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From the Division of Anaesthesia and Intensive Care, Queen’s Medical Centre Campus, Nottingham University Hospitals, Nottingham, UK.
Address correspondence to Iain K. Moppett, Division of Anaesthesia and Intensive Care, Queen’s Medical Centre Campus, Nottingham University Hospitals, NG7 2UH, Nottingham, UK. Address e-mail to iain.moppett{at}nottingham.ac.uk.
Abstract
BACKGROUND: Various groups have constructed simulations and models of cerebral blood flow and oxygenation, each with its strengths and weaknesses. We describe the development and validation of a novel computational model, the Nottingham cerebral simulator (NCS), designed for experimental and teaching use.
METHODS: Physiological hypotheses were converted into differential equations; these are solved numerically with respect to time. A battery of tests was derived from published literature against which to test the simulation: static and dynamic autoregulation responses; carbon dioxide reactivity; brain tissue oxygenation. The NCS was programmed to simulate the methodologies of published experiments and the results of the simulation and the published data were compared.
RESULTS: The NCS results are qualitatively and quantitatively similar to published data. The values for regulatory indices were (published values in parentheses): index of autoregulation 0.9 (0.9); transient hyperemic response ratio 1.3 (1.3), carbon dioxide reactivity 2.4%–4.7% mm Hg–1 (2–4.5); brain tissue oxygen tension 22 mm Hg (20–100).
CONCLUSIONS: The NCS is a credible model of cerebral blood flow and oxygenation, which warrants further use as an experimental and teaching tool.
Abnormalities of cerebral blood flow (CBF) and oxygenation are common in patients requiring surgery or intensive care, commonly due to traumatic brain injury, cerebrovascular disease secondary to hypertension, atheroma, or diabetes, and intracranial hemorrhage. Although clinicians have had a basic understanding of the various physiological principles underlying CBF and metabolism for many years, the complexity of pathology, temporal changes, and nonlinear interactions has made simple mental constructs inadequate to explain clinical findings.
To improve this situation, various groups have constructed simulations or models of CBF and metabolism, each with its strengths and weaknesses (1–6). Many of these models are research tools written using mathematical modeling software without easily accessible user interfaces. This article describes the development of a computational model of CBF and oxygenation, the Nottingham cerebral simulator (NCS), which is scientifically robust and designed to be usable both as an experimental and teaching tool. An accompanying article describes its use for investigating this aspect of cerebral oxygenation adequacy (7).
METHODS
Model Development
The NCS uses a lumped-parameter, iterative approach to generate a time-dependent simulation of blood flow and metabolism. A full description of the modeling equations is given in the online supplementary material (please see supplementary material available at www.anesthesia-analgesia.org). Pertinent aspects of the compartments used, simulation of fluid flow, passive and regulatory behavior of the various compartments, nutrient and gas exchange, and parameter assignment are described below.
Compartments
The system to be modeled (brain, blood vessels, cerebrospinal fluid (CSF), cranium) is split conceptually into various connected compartments, each of which has its own patterns of behavior. These compartments represent the average behavior of their physiological correlates (e.g., proximal arterioles), but are not intended to replicate any single identifiable vessel or cell. There is a compromise between increasing anatomical and physical correlation (requiring more compartments), and verifiable modeling of behavior and realistic computational load (requiring less compartments). The Monroe–Kellie hypothesis (8) is a well known and relevant example of a simple, four-compartment, lumped-parameter model.
The model structure is based on the work of Ursino and Lodi (1), using a similar distribution of compartments and passive behavior of vessels. Mean arterial blood pressure (MAP) drives blood flow through two internal carotid arteries, which split into an anterior communicating artery (ACOM) and middle cerebral artery (MCA). Blood then flows through two arteriolar beds (A1 and A2) to the capillaries, where gas exchange and CSF formation occur. Venous outflow is through proximal veins, bridging veins with Starling resistor behavior and the venous sinuses, where CSF is reabsorbed through a one-way mechanism. Final efflux is via a fixed resistance into the internal jugular vein. The cerebral system is enclosed within a closed box of variable compliance.
Fluid Flow
For each compartment, time-dependent processes, such as fluid flow, are expressed as differential equations. Total fluid volume is conserved at the junction between each compartment. The differential equations are not directly solvable, and so an iterative approach [Euler or Runge–Kutta as appropriate (9)] is used. Using the single-step Euler method, each equation is calculated for a very short time interval (500 µs) on the basis of initial conditions, and resulting values after the full sequence of calculations is used to provide the starting values for the next iteration. The single-step Euler technique is used for simplicity, and provides adequate temporal resolution with the time-step of 500 µs, without either excessive computational burden or mathematical instability. The Runge–Kutta approach is a refinement of this approach calculating intermediate values to avoid mathematical instability. It is computationally more efficient but at the expense of less transparent code for the nonmathematician.
Compartment Behavior
The MCA is described as a pair of compliant vessels. On the basis of experimental data, the pressure–radius relationship is exponential, though the elasticity of the vessel is less than that used by Hayashi et al. (10) and Ursino and Lodi (1), in accordance with Aaslid et al.’s data (11). This MCA radius is used to calculate MCA flow velocity (FV), assuming laminar flow. A branching network (such as the prearteriolar MCA branches) is more compliant than a single vessel, and so a linear compliance relationship, more than that of the single vessel, is described for the MCA network (5,6).
The ACOM represents all collateral flow in the model, since the conductance of posterior vessels is relatively small. It is modeled as a simple tube with adjustable resistance (6).
Resistance arterioles are defined as proximal and distal on the basis of average size and regulatory behavior, but vessel walls are modeled the same way for both compartments. Vessels conform to the law of Laplace, with elastic and active tension present, and walls have an appreciable thickness, which allows modeling of transmural pressure gradients. The maximal active tension achievable is a nonlinear function of vessel radius, consistent with experimental data (1).
The proximal veins are described as Starling resistors, based on the experimental work of Piechnik et al. (12). The relative surface areas and conductances of the veins used in the model are based on estimates derived from Piechnik et al. (12).
The compliance of the cranium is described using a single exponential function in accordance with the Monroe–Kellie hypothesis (8), such that with normal brain, blood, and CSF volumes, compliance is low, and becomes lower as these volumes increase.
Regulatory Behavior
The proximal and distal arterioles are under various regulatory controls. These are CSF pH [derived from arterial Paco2 using the Henderson–Hasselbalch equation (13)], arterial oxygen content (CaO2), transvascular pressure (inflow pressure–outflow pressure) (proximal arterioles), and individual blood flow (distal arterioles).
Each of these factors is modeled as a simple linear gain function, such that the further away from a set-point the factor is, the greater the stimulus attributable to that factor. Following appropriate scaling, the individual stimuli are summed, and this total stimulus defines the active tension of the vessel (considering the maximal active tension achievable). The effect of stimulation is described mathematically as a Boltzmann function (9), which means that near the central point the relationship between stimulus and tension is approximately linear, but at very high or low stimulus values, maximum and minimum values of tension are reached, defining maximal and minimal vasoconstriction of the vessel.
In accordance with experimental data, the interaction between CSF pH and pressure and flow reactivity is not simply summative (14–16). Rather, low pH reduces the gain function of pressure and flow reactivity and high pH enhances it.
All of these regulatory processes are time-dependent, with time constants derived from experimental data (1). In accordance with published data, low CSF pH also prolongs the time constant of pressure and flow reactivity (11,17).
Nutrient and Metabolite Exchange
Oxygen carriage in blood is modeled as oxygen binding reversibly to hemoglobin with a small amount in solution. This is solved numerically using the Severinghaus approach (18), with coiteration of blood pH and carbon dioxide content and using a user-defined blood temperature, set at 37°C in all simulations. Blood carbon dioxide content is calculated using the Douglas equation (19) and pH by iterative solution of Henderson–Hasselbalch equations (13).
The intracellular consumption of oxygen is modeled using a quantitative model of glycolysis and oxidative phosphorylation derived from Rapoport et al. (20) and Aubert et al. (21). Of note, this model describes mitochondrial oxygen consumption as a function of Michaelis–Menten kinetics for intracellular oxygen tension and pyruvate concentration, inhibited by adenosine triphosphate.
Transport of oxygen between capillary and brain tissue is modeled as diffusion limited (based on Aubert et al.’s approach), with the capillary behaving as a Krogh cylinder (22), and the brain tissue behaving as an oxygen sink. The modeled brain oxygen tension is from the "lethal" corner: the midpoint between capillaries at their venous end. The approach to oxygen delivery described by Mintun et al. (23), with empirical terms for oxygen diffusibility and solubility, was used during development of the model, but was found to be inadequate at describing oxygen tension at low flow. The limitation of oxygen diffusion in the NCS is a function of increasing intercapillary distance and the ease of passage of oxygen through tissue. Therefore, end-capillary oxygen content is a function of arterial oxygen and carbon dioxide content, diffusion limitation of oxygen flux, and brain tissue oxygen consumption.
Parameter Assignment
Since the vascular wall behavior is based on Ursino and Lodi’s original model, the same constants (achieved by curve fitting available data) have been used as in their work (1), unless justified otherwise. The gain functions of regulatory behavior are, of necessity, arbitrary, as they reflect the observed capacity of the cerebrovascular system to maintain homeostasis. The parameters for behavior of the ACOM are based on values published by Piechnik et al. (5). Similarly, Aubert et al.’s published data are used for the oxygen modeling (21).
Computational Structure
The coding of the NCS was performed using object-orientated Pascal within Delphi 6® (Borland, Cupertino, CA) running under Microsoft Windows XP®. The hardware for all the experimentation was a Dell Inspiron 500 m, Pentium M 1.4 MHz (Dell, Round Rock, TX). The executable file has been used with Athlon Duron 1800, and Pentium 4 processors with indistinguishable results. The coding structure parallels that of the mathematical models. The front end of the NCS is a custom-designed series of windows allowing a user to view tables and graphs of output from the model, and to alter input variables (MAP, Paco2, intracranial compliance, etc.) for the model. The executable file is available from the following URL: www.nottingham.ac.uk/smss/school/anesthesia/models/NCS/NCS_AandA_13Mar07.exe.
Validation Tests
For the NCS to be credible, it should allow reproduction of clinically observed behavior across a broad spectrum of physiological changes. Therefore, a battery of tests with published data for reproducible tests of human cerebral vascular and metabolic behavior was designed and used.
Autoregulation
The static autoregulation (SAR) curve is widely reproduced in standard textbooks as a triphasic response. Pressure passive CBF exists below and above the lower and upper limits of autoregulation, respectively, and CBF is almost constant over a range of MAP between the limits of autoregulation (the autoregulatory plateau). Human data to support this are scarce, but what there are suggest a lower limit of autoregulation at MAPs of around 80 mm Hg and an upper limit of around 160 mm Hg (24). This is an over-simplification as several previous workers (1,24) have shown that pressure responsive behavior still occurs above and below these thresholds. Furthermore, the limits of autoregulation are not precise points but, rather, areas where the gradient of the pressure/flow relationship starts to change significantly.
Mathematically perfect autoregulation, with a plateau gradient of 0, is nonphysiological, but the efficiency of SAR can be measured, by assessing the change in CBF (or more commonly MCA FV) in response to pharmacologically induced changes in MAP. An index of SAR has been defined as:
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where cerebrovascular resistance is calculated as MAP/MCA FV.
For "perfect" autoregulation, SAR should be 1 (i.e., MCA FV does not change with change in MAP); impaired autoregulation is implied by an index of <0.4; >0.6 is normal (15,16). Hypercapnia impairs autoregulation and is associated with a reduction of SAR, whereas SAR becomes closer to one with moderate hypocapnia (15,16).
Dynamic Autoregulation
Dynamic autoregulation tests assess the change in CBF during rapid changes in cerebral perfusion pressure. The most commonly used tests are Aaslid et al.’s thigh cuff technique (25), and the transient hyperemic response test (THR) (26,27). The thigh cuff test measures both the speed and strength of autoregulation (SA). The THR test is influenced much more by the SA. The thigh cuff technique is prone to a substantial degree of variability, partly because it involves the mathematical matching of two recovery curves: MAP after sudden lower leg tourniquet release (which is dependent upon the systemic vascular behavior of the subject) and MCA FV (dependent upon autoregulatory mechanisms). Therefore, although the thigh cuff test is well used in clinical research, this test was not considered suitable for inclusion.
The THR test, first described by Giller (26) and refined by Mahajan et al. (27) has been used extensively in research and the clinical arena (28,29). The test involves a continuous record of the MCA FV. A brief compression (3–10 s) of the ipsilateral common carotid artery (CCA) is commenced, which results in a sudden reduction in the MCA FV and, presumably, perfusion pressure. This provokes vasodilatation (if autoregulation is intact) in the vascular bed distal to the MCA. Thus, a transient increase in the MCA FV is seen on release of the compression (27). Two autoregulatory indices have been described. The THR ratio (THRR) is the ratio between MCA FV after release of compression (F3) and MCA FV before onset of compression (F1).
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The SA is calculated by normalizing the THRR for changes in the MAP of the MCA at the onset of compression. This compensates for the variable degree of compression of the CCA and compensatory flow around the circle of Willis.
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P2 is the larger value of either the estimated MAP in the MCA at the onset of CCA compression, as calculated by P2 = MAP x F2/F1, or 60 mm Hg [lower limit of autoregulation used by Mahajan et al. (27)]. F3 is MCA FV immediately after onset of compression. The normal range in healthy volunteers is well defined as 0.88–1.12. SA and THRR should be reduced in the presence of hypercapnia (reflecting a loss of pressure regulation).
Carbon dioxide Reactivity
The static CBF response to changes in arterial carbon dioxide is well described, with a quasilinear relationship between Paco2 and MCA FV within 10–15 mm Hg of normal Paco2. The gradient of this relationship is approximately 3.3%–4.5% mm Hg–1 for hypercapnia and 2% mm Hg–1 for hypocapnia at a MAP of 100 mm Hg (30).
Oxygenation
Oxygen delivery remains approximately constant in the presence of anemia and hypoxia. Values for brain tissue oxygen tension (PbO2) in normal brain are scarce, with quoted ranges of 25–100 mm Hg (3.4–13.7 kPa). Data from animals suggest a normal value of around 25–30 mm Hg (3.5–4 kPa) (31).
Simulations
The NCS was configured to represent a normal, adult, human brain. SAR was assessed by increasing MAP by 5 mm Hg every 10 (physiological) minutes from 50 to 180 mm Hg with Paco2 40 mm Hg (5.3 kPa), and SaO2 0.98. The process was repeated in reverse to exclude any hysteresis effects. Calculated values of CBF, MCA FV, intercranial pressure (ICP), PbO2, and SjO2 were collected at the end of each time period. These simulations were repeated with Paco2 increased in increments of 7.6 mm Hg (1 kPa) from 33 to 55 mm Hg (4.3–7.3 kPa). The effect of reducing SaO2 from 1.0 to 0.8 in 1% steps was also examined.
THR tests were simulated by suddenly increasing the resistance of one CCA to complete occlusion for 10 s and then returning the resistance back to normal. MCA FV was recorded from the ipsilateral side and THRR and SA calculated as shown above.
RESULTS
The SAR curves for MCA FV and CBF are shown in Figure 1 (compared with pooled clinical data). Given the almost parallel relationship between MCA FV and CBF, subsequent figures use MCA FV because this is more commonly measured and reported in clinical practice.
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At normocapnia, the lower limit of SAR in the NCS is approximately 60 mm Hg; the upper limit is around 150 mm Hg. The slopes above the upper limit and below the lower limit are 1.48% and 1.37% mm Hg–1, respectively.
Values of SAR are shown in Table 1, with good agreement between the NCS and published data, both at normocapnia and with change in arterial carbon dioxide.
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The effects of changes in Paco2 on MCA FV and ICP are shown in Figures 2–4 (Table 2).
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Comparisons between NCS and clinical data for the THR test are shown in Figure 5. THRR at normotension and normocapnia is 1.45, which is within the published range. Hypercapnia diminishes this (1.24 at Paco2 48 mm Hg) and hypocapnia increases it (1.48 at Paco2 33 mm Hg). A parallel effect on the normalized value, SA, is also seen. Figures 6–8 demonstrate the relationship between MAP, PbO2, SaO2, and SjO2.
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The NCS compares favorably with published data for SAR and dynamic autoregulation, carbon dioxide reactivity, and oxygen reactivity.
SAR demonstrates the expected triphasic response to change in MAP, with the upper and lower limits of autoregulation close to published values. The SAR is at the lower end of the range of published values (14–16,33,38). Hypercapnia diminishes SAR capacity, as demonstrated by a modeled reduction in SAR, and hypocapnia augments it. This is consistent with published data (16,34). Dynamic autoregulation as assessed by the modeled THR test is in good agreement with published data for normocapnia and hypercapnia (27,28). Modeled cerebral reactivity to carbon dioxide and oxygen are similar to published data (31,35,37,38). The modeled effects of changes in MAP and Paco2 on ICP are clinically trivial for disease-free patients, and are consistent with the Monroe–Kellie hypothesis. Clinical data demonstrating the effect of Paco2 on ICP in the normal human brain are lacking, but even in patients with traumatic brain injury and intracranial hypertension, hyperventilation induces changes of around only 3 mm Hg (36). Data from healthy pigs demonstrate similar Paco2-induced changes in ICP (40). Clearly, the data here are described for normal intracranial compliance; the changes seen with decreased intracranial compliance will be larger, and include much more temporal instability.
The changes in jugular venous and brain tissue oxygenation are qualitatively similar to the available data (39,41). The lower PbO2 seen with Kiening et al.’s data probably reflects the pathological state of his patients as opposed to the normal physiology demonstrated here.
Does this provide credible validation of the NCS? Model validation relies on several aspects. First, the physiological assumptions underlying the model must be appropriate and plausible; these have been presented in this article. Clearly, although an attempt has been made to use a "bottom-up approach," creating physiological models, rather than fitting data to match published values, there are layers of complexity left unexplored in the modeling assumptions, particularly with regard to the mechanisms of vasoreactivity. At a macroscopic level, we consider that the assumptions upon which the NCS is built are plausible.
There is inevitably a compromise in any model between pathophysiological fidelity, amenity to validation and practical utility (42). The NCS uses a lumped parameter approach, which means that heterogeneity is reduced, such as may be seen between gray and white matter or between different regions of the brain. At this stage of model development, this is an area for future work, but we do not feel it renders the model invalid. Most measures of CBF and metabolism, used clinically, are essentially global (transcranial Doppler, CBF, ICP, SjO2), and so simulating the average effects on these seems reasonable. For more localized measures (PbO2), the effects of pathophysiological changes can be modeled at hemispheric level, such that one side behaves differently to another, so that the qualitative effects can be demonstrated. Work to increase the spatial resolution of the model is in progress, and will be informed by the increasing body of positron emission tomography data. The construction of the model does mean that localized changes can be observed. As currently configured, the NCS does not simulate true three-dimensional behavior, in terms of gross anatomical behavior (e.g., tentorial herniation) or localizing a contusion to a particular volume of the model. However, there is some degree of spatial behavior. (a) The global pressure changes (e.g., ICP) which may be largely due to one area of the "brain" affect the whole model; (b) local changes in vascular resistance will affect the flow through parallel vessel beds (e.g., affecting MCA FV); (c) local changes in oxygenation affect global measures (e.g., SjO2). The degree to which local changes affect global measures is a function of the relative size of the volume affected. This independence of response is demonstrated here by the THR test, which invokes vasodilatation in only the hemisphere ipsilateral to the carotid compression.
Second, the results produced by the model should be consistent with empirical data. Within the confines of the experiments performed here, the NCS appears consistent with published data.
The effects of carbon dioxide on the SAR curve are difficult to interpret. Many of the data referring to changes in slope and position have been based on aggregation of a few data points from multiple individual subjects rather than full curves for each subject. [For a fuller review, see Panerai (32).] Therefore, it is impossible to say with confidence exactly what the NCS should match. The reduction in SAR reported with modest hypercapnia may partly reflect the shift of the autoregulation curve to the right, such that SAR is tested near the lower limit of autoregulation (37), though a change in the gradient of the plateau probably does exist (35). Hypotension reduces carbon dioxide reactivity in the NCS, which is consistent with clinical data (14,43), while there is a modest increase in carbon dioxide reactivity with hypertension (34,38). It is unclear from the literature what happens with marked hypercapnia and hypertension. Ursino and Lodi (1), in their modeling, generated FV–MAP relationships that converged at higher MAP, with a right-shift of the upper limit of autoregulation. This implies that hypercapnia just shifts the set-point for pressure and flow regulation, and sufficient vasoconstrictive stimulus will overcome this. The consensus view in the literature is that maximal vasodilation (probably from any cause) can prevent vasoconstriction, and thus marked hypercapnia would be expected to cause a left shift of the upper limit of autoregulation. With modest hypercapnia both of these effects may be evident, such that it is not possible to be certain whether the upper limit of autoregulation shifts right, left or at all. The NCS shows a right shift with modest hypercapnia, and a left shift with more marked changes.
As discussed previously, such data should, ideally, be matched in a blinded fashion. However, in practice, validation is part of the process of calibration of the model. In practical terms, the more complex the model, the less the prior knowledge of data becomes an issue. Altering values significantly in order to achieve one specific set of results is likely to lead to movement of model output away from desired values elsewhere within the model.
Third, validation should define the "model space" wherein reasonable confidence can be placed in the model. This does not necessarily mean that only those results directly tested can be viewed as valid. For instance, the correlation indices of autoregulation (e.g., pressure and oxygen reactivity indices) have not been directly validated here, but given that the processes governing them are all part of this more formal testing, it would seem reasonable to assume that results from those tests are likely to be valid as well. The battery of tests presented here is derived from published data, and so may provide a useful starting point for other researchers to publish the validation of their simulations. Validation of a complex, integrated, and multiscalar model such as the NCS can never be complete. Ultimately, the NCS is a model, not reality, so the question to be asked of the model is whether it is fit-for-purpose: does it produce the expected results and are the processes for producing these results plausible?
As models develop, more confidence in results can be expected, and the model space will become larger. On the basis of the results presented here, it would seem reasonable to use the NCS to investigate cerebral pathophysiology further. In the future, where possible, specific validation will be performed against the area to be studied.
No cerebrovascular model can be claimed as being completely novel, and this work builds on the work of Ursino and Lodi (1), Hardman et al. (44), Aubert et al. (21), and the Cambridge group (4,5,12), to create an integrated model, which incorporates plausible and published modeling techniques. Jung et al. (3) have published a compartmental model investigating the interaction between autoregulation and brain tissue oxygenation. The NCS uses a more physiological treatment of oxygen delivery to tissue, with cerebral metabolic rate for oxygen dependent upon oxygen availability, and oxygen carriage dependent upon blood pH, Pco2, and temperature. We believe that much of the novelty of the model comes from combining the various models previously presented, such that each is exposed to the output of the others. Such an approach involves ensuring that artificial oscillatory, positive-feedback, or divergent-feedback loops are not created. In addition, as detailed in the supplementary material, we have made some minor modifications to the models where we feel this is appropriate.
There are several advantages of this model. First, it is transparent with testable and plausible models of physiological function. These models are presented in full in the supplementary information for this article. Alternative techniques of modeling (2,45) use transfer function approaches to define the system behavior as a whole, without necessarily attempting to correlate this with particular physiological or anatomical constructs. Such models undoubtedly work and may be of benefit in predicting the dynamic response to clinical changes; but they may be less helpful in elucidating underlying mechanisms. Second, it is modular, such that each individual component can be run and tested separately. For instance, modeling of oxygen flux is completely separate from a computational standpoint. The model can therefore be run with this aspect switched on or off. Conversely, the developer can test the oxygen flux model separately from other aspects of the model. Thus, existing, discrete, published models have been integrated into a single model: Ursino and Lodi’s model of vascular behavior (1), the Cambridge approach to venous behavior and regulatory asymmetry (4,5,12), Aubert et al.’s cell level oxygen and glucose metabolism (21) and aspects of transcapillary gas exchange (44). Third, the model has a custom-designed user interface and can be run on any reasonably powerful personal computer. The user can change, within physiological limits, most of the clinically relevant variables (MAP, Paco2, SaO2, intracranial compliance, etc.) and directly observe the time-dependent response to these values. The executable file is available from the following URL: www.nottingham.ac.uk/smss/school/anesthesia/models/NCS/NCS_AandA_13Mar07.exe. The design of the NCS means that it can be used for several purposes. As an experimental tool, the NCS can be used to simulate specific pathophysiological states in a quantitative fashion, based on individual or pooled clinical data. With such a virtual patient, without ethical or physiological constraints, it is possible to generate and refine novel hypotheses before clinical trials and, possibly, to predict responses to treatment. Similarly, such virtual patients provide a validated teaching tool, such that teachers and students can have confidence that the pathophysiological effects seen are clinically credible.
In summary, the physiological models underlying the NCS have been presented, and the NCS has been demonstrated to compare favorably against published clinical data. The further use of the NCS as an experimental and teaching tool is warranted.
Footnotes
This article has supplementary material on the Web site: www.anesthesia-analgesia.org.
Accepted for publication July 5, 2007.
Reprints will not be available from the author.
REFERENCES
This article has been cited by other articles:
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  I. K. Moppett and J. G. Hardman Modeling the Causes of Variation in Brain Tissue Oxygenation Anesth. Analg., October 1, 2007; 105(4): 1104 - 1112. [Abstract] [Full Text] [PDF]
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; Cerebral blood flow (NCS): 
. The pooled clinical curve for MCA FV (normalized to 60 cm/s for mean arterial blood pressure 100 mm Hg) is derived from various sources collated by Panerai (
). Static index of autoregulation is 0.9 and lower and upper pressure passive gradients are 1.5% and 3.2% baseline mm Hg–1, respectively.
