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Noninvasive detection of intracranial hypertension using a simplified intracranial hemo and hydrodynamics model
BioMedical Engineering OnLine volumeÂ 14, ArticleÂ number:Â 51 (2015)
Abstract
Background
Monitoring of intracranial pressure (ICP) is highly important for detecting abnormal brain conditions such as intracranial hemorrhage, cerebral edema, or brain tumor. Until now, the monitoring of ICP requires an invasive method which has many disadvantages including the risk of infections, hemorrhage, or brain herniation. Therefore, many noninvasive methods have been proposed for estimating ICP. However, these methods are still insufficient to estimate sudden increases in ICP.
Methods
We proposed a simplified intracranial hemo and hydrodynamics model that consisted of two simple resistance circuits. From this proposed model, we designed an ICP estimation algorithm to trace ICP changes. First, we performed a simulation based on the original Ursino model with the real arterial blood pressure to investigate our proposed approach. We subsequently applied it to experimental data that were measured during the Valsalva maneuver (VM) and resting state, respectively.
Results
Simulation result revealed a small root mean square error (RMSE) between the estimated ICP by our approach and the reference ICP derived from the original Ursino model. Compared to the pulsatility index (PI) based approach and Kashifâ€™s model, our proposed method showed more statistically significant difference between VM and resting state.
Conclusion
Our proposed method successfully tracked sudden ICP increases. Therefore, our method may serve as a suitable tool for noninvasive ICP monitoring.
Background
Intracranial pressure (ICP) is the pressure inside the cranium that exerts on the neural tissue and cerebrospinal fluid (CSF). Normal range of mean ICP for a healthy subject in supine position is 5â€“15Â mmHg [1]. However, ICP can be elevated remarkably due to variety of intracranial pathologies such as intracranial hemorrhage, cerebral edema, brain tumor, etc. According to the Monroâ€“Kelli hypothesis, as ICP increases, cerebral perfusion pressure correspondingly decreases [2]. Therefore, increased ICP may cause ischemic stroke, neural damage, and even brain death. For this reason, monitoring of ICP is essential for preventing secondary brain damage. Currently, ICP monitoring is frequently considered for patients with severe brain injuries, cerebrovascular accidents, hydrocephalus, hypoxic brain injuries, central nervous system infections, and fulminant hepatic failures [3â€“5].
For direct ICP monitoring, an invasive surgical procedure involving drilling a burr hole in the skull for injection of a catheter is necessary. Therefore, invasive ICP monitoring methods have many disadvantages including the risk of infections and hemorrhage [6], highcost of surgical procedures, and the need for a trained neurosurgeon. Since many limitations of invasive ICP monitoring can make measuring the ICP difficult, noninvasive methods have been proposed to estimate ICP using related physiological variables [7â€“9]. However, previously proposed methods do not provide sufficiently accurate ICP values. Thus, they are not appropriate tools for routine general clinical use.
Recently, many researchers frequently used pulsatility index (PI) for estimating ICP noninvasively [10â€“12]. Measured cerebral blood flow velocity (CBFv) from transcranial Doppler (TCD) is known to be strongly related to ICP [11]. The PI can be calculated easily using the CBFv. The PI derived from CBFv is a useful indicator for identifying patients with raised ICP. Moreover, the mean deviation between the PIbased ICP value and invasively measured ICP was 4.2Â mmHg [13], indicating that PI based approach is clinically acceptable. However, PI based approach did not consider various factors except CBFv. Therefore, if the sudden increase in ICP does not affect the waveform of CBFv, we are unable to detect a sudden and developing intracranial hypertension [14]. Some noninvasive ICP methods used the morphological clustering algorithms to estimate the ICP value from TCD measurements of CBFv waveform [15, 16]. To generate the ICP estimate, the kernel regression mapping which is derived from morphological features from TCD based CBFv is necessary [16]. However, this method could not explain adequately the underlying mechanistic model. Furthermore, to get more accurate ICP estimates, the morphological approach needs many number of training set on a reference population.
On the other hand, many cerebral hemodynamics models, adaptable to noninvasive ICP estimation, have been reported so far. Ursino proposed hemo and hydrodynamic models about CSF fluid dynamics in 1988 [17, 18]. Later, the reduced Ursino model was reported using a simpler mathematical model [19]. This model identifies interactions among ICP, cerebral blood volume, and autoregulation. Especially, it has been shown to be efficient in providing cerebral autoregulation. However, this model still has a mathematically complex formula, which involves fitting model parameters such as the bridging vein resistance, and intracranial elastic coefficient.
Recently, Kashif et al. proposed a very simple hemodynamics model for noninvasive ICP monitoring by using the CBFv and arterial blood pressure (ABP) [20]. Their modelbased approximation of the ICP estimated some model parameters including intracranial resistance, and elastic coefficient through a physiological model of cerebrovascular dynamics. Kashif method seemed to be successful in tracking ICP changes. Nonetheless, this estimation algorithm may be unsuitable to respond to sudden increases in ICP because of the very long time window (60Â s).
In the current paper, we will propose a simplified intracranial hemo and hydrodynamics model for the detection of intracranial hypertension in real time. Our method does not need to estimate compliance parameters but only considers resistance parameters, thereby establishing a simpler intracranial hemo and hydrodynamics model compared to existing other models. Using our proposed model, we designed an ICP estimator with the direct current (DC) trends of ABP and CBFv as inputs. To verify the proposed method, we constructed the simulation cerebral blood flow (CBF) signal using the original Ursino model with a real ABP. We subsequently estimated the ICP using our proposed method from the ABP and simulation CBF. Finally, our method and two noninvasive ICP estimation approaches were applied to experimental data which consisted of ABP and CBFv. To assess the performances of the methods, we conducted test for the detection of sudden ICP change caused by Valsalva maneuver (VM). Since VM raises intrathoracic pressure which significantly affects systemic and cerebral circulation, ICP also suddenly increases during VM [21]. Therefore, VM phase can be regarded as intracranial hypertension state. Moreover, we compared the ICP estimation performance of our method with that of the PI method and Kashif method. To identify the discriminability about sudden increases in ICP during VM (intracranial hypertension state), statistical test was performed. We will show that our method has better detecting performance about sudden change of ICP than the PI method and Kashif method.
Methods
Pulsatility index based approach
Despite the close ICP estimation using the PI, it is unable to detect the absolute ICP level. PI based on the Gosling formula, and conventionally applied to a single beat, can also be used to monitor beattobeat changes. Given one pulse, PI is as follows:
where CBFv_{systolic}, CBFv_{diastolic}, and CBFv_{mean} represent the peak systolic velocity, the enddiastolic velocity, and the mean velocity for CBF, respectively. Since the PI is derived from the waveform of one pulse, the PI must be updated at the next pulse. The ICP can be estimated by a linear regression of the PI [11]. In order to estimate the ICP from the PI, we adopt the linear regression equations as follows,
where, a and b represent the regression coefficients. We utilized the values of the previous study [12] as the regression coefficients of Eq.Â (2). Additionally, we added some offset value to the regression coefficients in order to compensate for the gap between the estimated value and normal ranges of ICP (5â€“15Â mmHg). As a result, 5.305 and 4 were assigned to regression coefficients a and b, respectively.
In this study, we will refer to the ICP estimation approach based on the linear regression of the PI as the â€śPI methodâ€ť. In order to compare the performance of the PI method with that of our method, the estimated ICP was utilized.
Kashif method
Since radial ABP and ABP at middle cerebral artery (MCA) have different systolic upstroke time, an additional timeshift is needed for using the Kashifâ€™s simplified model (see FigureÂ 1). To find the timeshift Ď„, one should detect peaks of CBFv and ABP waveform within each beat. ABP at MCA can obtain as follow:
where P_{MCA} is the middle cerebral artery pressure, P_{r} is radial ABP, and Ď„ is the timeshift.
FigureÂ 1 illustrates the hemodynamics circuit of Kashifâ€™s simplified model. Q_{CBF} is CBFv and P_{ic}Â is ICP. The algorithm is assumed to be constant at mean ICP value over the estimation window. From this assumption, Q_{CBF} can be expressed with parameters R_{a} and C_{a} which represent resistance and compliance of intracranial artery:
To estimate ICP value, the algorithm follows two steps: First, the compliance parameter C_{a} is estimated, and then, the estimate of C_{a} is used to estimate R_{a} in the Kashifâ€™s simplified model. The second step is the estimation of ICP. The ICP estimation algorithm with Kashifâ€™s simplified model is briefly described as follows.

1.
ABP and CBFv are annotated for beat onsets. Here CBFv is assumed to be proportional to CBF [20].

2.
Parameters C_{a} and R_{a} are estimated within each one beat. Since most Q_{CBF} pass the compliance branch during the sharp transitions in P_{MCA}, the model can be simplified to a capacitoronly branch. Thus parameter C_{a} can be estimated. After obtaining the estimate of C_{a}, the estimate of CBF \({\hat{\text{Q}}}_{\text{CBF}}\) is obtained, and then we can estimate parameter R_{a} using two timeinstants of ABP and \({\hat{\text{Q}}}_{\text{CBF}}\). Estimation process of two parameters C_{a} and R_{a} are detailed in [20].

3.
The estimate of R_{a} is then substituted into the following Eq.Â (5), and an ICP estimate can be obtained for the given one cycle.
Proposed method: simple resistance model and simple resistance method
Many mathematical models have been utilized to estimate hidden health states such as ABP and ICP. Specifically, Ursinoâ€™s hemo and hydrodynamics model was the cornerstone of the modelbased ICP estimation field [18]. In this section, we will present a novel model, which was developed as a modification of the original Ursino model [18] and an ICP estimation algorithm based on the novel model. For the sake of simplicity, we will refer to the simplified model as the â€śSR modelâ€ť (simple resistance model) and our ICP estimation algorithm as the â€śSR methodâ€ť.
The SR model is derived from the original Ursino model [18]. FigureÂ 2 shows the simplification steps. First, we only consider the DC component of the ABP, which is the input of the original Ursino model. We can ignore the compliances in the original Ursino model, because the compliances have infinite impedance when the input is DC. From this step, we can get the resistance model without compliances. Next, we extract two simple circuits from the resistance model and we refer to them as the â€śSR modelâ€ť. The first circuit of the SR model is the intracranial hemodynamics model extending from the intracranial arteries to the capillaries, and the other circuit represents the intracranial hydrodynamics model.
Based on the SR model, the SR method was designed to estimate the ICP through a series of three processes (see FigureÂ 3). The first process involves low pass filtering (0.2Â Hz). Since the SR model considers only DC components, it is necessary to suppress the alternating current (AC) components of the ABP and CBFv. The next process involves capillary pressure estimation from the ABP and the CBF by using the first circuit of the SR model as follows:
where, P_{c} and P_{a} represent the capillary pressure and ABP, respectively. R_{a} represents the resistance of intracranial arteries and the Q_{CBF} indicates the CBF. In the last step, the ICP is calculated from the estimated capillary pressure and the second circuit of the SR model as follows:
where, P_{ic} and P_{vs} represent the ICP and venous sinus pressure, respectively. R_{f} and R_{o} represent resistances of CSF formation and outflow, respectively. EquationÂ (7) has the same meaning of the linear interpolation between the P_{c} and P_{vs}. We set the values of R_{a}, P_{vs}, R_{f}, and R_{o} according to one reference [18, 19]: R_{a}Â =Â 6Â mmHgÂ s/ml, P_{vs}Â =Â 6Â mmHg, R_{f}Â =Â 2,380Â mmHgÂ s/ml, and R_{o}Â =Â 523Â mmHgÂ s/ml.
One of the input data of the SR method is the CBF. Although it is difficult to measure CBF directly, the CBFv is approximately proportional to CBF [18]. Hence, we calculate the CBF by the proportional value of the CBFv as follows,
where Î± represents the proportional factor. We chose 0.15 as the value of Î± because CBF is about 11.67Â ml/s and CBFv is usually from 70 to 80Â cm/s for healthy people [22]. As a result, ICP can be simply estimated from low pass filtered ABP and CBFv using the SR method. The total process is depicted on FigureÂ 3.
Data
Since previous study already showed that peripheral and central mean ABPs was interchangeable [23], the SR method utilized DC trend of peripheral ABP from the index finger as the input. Furthermore, some methods also used noninvasively measured peripheral ABP for estimating ICP [16, 20]. Therefore, as the inputs of our method, ABP was measured from the left hand index finger using the NIBP100 (Biopac Systems, Inc., Santa Barbara, CA, USA). The system employed a tonometric technique that has been previously validated, which measured intraarterial pulse pressure [24]. CBFv was measured at the MCA via EZDop^{Â®} (DWL, Compumedics Germany GmbH, Singen, Germany) TCD ultrasound device. The waveform of ABP and CBFv are simultaneously collected by MP100 system (Biopac Systems, Inc., Santa Barbara, CA, USA) with 1Â kÂ Hz sampling frequency, respectively. Since it was known that ICP level was increased by the effect of a VM [21], the ICP tracking performance could be assessed by detecting a VM (intracranial hypertension state) when a subject alternately takes a rest and a VM. FigureÂ 4 represents the total 45s experimental protocol. A subject took a rest during the first 15Â s and then performed a VM during the next 15Â s. After that, the subject had a rest for 15Â s. To remove the uncertain states in each trial, we did not use the initial 5Â s of VM phase and 10Â s of later rest phase as indicated in FigureÂ 4. Eight healthy people (age, 29Â Â±Â 4; weight, 63.5Â Â±Â 9Â kg) participated in this experiment and each subject performed 20 trials in total. We informed the participants about the experimental procedures and potential risks. Written informed consents were obtained from all the subjects. The institutional review board (IRB) of the Gwangju Institute of Science and Technology approved all procedures and protocols in this study.
Results
Simulation
In order to verify the validity of the SR model and method, we performed a simulation based on the original Ursino model in MATLAB^{Â®} Simulink. As can be seen in FigureÂ 5, we simulated the equivalent circuit for the original Ursino model and utilized the real ABP data of the PhysioNet database [25] as the input of the circuit. We obtained simulated CBF and ICP data from the computer simulation. With the given real ABP and simulation CBF, we estimated ICP using the SR method, and it was compared with the simulation ICP (see FigureÂ 6). We calculated root mean square errors (RMSEs) between the estimated ICP and the simulation ICP for twenty data sets. The mean of RMSE for all simulation data was 1.36Â mmHg with a standard deviation of 0.2Â mmHg. That is, even though the SR model greatly simplifies the original Ursino model, the SR method shows high tracking performance for the ICP generated from the original Ursino model. For reference, model parameters of the original Ursino model are set to the appropriate values explained in [18, 19] in detail (see TableÂ 1).
Human subject experiment
In order to evaluate the SR method using human experimental data, we conducted the noninvasive detection of the intracranial hypertension phase using ABP measured from the left index finger and CBFv from the left MCA. The results of the noninvasively estimated ICP are shown in FigureÂ 7. The third row (c) in FigureÂ 7 reveals how our method can rapidly track increased ICP by VM. The fourth row (d) depicts the performance of Kashif method. It can react to the ICP elevation but its estimate is lagged. On the other hand, the bottom row (e) indicates that the PI cannot reflect the change at the VM phase well. Moreover, we computed the mean ICP value for resting and VM state using estimated ICP at each trial. The mean values for all trials are shown in FigureÂ 8 and we can see the difference of distribution among the SR method, the Kashif method, and the PI method. TableÂ 2 shows the mean and standard deviation values for resting and VM state. To verify the detection performance for ICP elevation, the onetailed paired t test was used between resting and VM state for each subject. When the result show the significant difference (pÂ <Â 0.05) between two phases for each subject, it is marked on TableÂ 2 with an asterisk. As a result, the PI method could not estimate ICP increase at VM state and the Kashif method was insufficient, while the SR method well tracked sudden increases in ICP at VM state.
Discussion
For estimating the ICP, we proposed the SR model consisting of two simple circuits utilizing intracranial hemo and hydrodynamics that tracks ICP changes accurately using two input signals (CBFv and ABP). The SR method was verified by simulation using the PhysioBank data [25]. Since the data did not include measured CBFv data, we generated simulation CBF and ICP signal using the original Ursino model, and then used simulation CBF and real ABP as input data for the SR method. To assess the performance of our proposed method, we used RMSE between estimated ICP and simulation ICP generated by the original Ursino model. The SR method showed a mean RMSE of 1.36Â mmHg, suggesting that this method can track ICP variation accurately. Although, the SR method is more simplified model than the original Ursino model, its ICP estimate was not significantly different with that of original Ursino model.
PI method has been widely used to estimate ICP noninvasively [10â€“12]. However, in this study, the limitation of PI was shown in terms of the ability of VM detection using human subject data. Real ABP and CBFv waveforms tend to rapidly change with VM. We assumed that real ICP would suddenly increase during the VM phase [21]. We confirmed that the estimated ICP using the SR method was elevated during the VM phase. Moreover, we showed the performance of detecting ICP changes using the statistical test. The SR method showed statistically significant differences between resting and VM state. However PI method could not show the differences because ICP elevation was not estimated during the VM phase. In other words, the SR method could successfully track ICP on the VM phase (intracranial hypertension) compared to the PI method. This is because PI was derived only from CBFv. If ICP was suddenly increased, CBFv could not always reflect ICP because higher ICP was also associated with several other physiological conditions such as ABP or PCO_{2} [26, 27]. Taken together, the PI method could not track the rapid change in ICP during intracranial hypertension caused by VM.
Recently, Kashif et al. also proposed new simplified model for estimating ICP [20]. In our human subject experiment, the Kashif method showed significant difference only for half of the subjects. This result suggested that the Kashif method could show better performance of ICP tracking than the PI method. However, their model estimates both resistance and compliance terms from the CBFv and ABP morphology, within the window. If CBFv and ABP are changing the level abruptly, it will be difficult to estimate these terms. Furthermore, since they calculate the ICP within a long window (60Â s), their method is not appropriate for detecting abrupt ICP changes. On the other hand, as shown in experiment results, the SR method could detect sudden increases in ICP by VM. Furthermore, because the SR method only considers the DC components and the resistance term without compliance term, it has strong points not only for the robustness to the motion artifacts, but also in the design of the adaptive algorithm for the model parameters (R_{a} and C_{a} in FigureÂ 1) that are regulated by cerebral autoregulation mechanisms.
Our investigation was to assess the feasibility of the SR method. However, in this study, we did not evaluate the SR method using the invasively measured ICP. Despite of this limitation, as shown in the results, the SR method could show sufficient performance to respond to abrupt changes in ICP immediately compared to other methods. In the near future, we have a plan to improve our proposed method using the invasively measured ICP in cooperation with a general hospital of Korea.
Conclusions
In this study, we proposed a simple hemoand hydrodynamics model (SR method) to estimate ICP noninvasively. We showed the SR method could successfully track sudden increases in ICP compared to two other methods (the PI method and the Kashif method). Accordingly, the present study suggests that our proposed method may be a great tool for monitoring rapid changes in ICP noninvasively and it would help patients with regulating ICP within the appropriate range.
Abbreviations
 ICP:

intracranial pressure
 CSF:

cerebrospinal fluid
 CBF:

cerebral blood flow
 CBFv:

cerebral blood flow velocity
 ABP:

arterial blood pressure
 PI:

pulsatility index
 TCD:

transcranial Doppler
 VM:

Valsalva maneuver
 SR:

simple resistance
 DC:

direct current
 AC:

alternating current
 IRB:

institutional review board
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Authorsâ€™ contributions
CP designed the model and algorithm, and analysed the data. KJL collected and interpreted data, and drafted the manuscript. JO participated in writing up and revising the manuscript. BL conceived the idea, participated in writing up and revising the manuscript. All authors read and approved the final manuscript.
Acknowledgements
The research was supported by a Grant from the Institute of Medical System Engineering (iMSE) in the GIST, Korea and also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF2014R1A1A2057801).
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Competing interests All authors declare that they have no conflicts of interest, including no financial, personal or other relationships with other people or organizations.
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Kwang Jin Lee and Chanki Park contributed equally to this work
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Cite this article
Lee, K.J., Park, C., Oh, J. et al. Noninvasive detection of intracranial hypertension using a simplified intracranial hemo and hydrodynamics model. BioMed Eng OnLine 14, 51 (2015). https://doi.org/10.1186/s1293801500513
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DOI: https://doi.org/10.1186/s1293801500513
Keywords
 Intracranial pressure
 Pulsatility index
 Intracranial hemo and hydrodynamics model
 Cerebral blood flow velocity
 Intracranial hypertension
 Valsalva maneuver