Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Caffeine and the Cerebral Vasculature: Pharmacokinetics, Vasoconstrictive Effects and Comparison to Hypertension By Joel Buishas Abstract: Caffeine is a well-known and widely utilized neuro-stimulant. It is also a vasoconstrictor and has been shown to reduce Cerebral Blood Flow (CBF) by an average of 27% [1]. Habitual users potentially subject themselves to hemodynamics similar to a patient with hypertension. A model was developed to further investigate the relationship between caffeine consumption and cerebral blood flow. This was done by determining the hemodynamics of the cerebral vasculature at rest via the construction of a system of conservation balance equations, the construction of a convective-destruction model to determine the concentration profile of caffeine within the cerebral vasculature, and the use of experimentally derived data to determine the vessel constriction coefficient (VCC) a value that relates the drug concentration in any given vessel with the increase in resistance due to caffeine induced constriction that the vessel will undergo. The effects of two, three, and four cups of coffee on the cerebral vasculature were then compared with patients with varying categories of hypertension. The model for the system at rest was validated by comparison to experimentally determined values for Cerebral blood flow (CBF),mean arterial pressure (MAP), and average blood flow rate through the internal carotid arteries (ICA) and the jugular veins (JV) (see table B for details). The results of the model showed a CBF of 750ml/min, a MAP of 84mmHg, and average blood flow rate of 334ml/min (ICA) and 374ml/min (JV). This suggests that the model accurately predicts the steady state hemodynamics for the cerebral vasculature at rest. The model for the system under the influence of caffeine was validated by comparison to the experimentally determined 27% decrease in CBF due to ingestion of 250mg of caffeine. The model yielded a CBF reduction of 38% the model decreases CBF by 11% more than expected. The system at rest and the caffeinated system were also validated by checking the overall mass balance. The model showed that the CBF of a person who habitually consumes two cups of coffee was 592 ml/min and was comparable to a patient with poorly controlled hypertension with an average CBF of 497 ml/min. This suggests that habitual consumption of caffeine can lead to a self-inflicted hypertensive state. Introduction: Hypertension is chronically elevated blood pressure, this condition can lead to a host of health problems including aneurism, stroke, and has even been linked with cognitive decline and dementia in elderly patients [2]. A prominent effect of hypertension is a reduction in the amount of blood supply to the brain. Hypoperfusion impairs the flow of oxygen and nutrients to brain tissue which can lead to brain ischemia and neural degradation [2]. Caffeine mirrors the effects of hypertension in that it increases pressure and resistance and decreases blood flow. According to the FDA the average American adult consumes 300 mg of caffeine per day [3]. Caffeine causes cerebral vasoconstriction by antagonizing adenosine receptors. It has been demonstrated that Caffeine has the ability to reduce CBF by an average of 27% [1]. Habitual caffeine intake causes the vascular adenosine receptor system to adapt to this vasoconstriction but, it has been shown that the adenosine receptors have a limited ability to compensate for high amounts of caffeine use [1], meaning that recurrent users of caffeine may have chronically low CBF levels. The goal of this series of network computations was to develop a mathematical model to help gain insight into the pharmacokinetics of caffeine in the human cerebral vasculature, examine the effect of caffeine on the hemodynamics of the system, and to compare the effect of caffeine to the effects of hypertension. A model was developed to further investigate the relationship between caffeine use and cerebral hemodynamics by focusing on the increase in resistance to blood flow due to the vasoconstrictive properties of caffeine. Methods: Figure 1: Visualization of Human Cerebral Vasculature The model for the human cerebral vasculature (shown above) has 42 vessels and 36 nodes which represent an input, an output, or a junction. The goal of the network computations was to determine the flow rate in all of the vessels and the pressure drop across each vessel in the system at rest. In order to solve the system, the inlet and outlet pressure are 100 mmHg and 5 mmHg respectively [3]. The connection logic of the vessels is given in the form of an .NWK file and it allows for the creation of 29 momentum balances equations for the system at steady state (given below). β πΉπππ€π πΌπ + β πΉπππ€π πππ = 0 (1) The length and vessel geometries are also known. This allows for the creation of 42 constitutive equations (given below). βP = F Ξ± (2) 128βπ’βπ πβπ· 4 (3) πΌ= (See appendix A for a complete list of balance and constitutive equations used in the model). The equations were put into the form of the standard linear algebra problem (3). Where A was the coefficient matrix, x was the vector of unknowns and b was the target vector. The equation was solved with LU decomposition in Matlab. Ax β b = 0 (4) . The complexity of the vessels between the Circle of Willis and the Venous system including the main branches of the cerebral artery, Pial network, Intracerebral arteries, Microcirculation, Intracerebral veins, and Pial veins necessitated an approach utilizing constrained optimization to obtain relevant resistance values in the vessels mentioned above. The optimal hydraulic resistance in these complex series of vessels was calculated by solving the system for an initial resistance value of 0.3 Pa*s/mm^3. The blood flow rate calculated was compared to the ideal blood flow rate of 750 ml/min the difference was considered the error. The process was repeated 1000 times incrementing the initial resistance value by 0.015% each time. The error surface was constructed by plotting the error against the incremented resistance values. The resistance with the lowest error was chosen as the ideal resistance (See table A for ideal resistances). To determine the concentration profile of caffeine in the cerebral vasculature for any dose steady state mass balances with convection and destruction terms were constructed for each of the 36 nodes in the system using equations 48 below. β πΌπ β β πππ = π·ππ π‘πππ¦ππ (5) Equation 4 above describes the mass balance for molar flux of caffeine for each vessel in the cerebral vasculature. βππ=1 Ξ¦ππ ππ (6) Equation 5 above describes the molar flux into the node. Where n is the number of vessels going into each node, Q is the flow rate obtained from the system at rest, and Ξ¦ππ is the unknown molar concentration of caffeine in each inflow. βπ π=1 Ξ¦π ππ (7) Equation 6 above describes the molar flux out of the node. Where m is the number of vessels leaving the node, ππ is the flow rate out of the node obtained from the system at rest and Ξ¦π is the unknown molar concentration of caffeine in the outflow. β36 π =1 Ξ¦π β ππ β ππ (8) Equation 7 above describes the destruction term for the each mass balance equation. Where Ξ¦π is the unknown molar concentration of caffeine in the blood leaving the node, ππ is the known volume of blood leaving the node, and ππ is the unknown destruction constant and represents the removal of caffeine from the system as it is absorbed by the vessels in (see appendix B for an example network to demonstrate construction of necessary mole balances). The destruction constant k was determined by Newton et. al. to be a linear function of caffeine concentration (Ξ¦). A linear regression was performed on the data obtained from Newton et. al. to obtain an equation for k given below. ππ (π·) = -0.017* Ξ¦π + 0.1607 (8) Both k and Ξ¦are unknowns, Figure 2 below is a schematic representation of the method used to solve the system of two unknowns and two equations. An initial guess was made to solve the system for Ξ¦, kβ was then calculated using equation 8 above. Then kβ was compared to the previously determined k by finding the infinity norm for the difference between k and kβ. k was then updated to kβ and the system was solved again for Ξ¦. Once the difference between k and kβ was smaller than 0.001 the model obtained the desired concentration profile and k vector. Figure 2: Schematic for finding the solution of the system of two equations and two unknowns consisting of the concentration vector and destruction constant using an initial guess of k to solve the system for π· then iterating and updating k until the infinity norm is sufficiently small Experiments by Lunt et. al. determined that a 250mg dose of caffeine results in a 2% reduction in middle cerebral artery (MCA) diameter. According to equation 3 this corresponds to an increased resistance value. With this information and the concentration profile from the model, the vessel constriction coefficient (VCC) was calculated using equation 9a and 9b below. ββ ππΆπ΄ ππΆπΆ + πΌπππ ππΆπ΄ = πΌπππ€ ππΆπ΄ (9a) ππΆπΆ = πΌπππ€ ππΆπ΄β πΌπππ ππΆπ΄ ββ ππΆπ΄ (9b) The VCC relates the drug concentration in any given vessel with the increase in resistance due to caffeine induced constriction that the vessel will undergo. Given that the diameter of the middle cerebral artery is 3.9mm the reduced MCA diameter is 3.8mm. The new resistance value was calculated to be 0.53PA*s. The VCC was calculated to be 1.74(PA*s)/mole. The concentration profile was then determined for two, three, and four cups of coffee, the resistances in each vessel were altered using the VCC, and the pressure drop and blood flow rates were recalculated using the method for the system at rest. Results: Pressure drops, resistances, and flow rates in the right and left ICA, Microcirculation, right and left IJV calculated from the network equations for the system at rest are shown to the right in table A, B, and C. The model performed as expected; an increase in the caffeine dosage correlates to an increase in resistance to flow and pressure drop across the vessels along with a decrease in the flow rate through the vessels. The results for the concentration profiles obtained for 2, 3, and 4 cups of coffee are illustrated by Figure 3. The data obtained conforms to expectations; the caffeine concentration exponentially and asymptotically approaches zero as distance from the inlet increases. Knowledge of the local concentration of caffeine in each vessel allows for a targeted approach to modeling the vasoconstrictive effects of caffeine on the cerebral vasculature Blood Flow Rates [ml/min] for System at Rest and Insulted System RICA LICA Micro RIJV LIJV CBF 0 oz coffee 333.9 343.3 749.9 364.8 385.1 749.9 8 oz coffee 247.6 251.2 592.4 293.4 298.9 592.4 16 oz coffee 170.3 172.4 413.4 205.3 208.1 413.4 24 oz coffee 129.0 130.5 316.2 157.3 158.9 316.2 Table A: Flow rates for key vessels in human cerebral vasculature for 0, 2, 3, and 4 cups of coffee. Pressure Drops [Pa] for System at Rest and Insulted System Rest 8 oz 16 oz 24 oz coffee coffee coffee 1854 1578 1396 RICA 1114 1870 1590 1406 LICA 1130 10820 922.4 994.7 1045 Micro 282.3 273.3 274.5 RIJV 120.9 282.3 273.3 274.5 LIJV 120.9 Table B: Summary of pressure drops across key vessels in human cerebral vasculature for 0, 2, 3, and 4 cups of coffee. Resistances [Pa] for System at Rest and Insulted System Rest RICA LICA Micro RIJV LIJV 0.2001 0.1975 0.0001 0.0198 0.0188 8 oz coffee 0.4492 0.4466 0.0934 0.0577 0.0566 16 oz coffee 0.5560 0.5534 0.1443 0.0798 0.0788 24 oz coffee 0.6492 0.6465 0.1984 0.1047 0.1036 Table B: Summary of pressure drops across key vessels in human cerebral vasculature for 0, 2, 3, and 4 cups of coffee. Caffeine Concentration [mMole] 0.35 Concentration Profile of Caffeine 0.3 0.25 0.2 2 Cups Coffee 0.15 3 Cups Coffee 4 Cups Coffee 0.1 0.05 0 Distance from Inlet Inlet Veins COW Figure 3: The concentration profile of caffeine for 2, 3, amd 4 cups of coffee in the cerebral vasculature. The concentration is higher in the Circle of Willis due to the convergence of the inlets. Validation: The model for the cerebral vasculature at rest was validated by comparing CBF, MAP, and flows in the ICA, right and left IJV. The overall CBF was 750.14 ml/min and it was calculated by adding the blood flow of the inputs in the system, the Internal Carotid, Vertebral, and Basilar arteries. The Mean Arterial Pressure was computed to be 84.3mmhg and it was calculated by taking the average pressure at each node of all the arteries in the system up to the microcirculation. The flow in the Internal Carotid artery was 334.2ml/min and the flow in the right and left jugular vein was 385.3ml/min and 364.8ml/min respectively. The model for the caffeinated system was validated by comparison to the experimentally determined CBF reduction due to ingestion of 250mg of caffeine by Lunt et. al. See table D below for summary and comparison to literature values). The computations for the system at rest were validated by checking the overall mass balance using equation 10 below. The model for the caffeinated system was validated by hand checks of randomly selected mole flux equations. β π΅ππππ πΉπππ€ πΌπ = β π΅ππππ πΉπππ€ πππ (10) The overall mass balance equation validated the computations for the system at rest and the randomly selected mole flux equations validated the model for the concentration profile of caffeine. Table D shows that the model reliably predicts the steady state and caffeinated hemodynamics of the system at rest. Literature Model CBF CBF250mg MAP ICA 750.0 547.5 87.00 239.0 749.9 465.4 84.30 334.2 LIJV 357.0 385.3 RIJV 309.1 364.8 Table D: Comparison of experimentally determined values for hemodynamics of cerebral vasculature and the values calculated from the model. CBF[ml/min], MAP[mmHg], flow rates[ml/min]. Discussion: The results of the series of network computation suggest that caffeine has a significant effect on the hemodynamics of the cerebral vasculature. Two cups of coffee (16oz) correspond to a 21% reduction CBF. Two cups also increases MAP to 85.9mmHg. Three cups significantly reduces CBF by 45% and increases MAP to 87.5mmHg. Four cups reduces CBF of 58% and increases MAP to 88.7. This is significant because the average person suffering from poorly controlled hypertension has a CBF of 597ml/min which is a 120 20% decrease [3] and a MAP of 110mmHg. Caffeine is the most widely consumed neurostimulant in the world and the average American consumes about 300mg of the drug daily. The data from the model suggests that this has serious implications for possible caffeine induced hypoperfusion because the model shows significant link between caffeine use and CBF reduction even though even larger doses of caffeine do not seem to affect MAP as much as CBF (see Figure 4-5 for summary). MAP in Cerebral Vasculature MAP [mmHg] 110 100 90 80 70 60 Rest 16oz 32 oz 64 oz Hypertension Figure 4: MAP for the cerebral vasculature at rest compared to MAP with 2, 3, and 4 cups of coffee and MAP of average patient with poorly treated hypertension. 800 CBF Levels in Caffeinated Vasculature CBF [ml/min] 700 600 500 400 300 200 100 0 Rest 16oz 32 oz 64 oz Hypertension Figure 5: CBF for 2, 3, and 4 cups of coffee compared to normal CBF and average CBF of patients with poorly controlled hypertension. Conclusion The model demonstrated that for steady state blood flow through the human cerebral vasculature physiologically meaningful values can be obtained for blood flow rates and pressure drops with knowledge of the logical connectivity of the network, the physical geometry of the blood vessels, and the input and output pressures. The values calculated for overall CBF and MAP as well as localized blood flow rates through key arteries and veins were reasonably similar to the values found in the literature. The model further demonstrated that a convective destruction model for the flow of caffeine through the cerebral vasculature can reasonably approximate the effects that caffeine consumption has on CBF. Ingestion of common amounts of caffeine can have profound effects on the hemodynamics of the cerebral vasculature. Most notably the vasoconstrictive effects of caffeine could lead to a self-induced hypoperfusive state. Acknowledgements: M. A. Adicott et. al., βThe Effect of Daily Caffeine Use on Cerebral Bloodflow: How Much is Too Much?β Human Brain Mapping, vol. 30, pp.3102β3114, 2009. M. Muller et. al., βHypertension and Longitudinal Changes in Cerebral Blood Flow: The SMART-MR Study,β Ann Neurol, vol. 71, pp. 825β833, 2012. L. P. Somogyi, βCafeeinee intake by the U. S. Population, Prepared for the Food and drug Administration, 2010. M. Zagzoule and J.P. Marc-Vergnest, βA Global Mathmatical Model if the Cerebral Circulation in Man,β Biomechanics, vol. 12, no. 12, pp.1015-1022, 1986. R. Newton et al., βPlasma and Salivary Pharmacokinetics of Caffeine in Man,β Eur J Clin Pharmacol, vol. 21, pp 4552, 1981 M. Lunt et al., βComparison of caffeine-induced changes in cerebral blood flow and middle cerebral artery blood velocity shows that caffeine reduces middle cerebral artery diameter,β Physiological Measurement, vol. 25, pp.467-474, 2004. K. Sato et. al., βThe Distribution of Blood Flow in the Carotid and Vertebral Arteries During Dynamic Exercises in Humans,β J Physiol, vol. 589, pp. 2847β2856, 2011. G. Ciuti et. al., βDifferences Between Internal Jugular Vein and Vertebral Vein Flow Examined in Real Time with the Use of Multigate Ultrasound Color Doppler,β AJNR, vol. 34, 2013.