Application of Lead Transport through Brain Capillary for Determination of Weight, Brain Damage, and Encephalization Quotient in Humans

Abstract

The ability of lead to cause brain damage and reduce intelligence quotient has been established. However, transport of lead through brain capillary has not been elucidated. Hence, plasma and brain tissue kinetics of lead was studied mathematically. Literatures were searched for formulas that could be used for the determination of relationship between plasma and brain tissue kinetics of lead with an interest to discovering the residence time of lead residues in brain. Findings have shown that 5μg/dl of lead in plasma permeates the brain of human weighing 20 kg faster than that of 40 kg and 70 kg body weight, respectively. The surface area of permeability of brain cell is higher, in low body weight human than in high body weight human. Time of exposure and concentration of lead are higher in low body weight human as compared to high body weight human. Hence, neonates and children are more vulnerable to brain damage than adult human.

1. Introduction

Plasma concentration (>5 to >100 μg/dl) of lead can cause neurological, cardiovascular, hematological, reproductive, renal, immunological, and respiratory problems [1]. The reported lead concentrations of surface sample of soil was 23–35 mg/kg soil, whereas the concentration of the lead elute from soil was 0.6 mg/L, respectively [2]. Lead has the ability to penetrate brain having molecular weight of 207.28 g [3] and elimination half-life of 18 months. Highly contaminated soil could have the concentration of lead 3.03 times higher than the maximum limit for agricultural soil and 1.97 times higher than the value limit for fodder [4], suggesting that lead is very stable in soil and toxic to human [5]. However, soil concentration of lead (11.42 mg/L) could decrease during rainy season relative to dry season [6]. Lead exerts opposite effects on antibody response and phagocytosis [7]. Some plants such as Cyamopsis tetragonoloba and Sesamum indicum could tolerate lead concentration of up to 1000 mg/kg; hence, they could be used for bioremediation of soil heavily contaminated by lead [8]. The factors responsible for penetration of central nervous system acting agents are lipid solubility, pH, and molecular weight [9]. Hence, toxicological study of chemicals is necessary for the identification of potential toxicants [10]. Severe lead poisoning in young children and neonatal rats may cross microvessel endothelium of the brain. There is evidence that lead can cause brain damage, and lead uptake in the endothelium is reduced by calcium adenosine triphosphatase (ATPase) pump [11]. In view of this, transport of lead through brain capillary was mathematically assessed with a view to identifying pathogenesis of brain injury caused by lead in humans.

2. Materials and methods

2.1 Calculation of blood and plasma lead concentration

Literatures were assessed with a view to obtaining formulas that could be used for the calculation of lead transport through brain capillaries and its pathogenesis of causing brain damage and low intelligence quotient. Measurement of red blood cell (RBC) partitioning of lead is done as follows:

$$\mathit{\text{Plasma Imax}},u-\mathit{fup}\left(\mathit{\text{Plasma Imax}}+\frac{F_a\times F_g\times K_a\times \mathit{\text{Dose}}}{\frac{\mathit{Qh}}{\mathit{Rb}}}\right)$$E1

where $\mathit{\text{Imax}}=C_{\mathit{max}}\left(\mathit{\text{μmol}}\right),\mathit{\text{Dose}}\left(\mathit{\text{μmol}}\right),\mathit{fup}=$ fraction of unbound drug in plasma (lower limit, 0.01), $K_a$= absorption rate constant (0.1 mi$n^{-1})$, $F_a$= fraction absorbed (1), $F_g$= fraction escaping gut metabolism (1), $\mathit{Qh}$= hepatic blood flow (1.6 L/min), and $\mathit{Rb}$= blood–plasma concentration ratio [12].

$$\text{Distribution of lead to}\mathrm{red}\text{blood cells}\left(\%\right)=\left(1-\frac{\mathit{\text{Plasma conc}}\times \left(100-\mathit{HC}\right)}{\mathit{\text{Blood conc}}\times 100}\right)\times 100$$E2

$$\text{Blood to plasma ratio}=\frac{\mathit{\text{Blood Conc}}}{\mathit{\text{Plasma Conc}}}$$E3

$$\mathit{Hb}=\mathit{PV}-\left(\frac{\mathit{\text{CrCl}}\times D\times \mathit{Scr}\times 72}{K\times \left(140-\mathit{Age}\right)}\right)\times 12.5\times \frac{1}{0.33}$$E4

$$D=\frac{\mathit{Pcr}}{\mathit{Scr}}\times 144.$$E5

$$\mathit{RDB}=\mathit{RRW}\times 80\mathit{ml}1\mathit{kg}\times \frac{\mathit{\text{Desired}}\mathit{PCV}-\mathit{\text{Recipient}}\mathit{PCV}}{\mathit{\text{Donor}}\mathit{PCV}}$$E6

2.2 Blood and tissue kinetics of lead

$$\mathit{Cl}=\raisebox{1ex}{$\mathit{DR}$}\!\left/ \!\raisebox{-1ex}{$\mathit{Css}$}\right.$$E7

$$\mathit{LD}=\mathit{Css}\times \mathit{Vd}$$E8

The first-order equation that describes the release of lead from biological system is concentration-dependent and can be expressed as [13]:

$$log{C}_t=\frac{log{C}_o-K_t}{2.303}$$E9

where $C_o$= initial concentration of lead and $C_t$= concentration of lead in solution at time t. slope equals $-\raisebox{1ex}{$K$}\!\left/ \!\raisebox{-1ex}{$2.303$}\right.$ [14]. The elimination rate constant (1.16 h⁻¹) terminal half-life (0.6 h⁻¹) and volume of distribution (1.03 L/kg) have been reported for 60 kg weighted man.

Hence, terminal half-life

$$\left(t\frac{1}{2}\beta \right)=\frac{\mathit{Vd}}{\mathit{PCl}}\times 0.693$$E10

where $\mathit{PCl}$ = plasma clearance. However, initial concentration ($C_o$) is calculated as:

$$C_o=\frac{D}{V_{\mathit{app}}}$$E11

where D = dose of lead; V_app = apparent volume of distribution, when renal function is not impaired the serum concentration:

$$\left(C_s\right)=\frac{\mathit{\text{observed concentration}}}{0.2x\mathit{\text{Albumin}}\left(g/\mathit{dl}\right)+0.1}$$E12

When there is end-stage renal failure, the serum concentration is calculated as:

$$C_s=\frac{\mathit{\text{observed concentration}}}{0.1x\mathit{\text{Albumin}}\left(g/\mathit{dl}\right)+0.1}$$E13

Integration of exposure time with toxic dose of lead is presented as:

$$D=\frac{T^n}{K}$$E14

where D = dose, T = time of exposure, and K = concentration of toxicant causing toxicity [15].

2.3 Translation of lead dose in animals to human

$$\mathit{HED}=\frac{\mathit{\text{Animal dose}}\times \mathit{Km}}{\mathit{\text{Human}}\mathit{Km}}$$E15

Animal dose and animal Km are substituted with 40 and 20 kg as well as 31.3 and 25.0, respectively [16].

2.4 Transport of lead through brain capillary

Lead can be transported through brain capillary having the rate constant:

$$\left(\mathrm{Kin}\right)=\frac{\mathit{QE}}{\mathit{\text{Vbrain}}}$$E16

$$E=1-e^{\frac{-\mathit{PSA}}{Q}}$$E17

$$\text{Alternatively}{E}_r=\frac{\mathit{Cin}-\mathit{\text{Cout}}}{\mathit{Cin}}$$E18

where Q = brain capillary blood flow, E = fraction of lead that flow into the brain, V_brain = volume of brain, E_r = extraction ratio of lead, PSA = permeability surface area ($\left({\mathit{MS}}^{-1}{m}^2\right)$ of blood-brain barier, C_in = concentration of lead entering the brain capillary $\left(\mathit{mol}{L}^{-1}\right)$, and C_out = concentration of lead leaving the brain capillary [17, 18].

The passive flux (QPas) of lead across blood-brain barrier between plasma and the brain extracellular fluid (ECF) is given as:

$$\mathit{\text{QPas}}=P\left(C_{\mathit{pl}}-C_{\left(\mathit{ECF}\right)}\right)$$E19

where QPas = passive flow rate $\left(\mathit{mol}{m}^{-2}{s}^{-1}\right)$, P = permeability of the BBB $\left({\mathit{MS}}^{-1}\right)$, $C_{\mathit{pl}}$=concentration of the lead in the plasma $\left(\mathit{mol}{m}^{-3}\right)$, and $C_{\mathit{ECF}}$= concentration of lead in the ECF [19]:

$$\frac{∆C_{\mathit{ECF}}}{∆t}=\mathit{\text{kBBB}}\left(C_{\mathit{pl}}-C_{\mathit{ECF}}\right)$$E20

$$V_{\mathit{ECF}}=\frac{∆\left(\mathit{ECF}\right)}{∆t}=\mathit{\text{CLBBB}}\left(C_{\mathit{pl}}-C_{\mathit{ECF}}\right)$$E21

$$C_{\mathit{ECF}}=\frac{A_{\mathit{ECF}}}{V_{\mathit{ECF}}}$$E22

Cerebral metabolic rate (CMR) scales with brain volume, hence:

$$\frac{\mathit{CMR}}{V}=\alpha V^{0.167}$$E23

$$\text{Density of neuron}\left({\mathrm{D}}_n\right)=\alpha V^{0.167}$$E24

$$\text{The capillary length density}\left({\mathrm{C}}_n\right)=\alpha V^{0.167}$$E25

Total length of capillary is proportional to the number of neurons [20].

$$\text{Capillary diameter}\left({\mathrm{C}}_d\right)=\alpha V^{0.08}$$E26

It is $7\mathit{\mu m}$diameter in human brain [21]. The flow rate of blood to the brain is $800\mathit{mL}/\mathit{min}$ [22]where $∆C_{\mathit{ECF}}$ = change in lead concentration of extracellular fluid, KBBB = rate constant of lead transport across the BBB ($S^{-1})$, CL BBB = transfer clearance of lead transport across the BBB $\left(m^3{S}^{-1}\right)$, $A_{\mathit{ECF}}$ = molar amount of lead in the brain ECF $\left(\mathit{mol}\right)$, and $V_{\mathit{ECF}}$= volume of the brain ECF $\left(m^3\right)$ [23, 24, 25].

$$\text{Passive permeability}\left(p\right)=\mathit{\text{Ptrans}}+\frac{D_{\mathit{\text{para}}}}{W_{T\mathrm{J}}}$$E27

where Pt = passive transcellular permeability $\left({\mathit{ms}}^{-1}\right),D_{\mathit{\text{para}}}$ = diffusity of lead through the BBB intercellular space $\left(m^2{s}^{-1}\right)$, and $W_{T\mathrm{J}}$ = width of tight junction (m) [24].

$$\text{Total flux}\left({\mathrm{Q}}_{\text{total}}\right)={\mathrm{P}}_{\mathrm{tot}}\left(C_{\mathit{pl}}-C_{\mathit{ECF}}\right)$$E28

$${\mathrm{Q}}_{\text{total}}={\mathit{PAF}}_{\mathit{\text{in}}}\left(C_{\mathit{pl}}\right)-{\mathit{PAF}}_{\mathit{\text{out}}}\left(C_{\mathit{ECF}}\right)$$E29

where P_total = rate of active and passive transport across BBB, ${\mathit{PAF}}_{\mathit{\text{in}}}$ = affinity of lead to active transport into the brain, and ${\mathit{PAF}}_{\mathit{\text{out}}}$ = affinity of lead to active transport out of the brain [25].

$$P_{\mathit{tot}}=P_{\mathit{pas}}\times C_{\mathit{\text{part}}}$$E30

$P_{\mathit{pas}}$ = passive permeability to BBB; $C_{\mathit{\text{part}}}$= coefficient of partition [26].

$$\text{Active clearance}\left({\mathit{Cl}}_{\mathit{act}}\right)=\frac{\mathit{Tm}}{\mathit{Km}+C}$$E31

where $\mathit{Tm}$ = maximum rate of lead transport across the BBB ($\left(\mathit{\text{μmol}}{L}^{-1}{S}^{-1}\right)$, K$m$ = concentration of free lead $\left(\mathit{\text{μmol}}{L}^{-1}\right)$ at which half of $\mathit{Tm}$ is attained, and C = concentration of lead in plasma [27].

Change in lead concentration within the cells of the brain is given as follows:

$$\frac{∆C_{\mathit{ICF}}}{∆t}=K_{\mathit{\text{cell}}}\left(C_{\mathit{ECF}}-C_{\mathit{ICF}}\right)$$E32

$$V_{\mathit{ICF}}\frac{∆C_{\mathit{ICF}}}{∆t}=C_{\mathit{\text{cell}}}\left(C_{\mathit{ECF}}-C_{\mathit{ICF}}\right)$$E33

$$C_{\mathit{ICF}}\frac{A_{\mathit{ICF}}}{V_{\mathit{ICF}}}$$E34

where $C_{\mathit{ICF}}$ = concentration of lead in the brain ICF $\left(\mathit{\text{μmol}}{L}^{-1}\right)$, $K_{\mathit{\text{cell}}}$= rate constant of lead transport across the cell membrane $\left(S^{-1}\right)$, and $V_{\mathit{ICF}}$= apparent volume of distribution in the brain ICF [28].

$$\text{Dissociation constant}\left(\mathit{kd}\right)=\frac{k_{\mathit{on}}}{k_{\mathit{off}}}$$E35

where $\mathit{kd}=45.62\mathit{nM}\left(0.91\mathit{\mu g}/\mathit{dL}\right)$ that has been reported for on-site lead detection using a biosensor device [29].

2.5 Michaelis-Menten kinetics of lead

Clearance of lead by Michaelis-Menten kinetics is given as follows:

$$\mathit{\text{CLact}}-\mathit{\text{cell}}=\frac{\mathit{Tm}-\mathit{\text{cell}}}{\propto \left(\mathit{Km}-\mathit{\text{cell}}+C\right)}$$E36

where $\mathit{\text{CLact}}-\mathit{\text{cell}}$ = active transfer clearance of free lead across the cell membrane, C = concentration of lead in the brain ECF or ICF, $\mathit{Tm}-\mathit{\text{cell}}$= maximal veolocity of the transporter, and $\mathit{Km}-\mathit{\text{cell}}$= Michaelis –Menten constant [30].

Enzyme metabolic clearance $\left(\mathit{\text{φmet}}\right)$ is given as follows:

$$\mathit{\text{φmet}}=V_{\mathit{max}}\frac{C}{\mathit{Km}+C}$$E37

where $\mathit{\text{φmet}}$ = flux of the enzymatic metabolic reaction $\left(\mathit{\text{mmol}}{L}^{-1}\mathit{mi}{n}^{-1}\right)$, $V_{\mathit{max}}$ = maximum flux of the reaction $\left(\mathit{\text{mmol}}{L}^{-1}\right)$, C = concentration of substrate in ECF or ICF ($\left(\mathit{\text{mmol}}{L}^{-1}\right)$, and $\mathit{Km}$ = affinity of coefficient of the enzyme substrate $\left(\mathit{\text{mmol}}{L}^{-1}\right)$ [31]. Three-dimensional model that integrates lead transport through BBB and lead binding within the brain could predict lead distribution in the brain [32]. One kilogram equals 1000 mililiters [33].

2.6 Relationship between brain mass and encephalization quotient

$$\text{Encephalization quotient}\left(\mathrm{EQ}\right)=\frac{\mathit{\text{Brain mass}}}{0.14\times \mathit{\text{Body weigh}}{t}^{0.528}}$$E38

$$\text{Brain mass}\left(\mathrm{E}\right)=k_p\beta$$E39

where k = 0.14, p = body weight, and β = 0.528 [34, 35].

$$\text{Brain volume}\left({log}_{10}\left(B\right)\right)=3.015+0.986{log}_{10}C$$E40

where B = brain size (mm³) and C = internal cranial capacity (mm³).

$$\text{Also brain volume}\left(V_{\mathit{\text{brain}}}\right)=\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\times \mathrm{\pi }\times r^3$$E41

where

$$\mathrm{\pi }=3.14159\text{and}\mathrm{r}=\text{radius}=\frac{\mathit{\text{diammeter}}}{2}$$E42

$$T\frac{1}{2}\beta =\frac{0.693}{\beta }$$E43

Lead concentration (Ct), plasma clearance (Pcl), calculated administered lead and time of exposure to lead were extrapolated to 60, 40, and 20 kg weighed human, using human equivalent dose formula.

2.7 Parameters for the determination of therapeutic and toxic agents across brain cells

The relevant parameters that can be used for the determination of therapeutic and toxic agents across brain cells are as follows: capillary radius (3–5 ×${10}^{-6}m)$, capillary surface area (15–25$m^2)$, intercapillary distance (40–60 ×${10}^{-6}m)$, capillary blood flow rate (0.3–200 × ${10}^{-1}L{\mathit{min}}^{-1})$, BBB passive permeability $\left(6\times {10}^{-8}-{10}^{-6}{\mathit{ms}}^{-1}\right)$, BBB rate constant (1.4 × ${10}^{-4}-1.4\times {10}^{-2}{S}^{-1})$, BBB transfer clearance $\left(113-850\times {10}^{-5}L{S}^{-1}\right)$, BBB trancellular permeability $\left(0.6-10\times 10^{-7}{\mathit{ms}}^{-1}\right)$, BBB paracellular diffusity $\left(550-767\times 10^{-12}{m}^2{s}^{-1}\right)$, width tight junction $\left(0.3-0.5\times 10^{-6}m\right)$, active transport velocity $\left(22-167\mathit{\text{μmol}}{L}^{-1}{S}^{-1}\right)$, concentration to reach half of $\mathrm{Tm}\left(4.5-5\times {10}^3\mathit{\text{μmol}}{L}^{-1}\right)$, BBB surface area $\left(12-18167m^2\right)$, blood cebrospinal fluid barrier (BCSFB) surface area $\left(6-9m^2\right)$, cerebrospinal fluid (CSF) flow rate $\left(50-67\times 10^{-7}{\mathit{LS}}^{-1}\right)$, brain ECF flow velocity $\left(2-8\times 10^{-7}{\mathit{ms}}^{-1}\right)$, brain ECF volume fraction (0.23–0.49), tortuosity (1.5–1.7), effective diffusion constant $\left(0.1-15\times 10^{-10}{m}^{-2}{s}^{-1}\right)$, cellular uptake rate $\left(0.22-304.3s^{-1}\right)$, cellular transfer clearance $\left(4.2\times 10^3-3\times {10}^{5}L{S}^{-1}\right)$, ICF volume (960 L), association rate constant $\left(2.8\times 10^{-5}-2.8\times {10}^2\mathit{\text{μmol}}{L}^{-1}{S}^{-1}\right)$, binding site concentration $\left(1\times {10}^{-3}-5\times {10}^{-1}\mathit{\text{μmol}}{L}^{-1}\right)$, affinity constant $\left(0.003-528\times 10^3\mathit{\text{μmol}}{L}^{-1}\right)$, maximum reaction flux $\left(5.76\times 10^2-1\times 10^9\mathit{\text{μmol}}{L}^{-1}{\mathit{min}}^{-1}\right)$, and elimination rate constant $\left(1.1\times {10}^{-7}-6.8\times 10^4{S}^{-1}\right)$ have been reported for human brain [12].

3. Results

Table 1 shows kinetic parameters of lead in various compartments of brain of 20, 40, and 60 kg weighted adult humans.

Parameters	Value
Weight (kg)	60	40	20
Volume of brain (mm^3)	4400	3000	1500
Fraction of blood flowed into the brain (μg/dl)	5.0	5.0	5.0
Rate constant of brain transport through capillary (kin) (L/min)	3.4 × 10^−4 to 2.3 × 10^−1	5 × 10^−4 to 3.3 × 10^−1	1.0 × 10^−3 to 6.7 × 10^−1
Permeability surface area (m^2)	0.064	0.25	1.13
Concentration at time (Ct) (mol/s)	1.87	2.24	2.81
Plasma clearance (Pcl) (L/S)	1.19	1.43	1.78
Dose of administered lead CD	5.15	6.17	7.73
Time of exposure (T) (h)	5.20	6.23	7.80
Brain diameter (mm)	20.4	17.9	14.2
Brain radius (mm)	10.2	8.9	7.1
Brain elimination half-life (S^−1)	6.3 × 10^−8–1.0 × 10^−3	6.3 × 10^−8–1.0 × 10^−3	6.3 × 10^−8–1.0 × 10^−3
Blood lead level (μg/dl)	0.52–8.38	131–7.29	2.1–6.2
Blood-to-plasma ratio	0.1–1.7	0.3–1.5	0.4–1.2
Erythrocytes lead level (μg/dl)	3.38	2.29	1.2
Brain mass (kg)	4.4	3.0	1.5
Encephalization quotient	3.6	3.1	2.2

Table 1.

Kinetic parameters of lead in the brain of humans of varying weights.

4. Discussion

The increased rate constant of lead transport through brain capillary, permeability surface area, concentration of lead in the brain, and time of exposure to lead in 20 kg weighed human as compared to 40 and 60 kg weighed humans agree with the report of Nicholson [35] indicating that young humans are more vulnerable to plumbism. The increased plasma clearance of lead in the human of 20 kg body weight as compared to 40 and 60 kg body weight human agrees with the report indicating that children have the ability to eliminate lead faster than adult [35]. Absorption of lead by bone and teeth is 94% in adult as compared to 70% in children [36]. Half-life of blood lead is 40 days in human. Renal insufficiency caused by plumbism could delay lead elimination. Lead concentration lower than 5 μg/dL is associated with reduced academic performance. Tyrosine and phenylalaine are the two main binding sites in albumin. The binding site is ${\mathit{Tyr}}_{84}$ and ${\mathit{Cys}}_{34}$ [37]. The allowable lead limit in drinking water is $15\mathit{Ppb}\left(73\mathit{nM}\right)$ [38, 39]. Serum albumin consists of 585 amino acids which have three structural domains stabilized in disulfide bonds with binding sites for fatty acids, glycerol, and metal ions. The ability of lead to bind serum albumin is used to detect micromolar concentration of lead ions in biological solution [40, 41, 42]. Centre for disease control’s (CDC’s) limit of 5 μg/dl in blood is contrary to revised limit of 3.5 μg/dl, but even 3 μg/dl has caused diminished cognitive function [43]. Protein kinases regulate the development of brain capillaries and expression of blood-brain barrier. Lead could stimulate protein kinase, disrupting BBB development at the regulation of neuronal development. More so, low doses of lead can stimulate protein kinase C that may enhance the release of neurotransmitters [44]. Protein kinase C is most sensitive to lead followed by calmodulin-protein kinase C and cyclic adenosine monosphosphate protein kinase [45]. Toxic action of lead is influenced by the interaction between endothelial cells and astrocytes [46]. Genetic and environmental factors could make some particular children more vulnerable to lead neurotoxicity [47]. Human brain is made up of 100 billion neurons, which consumes 15–20 W power. Brain consumes 15–20% of consumed glucose [48]. Utilization of adenosine triphosphate (ATP) in gray matter and white matter are 9.5 $\mathit{\text{μmol}}{g}^{-1}{S}^{-1}$ and 3 $\mathit{\text{μmol}}{g}^{-1}{S}^{-1}$, respectively, signifying that 77% energy is consumed by cortical gray matter, which is 50% of brain volume. Components of gray matter are dendrites, neurons, glial cells, unmyelinated axons, and capillaries, but components of white matter are glial cells, myelinated axons, and capillaries. The density of brain capillary is 2–4 times more in gray matter [49]. Adult human brain weighs 1500 g and occupies 1200 cm³, with surface area of microvessels (100–200 cm²$g^{-1}$) [50]. Brain extracellular space constitutes 15–30% of the brain volume and brain vasculature 3% of the brain volume [51]. Increased size of human brain from 400 cm³ to 1200 cm³ [52] indicates increased cognition capacity of modern human. Serum creatinine$\left(0.88\pm 0.2\mathit{mg}/\mathit{dl}\right)$ has been reported for human with blood lead level of $2.36-2.54\mathit{\mu g}/\mathit{dl}$ [53]. Blood level of $24.43\pm 5.31\mathit{\mu g}/\mathit{dl}$ has been reported for traffic policeman in Taiwan [54]. Less than 1.5 min cerebral perfusion of labeled lead chloride was fast, providing a space of 9.7 mol/100 g of frontal cortex at 1 min. The influx was linear with concentration of 4 μM. Albumin (5%), cistern (200 Mm), and ethylene diamine tetraacetate (EDTA) (1 μm) slipped lead uptake. Potassium reduces lead 203 uptakes [55]. Concentration of lead in blood $\left(2.1-6.2\mathit{\mu g}/\mathit{dl}\right)$ has been reported for children [56] and 0.52–8.38 $\mathit{\mu g}/\mathit{dl}$ in adults [57]. Brain weight of man decreases by 2.7 g and that of human by 2.2 g per year with increasing age. Also brain weight increase of 3.7 g is independent of sex [58]. However brain weight increased by 0.78 g/year for 80 years between 1860 and 1940, amounting to 62.4 g [59]. Cognitive ability is dependent on number of neurons [60]. White matter decreases in old (75–85 years) as compared to young by 11% [61]. Hence, there is a need to revise the toxic reference value of lead in children. The reference value of 3.5 μg/dl should be revised to guide clinical and public intervention for individual children [62], because the relationship between encephalization and intelligence could be affected by low allometric value, when linear regression line was used [63]. Brain size, different regions of the brain including cerebral cortex, cortical thickness, frontal cortex, parietal cortex, cerebellum, and experience correlated positively with intelligence. Therefore, gene and environmental influence plays a key role in intelligence quotient [64], as such brain size based on cognitive equivalence is preferred to the encephalization quotient in empirical cognitive studies [65]. Environment could affect the development of neural tissues [66].

5. Conclusion

Lead fragments permeate blood–brain barrier of a young human weighing 20 kg body weight faster than those of humans weighing 40 and 60 kg body weights. However, rate constant of brain transport, permeability surface area, lead concentration in the brain, and exposure time of lead are higher in children leading to low encephalization quotient.

Abbreviations

Hb	haemoglobin
PV	plasma volume
D	depuration
Scr	serum creatinine
K	constant
Pcr	plasma creatinine
RDB	required donor blood
RRW	recipient real weight
PCV	packed cell volume
Cl	clearance
DR	dose rate
Css	steady state concentration
LD	loading dose
Vd	volume of distribution
HED	human equivalent dose
Km	metabolism consant
Kin	rate constant of lead transport through brain capillary
VECF	extracellular fluid volume
α	flow rate of blood to the brain
AICF	molar amount of lead in intracellular fluid
Kon	dissociated lead
Koff	original lead
β	elimination rate constant of lead