Intracranial Pressure Increment Using an Electrical Circuit Model of Cerebral Circulation - Report Example

Name Course Institution Instructor DATE A Simulation Study of Intracranial Pressure Increment Using an Electrical Circuit Model of Cerebral Circulation An electrical circuit model of the cerebral circulation is design to simulate the changes in the intracranial pressure (ICP) and the cerebral blood volume (CBV) by use of a small signal approximation using the palatial component. The results obtained will show changes in pulsatile wave of ICP. The increase of ICP influences not only the intracranial compliance but may also influence the resistances of the arteries and veins. Therefore, the simulation of ICPPW and CBVPW is used to investigate the effects of changes of the arterial and venous resistances on the vascular flow, as well as to estimate the effect of the intracranial compliance. With regard to the CBV, the modeling results are useful for application to rheoencephalography (REG) using electrical impedance method for noninvasive ICP monitoring. The model explains the physiological strong coupling in intracranial pressure cerebral blood volume (CBV), cerebrospinal fluid dynamics, and the action of cerebral blood-flow (CBF) regulatory mechanisms are examine. The shape of the cranial volume-pressure curve is explained by changes in the venous bed caused by various degrees of collapse and/or distension. The model allows experimental results on cerebral vessel dilatation and cerebral blood-flow regulation, following cerebral perfusion pressure decrease, to be satisfactorily reproduced. Moreover, the effect of cerebral blood volume changes induced by autoregulatory adjustments on the intracranial pressure time pattern can be examined at different levels of arterial hypotension. Introduction The cerebral vascular bed was represented by a single arterial compartment and two venous compartments in series. The lumped parameter formulation for the vascular compartments was derived from a one-dimensional theory of flow in collapsible tubes. It was assumed in the model that the cranial volume is constant. The results show that most of the additional volume of cerebrospinal fluid Cerebral blood flow depends upon the perfusion pressure and the vascular resistance. The blood flow can be expressed as being directly proportional to the perfusion and inversely proportional to the vascular resistance. The change in blood pressure in the arteries is caused by the heart which pumps blood from its left ventricle into the aorta, vessel resistance arises from friction which in turn is dependent upon the blood viscosity and inversely on the vascular area. Therefore blood flow tends to be slowest in the small vessels of the capillary bed, thus allowing time for the exchange of oxygen to surrounding tissues by means of diffusion though the capillary walls. Although these models provided an efficient structure for simplifying the otherwise complex anatomic structures of the coupled CBF and CSF circulatory systems, they are passive models lacking specifications of how the model parameters such as resistance of blood flow should change with state variables Material and methods An Astable circuit is used as a pulse generator. It produces a square wave: a digital waveform with sharp transitions between low (0V) and high (+Vs). It is called Astable because the output keeps changing from low to high. 555 circuit with value R1 =10k and R2 =100k, C1 =.01uF The time period (T) of the square wave is the time for one complete cycle, but it is usually better to consider frequency (f) which is the number of cycles per second. T   = time period in seconds (s) f    = frequency in hertz (Hz) R1 = resistance in ohms () R2 = resistance in ohms () C1 = capacitance in farads (F) The time period can be split into two parts: T = Tm + Ts Mark time (output high): Tm = 0.7 × (R1 + R2) × C1 Space time (output low): Ts = 0.7 × R2 × C1 A diode has been added in parallel with R2 in order to achieve a duty cycle of less than 50%. This passes R2 during the charging part of the cycle so that Tm depends only on R1 and C1 Tm = 0.7 × R1 × C1   (ignoring 0.7V across diode) Ts = 0.7 × R2 × C1   (unchanged) Therefore, Tm = 0.7 × 10 × 103 × 0.01 × 10-6 = 7 × 10-5s Ts = 0.7 × 10 × 0.01 × 10-6 = 7 × 10-8s Duty cycle with diode  = Tm = R1 Tm + Ts R1 + R2 Duty cycle with diode  = 10k = 0.09 10k + 100k The 555 timer generate a signal and the out put from it is used as an input to the circuit below. Schematic diagram of cerebral circulation Based on the diagram Schematic diagram of the cerebral circulation shown above a simple electrical circuit model of the cerebral circulation shown below is obtained. This is the electrical equivalent circuit of a cerebral blood flow (CBF) and CSF circulation model. To simplify the model, elements of the cerebral blood vessels are treated as passive elements of C, R etc. The upper figure defines the model parameters and the lower figure shows the auto regulatory relationship between vascular resistance (CVR) and CPP. Ao = arterial blood pressure; A = arterial pressure in basal cerebral arteries; B = cerebral venous pressure; D = intracranial pressure; Ca = compliance of arterial bed; Cv = compliance of venous bed. If = CSF formation rate; RCSF = CSF reabsorption; Rb = resistance of bridging veins; Ra = resistance of basal arteries; CVR = main cerebrovascular resistance. TABLE II DEGREES OF ICP AND THE INTRACRANIAL COMPLIANCE Hydrodynamic Electrical Pressure (mmHg) Voltage (V) Flow (Kl/sec) Current (A) Viscous drag (mmHg sec/Kl) Resistance (Ω) Compliance (Kl/mmHg) Capacitance (q/V) Volume (Kl) Charge (q) (Kl=kiloliter) Results Compliance which is represented by the capacitance is defined as the ratio of the increase of volume to the increase of pressure. Since the materials determining the compliance of the vessels of the cerebro-vascular system are not well known, the values of Ca, Ck, and Cv are estimated from pressure-volume curves of the arterial and venous systems of the systemic circulation. The figure below shows the waveform at each point of the circuit for normal ICP. Normal 2.1 farads 1.jpg THE CAPACITOR USED FOR (Cb) HAD A VALUE OF 2.1microFarads Increasing mode .33 farads 2.jpg the capacitor (Cb) had a value of .33 micro Farads and represent the increasing section. Formulae for deriving the pressure volume index (PVI), volume pressure response (VPR) and the CSF outflow resistance (Ro) where Po is the baseline CSF pressure, Pp is the peak pressure resulting from a bolus volume injection Vo and P2 refers to the pressure point on the return trajectory at time T2 (usually selected at 2 min post injection). ICP = formation rate _ outflow resistance + venous pressure. Discussion The discussion is based on the table below of different conditions of the simulation. TABLE ANALOGY OF HYDRODYNAMICAL AND ELECTRICAL SYSTEMS degree ICP ICP (mmHg) Compliance (ml/mmHg) Cb (μF) Normal 05 - 15.0. 2.22 - 0.72 2.22 - 0.72 Increasing Moderately 30 -50 0.36 - 0.72 0.36 - 0.72 Increasing severely >50 Read More