are investigated to improve the safety of lithium therapy. In particular, lithium ascorbate is characterized by low toxicity (class 5, LD50 - 6334 mg/kg, toxicity is 8.4 times less than that of lithium carbonate) [6].  At the same time, the psychoneurological efficacy of lithium ascorbate is achieved in lower dosages (10... 20 times less than the daily dose of lithium carbonate) [7]. Anxiolytic, antidepressant [8], neuroprotective [9] and mnestic effects of lithium ascorbate have been established [10].

Thus, our results suggest that a drug developed on the basis of lithium ascorbate will achieve the desired therapeutic effect in significantly lower dosages than lithium carbonate. For a more complete characterization of lithium ascorbate as a pharmaceutical form, it is necessary to carry out pharmacokinetic studies, the results of which will show the characteristics of lithium ascorbate absorption by the human body.

This paper presents the results of a complex experimental study of the pharmacokinetics of lithium ascorbate in a dose of 1000 μg/kg (taken for 1..3 months) [11]. To study the pharmacokinetics and distribution of lithium in tissues, it was decided to use a single administration of a 10-fold dose of 100 μg/kg, i.e. 1000 μg/kg. Since the LD50 of lithium ascorbate is 6334 mg/kg [6], a dose of 1000 μg/kg of elemental lithium is quite far from acutely toxic.

Materials and methods

Male Wistar white rats weighing 200–250 g (n=54, 9 groups of 6 animals each) were used as a model object. All procedures and experiments on rats were carried out in accordance with international rules for the handling of animals; the study was carried out in accordance with the decision of the Ethics Committee of the Ivanovo State Medical Academy dated March 24, 2016. The animals were kept in rooms with the same conditions, in cages of 6 rats each, in temperature of 19–21°C. Animals were fed daily with mixed feed at the rate of 40–50 g per individual. Preparation of solutions. The probing was carried out with a solution of lithium ascorbate, 1 ml of which contained 250 μg of elemental lithium. To obtain a dose of 1000 μg/kg, an animal weighing 250 g needs to receive 250 μg of elemental lithium, i.e. 1 ml of solution. The required volume of solution was calculated based on the weight of the animal. Lithium ascorbate dihydrate powder was used to prepare the solution. The molecular weight of anhydrous lithium ascorbate is 178 g/mol, lithium ascorbate dihydrate is 214 g/mol. In lithium ascorbate dihydrate, lithium and ascorbate anion are represented in a molar ratio of 1:1 and in a mass ratio of 1:71.33. Thus, 250 μg of elemental lithium is contained in 250*71.33=17.84 mg of lithium ascorbate dihydrate.

Conducting an experiment. Probing with lithium ascorbate solution in a dose of 1000 μg/kg (based on lithium elemental acid) was carried out, then groups were selected at 9 time points - 0 min, 45 min, 1 h, 1.5 h, 3 h, 6 h, 12 h, 24 h, 48 h. Using mass spectrometry, lithium levels were determined in 11 various biosubstrates – whole blood, brain, frontal lobe of the brain, heart, aorta, lungs, liver, kidneys, spleen, adrenal glands, femur.

Determination of lithium levels. When determining the levels of lithium, tissues homogenates of the studied biosubstrates were obtained. Samples of homogenates were taken in plastic tubes and diluted 5 times with bidistilled and deionized water. In mass spectrometry, indium was introduced into the solutions as an internal standard in a concentration of 25 μg/L. Calibration solutions were prepared from VTRC standard solutions with a known content in the range of 5-1000 μg/L (10-7%). Resulting solutions were analyzed on the Plasma Quad PQ2 Turbo mass spectrometer with ionization in inductively coupled plasma (VG Elemental, England). The operational power of the microwave generator was 1.3 kW. The flow rate of plasma-forming gas (argon) was 14 l/min, flow rate of transport gas was 0.89 ml/min. Each sample was exposed 3 to 10 times, the signal integration time was 60 seconds. This method is recognized as the most accurate and efficient and allows performing a high-precision quantitative analysis of the content of 68 elements of the D.I. Mendeleev’s periodic table of (including lithium) in various biosubstrates.

Pharmacokinetic analysis. During the analysis, the methods of multi-chamber and chamber-free pharmacokinetic analysis were used. The multi-chamber analysis was carried out using the SimBiology package as part of the MATLAB-2016 software package [12], and the chamber-free analysis - using Excel spreadsheets supplemented with modules of the PKSolver software package [13]. 

Results

As a result of the pharmacokinetic experiment, pharmacokinetic curves (PK curves, i.e. concentration-time dependencies) were obtained for tissue homogenates of various organs (Fig. 1).

Fig. 1. Pharmacokinetic curves of lithium content in tissue homogenates following administration of lithium ascorbate in a dose of 1000 μg/kg (based on elemental lithium). (A) homogenates of brain, whole blood, and liver tissues, (B) other organs.

 

The PK curves obtained for various biosubstrates differ significantly in the nature and degree of change in lithium concentrations over time. Estimating the “distance” between the curves as the standard deviation of the curves from each other made it possible to cluster FC curves using the metric condensation analysis method [14]. As a result of clustering, it was found that all PK curves, except for PK curves for the liver, heart, and femur, form a sole cluster (Fig. 2).

Fig. 2. Results of PK curve clustering for various biosubstrates

 

Visual analysis of PK curves shows that within 1... 2 hours after lithium ascorbate probing, there is an intensive accumulation of lithium in all tissues examined. Maximum peak lithium concentrations (Cmax) are found in tissue homogenates of the liver and heart, and the minimal ones are found in the homogenates of the lungs and aorta. 

It should be noted that lithium concentrations in whole blood and in the frontal lobe of the brain remained very stable for at least 40... 45 hours after passing the peak of concentration. This observation may indicate, firstly, the preferential accumulation of lithium in whole blood and in the frontal lobes during the administration of lithium ascorbate and, secondly, the maintenance of lithium concentrations in these organs due to some “depot” of lithium. 

Results of the multi-chamber pharmacokinetic analysis of lithium ascorbate

For the multi-chamber PK analysis, the PK curve for the lithium content in whole blood was used (Fig. 3) since the analysis of drug content in the blood is the basis of the pharmacokinetic analysis. This curve is characterized by a pronounced peak of lithium concentrations after 1... 1.5 hours after probing and a rather sloping area indicating slow elimination of lithium from the blood.

Fig. 3. Pharmacokinetics of lithium levels when lithium ascorbate is administered in whole blood. (A) Source data. (B) Mean PK curve.

To obtain the most adequate multi-chamber model, one-, two-, three- and four-chamber models in various configurations were studied. As a result of the modelling, it was found that the simplest model that most accurately describes the studied PK curve (Fig. 3) is a three-chamber model that includes the gastrointestinal tract (1st compartment), whole blood (central, 2nd compartment) and lithium depot (3rd compartment), and lithium is eliminated from the central compartment, rather than from the depot (Fig. 4).

Fig. 4. A three-chamber model of lithium ascorbate pharmacokinetics obtained from multi-chamber pharmacokinetic modeling in the MATLAB medium. The legends of the corresponding constants (k12, Kcd, Kdc, Ke_central) used in the text of the article are given.

The quality of the studied multi-chamber models was characterized by the values of the standard deviation of concentrations between the theoretical and experimentally obtained PK curves, as well as by the correlation coefficient between the theoretical and experimental values of lithium concentrations when lithium ascorbate was administered in whole blood (Fig. 5). For the resulting three-chamber model, shown in Fig. 4, the standard deviation of the concentrations was ɑ =3.4 μg/L (with a correlation coefficient of 0.92), which indicates an acceptable quality of the resulting model.

Fig. 5. Quality values of the three-chamber PK model. (A) Experimentally obtained points of the PK curve (“whole blood”) and a theoretical PK curve (“three-chamber model”). The standard deviation of lithium concentrations was ɑ =3.4 μg/L. (B) Correlation between theoretical and experimental values of lithium concentrations. Correlation coefficient r=0.92.

The resulting model is optimal in terms of quality and complexity. Simpler multi-chamber PK models were characterized by much lower quality. More complex models did not lead to a significant improvement in the quality of the model. 

For example, removing the “depot” compartment from the model in Fig. 4 led to a significant increase in the standard deviation of concentrations (ɑ=10 μg/L), as well as the removal of the gastrointestinal compartment (ɑ =15 μg/L). Modelling of the elimination process from the depot alone also dramatically reduced the quality of the model (ɑ=5.6 μg/L), while modelling of elimination from both the depot and the central compartment did not improve the quality of the model (ɑ =3.5 μg/L). The inclusion of the exchange process between the depot and the gastrointestinal tract in the model also reduced the quality of the model (ɑ=4.5 μg/L). 

Thus, the three-chamber model of lithium ascorbate pharmacokinetics, in which the salt solution passes from the gastrointestinal tract to the central compartment (whole blood), then to the depot, and elimination occurs only from the central compartment (Fig. 4), is the most adequate of the studied multi-chamber models. PK modelling made it possible to obtain quantitative estimates of the corresponding constants of the rate and volume of compartments (Table 1).

Table 1. Parameters of the three-chamber model of lithium ascorbate pharmacokinetics. The standard deviation of concentrations is 3.4 μg/l, the correlation coefficient is 0.92. 

Thus, the modelling showed that the depot volume is about half that of the central compartment (i.e., whole blood, see Table 1). Lithium ascorbate is rather quickly transferred from the gastrointestinal tract to the blood (k12=0.67 1/h) and is eliminated rather slowly from whole blood (which corresponds to a low value of the constant ke_Central=0.0068 1/h). The rate of lithium exchange between the blood and the depot is comparable to the rate of transfer from the gastrointestinal tract to the blood, and the transfer of lithium from whole blood to the depot (Kcd=0.41 1/h) is slightly faster than the reverse transfer of lithium from the depot to whole blood (Kdc=0.27 1/h). 

Unfortunately, the available PK data do not allow us to make quantitatively reliable conclusions about which organs make up the lithium depot. However, a comparison of the dynamics of lithium concentrations in the depot obtained as a result of modeling with the dynamics of the lithium concentration in the “depot” consisting of the brain, aorta, adrenal glands, and femur indicates a certain similarity in the change in concentrations (Fig. 6). Obviously, a depot consisting of these organs at least makes it possible to stabilize lithium concentrations after the first 10 to 15 hours of the experiment.

Fig. 6. Dynamics of concentrations in the lithium “depot” during the administration of lithium ascorbate obtained as a result of multi-chamber PK modeling. Experimental data for the depot were obtained by summing up the lithium content in the brain, aorta, adrenal glands, and femur.

The results of the multi-chamber modelling are also confirmed by comparing the elimination curve obtained according to the three-chamber model (Fig. 4) corresponding to the “zero” compartment (denoted in Fig. 4 as “lithium excretion”) with the levels of lithium experimentally measured in urine (Fig. 7). The correspondence between the experimental and calculated data on the dynamics of lithium levels in urine showed satisfactory values of correspondence (standard deviation of concentrations ɑ=5.2 μg/l, correlation coefficient r=0.85).

Fig. 7. Dynamics of lithium levels in urine when taking lithium ascorbate. (A) PK curves (B) Correlation between theoretical and experimental values of lithium concentrations. Correlation coefficient r=0.85.

(А)

(B)

Chamber-free pharmacokinetic analysis of lithium ascorbate

Chamber-free analysis makes it possible to characterize such commonly used PK parameters of the drug as area under the curve, clearance, half-life, time and maximum value of the achieved concentration tmax, Cmax, volume of distribution, etc. (Table 2). Chamber-free model parameters were calculated for all studied biosubstrates based on the corresponding PK curves (Table 3). 

Table 2. Studied pharmacokinetic parameters of the chamber-free model of lithium ascorbate

The PK values of lithium ascorbate parameters obtained in the сhamber-free analysis confirm the above conclusions. 

First, the time to reach maximum (tmax) was 1-1.5 h for most biosubstrates (except for the spleen, adrenal glands, and femur, in which tmax=12... 24 hours). 

Secondly, lithium accumulates most steadily in the frontal lobe (Clast = 40.5 μg/L – the highest concentration value after 48 h among the studied biosubstrates). This finding is also confirmed by the value of the area under the curve: the AUCt value for the  frontal lobe was  2094 μg/L*h, while, for example, for the liver (in which the highest peak lithium concentrations were noted) - 2031  Lithium was also effectively accumulated in the heart (AUCt=2123 μg/L*h) and in the adrenal glands (AUCt=1969 μg/L*h). 

Thirdly, a low value of the slope of the final elimination segment (Lz) and a high value of the half-life (T1/2) were characteristic of all biosubstrates, especially for whole blood (Lz=0.005 1/h, T1/2=141 h), brain, including frontal lobe (Lz=0.007 1/h, T1/2=210 h), kidneys (Lz=0.004 1/h, T1/2=179 h) and femur (Lz=0.002 1/h, T1/2=451 h). The accumulation of lithium in the frontal lobe and femur is confirmed by the lowest clearance values for these biosubstrates (frontal lobe – CL=0.017 l/h; femur – CL=0.011 l/h). Thus, lithium ascorbate contributes to the maintenance of stable lithium ion concentrations in whole blood and in the brain, which is important for the implementation of the preventive and therapeutic potential of lithium ion.

Table 3. Values of pharmacokinetic parameters of the chamber-free model of lithium ascorbate when administered in a dose of 1000 μg/L. 

Conclusion

A complex experimental study of the pharmacokinetics of lithium ascorbate (in a dose of 1000 μg/kg) was carried out. Pharmacokinetic curves were obtained for whole blood and tissue homogenates of 10 various biosubstrates (brain, frontal lobe of the brain, heart, aorta, lungs, liver, kidneys, spleen, adrenal glands, femur). A multi-chamber pharmacokinetic analysis showed that the stabilization of lithium levels in the blood and brain is maintained by a special lithium “depot” consisting probably of the adrenal glands, spleen, aorta, lungs, and femur. Lithium concentrations in whole blood and in the frontal lobe of the brain remained very stable for at least 40... 45 hours after passing the peak of concentration. The PK values of lithium ascorbate parameters obtained in the chamber-free analysis confirm the above conclusions and show that lithium ascorbate contributes to the maintenance of stable lithium ion concentrations in the blood and in the brain, which is important for the implementation of the preventive and therapeutic potential of lithium.

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