Keywords: cerebrospinal fluid, pulsation, modelling.

Knowledge of basic hydrodynamic processes of the craniospinal compartment is important for treatment of patients suffering from illness which these hydrodynamics dependencies influence (head trauma, CSF resorption impairment). The function of the cerebrospinal fluid is not only protective but it is now known that CSF plays important role in the transportation of information substances (hormones, mediators, neuropeptides etc.), displacement of metabolic products of neurons as well as in temperature conduction.

The model of the craniospinal system was built up on an existing model of the cardiovascular system developed and described earlier. This model of the CVS contains baroreflex autoregulation and respiration activity. It is possible to change all parameters of the cardiovascular system. Volume pulsations of the cerebral arteries are transferred to the compartment representing brain and ventricular systems. Mathematically this transfer of pulsation is solved by linear coefficient. The ventricular system is connected with the compartment representing intracranial subarachnoidal spaces. This compartment is also connected with compartments representing arachnoidal granulations (therefore the majority of the CSF resorption is held here) and compartments representing individual segments of the spinal canal (it means the cervical, thoracic and lumbar segments). All compartments of the model contain physical properties: pressure, compliance, residual volume, forming/resorption of the CSF.

In the model of the CSF transportation is assumed by circulation of an uncompressible fluid in the elastic spaces of the craniospinal system. Changes of hydrodynamical variables in time (i.e. pressures, flows and volumes) must satisfy balances of mass and balances of momentum.

Cerebrospinal fluid fulfills subarachnoidal spaces and cerebral ventricles. Movements of the CSF are caused by the place where it is formed and its resorption and also by rhythmical movements of the vascular and cerebral compartment in the closed cavity of the cranium and spinal canal. During cardiac cycle blood volume and therefore cerebral volume periodically changes in contrast to continuous constant venous outflow from intracranium. Early systolic blood/brain volume increases must be compensated by the decrease of the intracranial CSF volume by rapid displacement of relatively large volume of the CSF to the cervical part of the spinal canal. This is possible because of higher compliance of the spinal canal due to the different structure of the epidural venous plexuses rather than the intracranial venous sinuses. It was published earlier that the cerebral tissue has also a high compliance because of the elastic vessels. But during cardiac systole compliance of the brain is exhausted and therefore these pulsations are transferred to the CSF. These pulsations of the pressure are called "cardiac related pulsations". Under physiological conditions the amplitude of these pulsations is maximally 5mmHg. The craniospinal system is also influenced by the respiratory movements which produce cyclic changes of the spinal canal volume. This modulation of cardic related pulsation is not visible during shallow breathing but is prominent during deep (forced) breathing.

Fitting of the model was performed to reach shape and amplitudes of the curves measured in humans during direct pressure measurements and MRI CSF flowmetry. By the proper coefficient gama adjustment of the volume pulsation transfer we created a generator of the volume and the pressure pulses in the craniospinal system. Pressure pulses in the craniospinal system are possible elicited only if the time constant (RC) of the whole system is tuned up to heart frequency range. Compliance of the craniospinal system is not linear, therefore in our model it is possible to adjust the nonlinear compliance for each compartment by adjusting its limits and exponencial coefficient alfa. The base level of the pressure is dependent on the outflow resistance, CSF production and resorption, and residual volumes of compartments. Resistances between compartments were chosen to reach an appropriate shape of the pressure and flow curves. In MRI CSF flowmetry is seen rapid early systolic caudal flow followed by slow diastolic cranial flow in craniocervical connection. This situation should be fitted only by adjusting compliance of the spinal canal two orders higher than intracranial compliance. By this adjustment we reached the same shape of flows and pressures.

The model presented for the cerebrospinal fluid transportation is able to simulate the physiological condition and model should be used for describing the physical properties of the system in physiological as well as for pathological situations.

Acknowledgement

This project was supported by grants No. 106/03/0958 and No. 106/03/0464 of the Czech Grant Agency.

1

A. Marmarou, K. Shulman, R. Rosende, A nonlinear analysis of the cerebrospinal fluid system and intracranial pressure dynamics, Journal of Neurosurgery, 48(3), 332-344, 1978. doi:10.3171/jns.1978.48.3.0332

2

Schroth G., Klose U., Cerebrospinal fluid flow. I - III. Physiology of cardiac-related pulsation. Neuroradiology, 35(1), 1-24, 1992. doi:10.1007/BF00588270

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