the blood - brain barrier ( bbb ) is formed by specialized endothelial cells lining capillaries in the central nervous system ( cns ) , and it prevents or slows the passage of some drugs and other chemical compounds , radioactive ions , and disease - causing organisms , such as viruses , from the blood into the cns . bbb breakdown is associated with many cns - related pathologies , including inflammatory diseases such as multiple sclerosis   and chronic and acute cerebrovascular pathology [ 2 , 3 ] . pathological modifications of the bbb have also been well described in degenerative diseases such as alzheimer disease ; in addition , it has been shown that in brain tumors the bbb is structurally and functionally abnormal .   quantitative investigation of bbb permeability is possible using magnetic resonance imaging ( mri ) , and it has been applied to the study of brain tumors [ 6 , 7 ] . in particular , experimental and clinical studies have demonstrated that dynamic contrast - enhanced ( dce ) mri , with a macromolecular contrast agent ( ca ) , can be used to quantify microvascular permeability in tumors   and that permeability increases with increasing histological tumor grade [ 7 , 9 ] . different theoretical models have been proposed for the analysis of dce - mri data in order to find a more accurate approach for the tumor vascular bed and discriminate blood flow and vascular permeability . these models include the standard   and the extended tofts - kety ( etk ) models [ 11 , 12 ] , the adiabatic tissue homogeneity ( aath ) model [ 13 , 14 ] , the two - compartment exchange model ( 2cxm ) [ 1517 ] , the distributed capillary adiabatic tissue homogeneity ( dcath ) model , and the gamma capillary transit time model ( gctt ) . the absolute quantification of permeability parameters may substantially differ on the basis of the specific model adopted to fit the dce experimental data . the purpose of this study was to quantify permeability parameters in patients with different histological types of brain tumors by using two different theoretical algorithms . to this aim , we compared the volume transfer constant between blood plasma and the extravascular extracellular space ( ees ) ( k ) , the volume of ees per unit volume of tissue ( ve ) ( with 0  ve  1 ) , the vascular volume fraction within the tissue ( vp ) , and the washout rate from the ees back into the blood plasma ( kep ) . these parameters were calculated using the patlak algorithm , which assumes that kep is small , and therefore negligible , and the etk model . additionally , the results were evaluated in order to understand if the permeability metrics obtained with the two methods correlated with histological grade . twenty - five adult patients ( eight females and seventeen males ; mean age  standard deviation = 54.6  10.0 years ; age range = 3775 years ) with different brain tumors were enrolled in this study . the histological grade of each lesion was determined by using the world health organization ( who ) classification of brain tumors . mri examinations were performed on a 1.5-t clinical system ( siemens magnetom avanto , erlangen , germany ) with an 8-channel head coil , and the following imaging sequences were acquired : t1-weighted ( tr / te = 500/10  ms ; acquisition matrix = 320  384 ; nex = 1 ; field of view = 250  300 mm ; slice thickness = 5 mm , flip angle = 80 ) , t2-weighted ( tr / te = 3800/95  ms ; acquisition matrix = 320  384 ; nex = 2 ; field of view = 250  300  mm ; slice thickness = 5  mm , flip angle = 150 ) , and fluid attenuated inversion recovery ( flair ) ( tr / te = 9000/119  ms ; acquisition matrix = 320  384 ; nex = 1 ; field of view = 250  300  mm ; slice thickness = 5  mm , flip angle = 150 ) . before intravenous injection of the ca , fast low - angle shot ( flash ) axial 3d t1-weighted images ( tr / te = 6.7/1.0  ms ; acquisition matrix = 320  384 ; nex = 1 ; field of view = 250  300  mm ; slice thickness = 5  mm ) were acquired with multiple flip angles ( 5 , 10 , 15 , 20 , and 30 ) . acquisition of a dce - mri sequence was started immediately after intravenous administration of a gadolinium - based ca ( gadobutrol 0.1  ml / kg , gadovist ) by a power injector ( spectris solaris ep medrad ) at a rate of 5  ml / s . dynamic axial 3d t1-weighted turboflash images ( tr / te = 6.7/1.0  ms ; acquisition matrix = 320  384 ; nex = 1 ; field of view = 250  300  mm ; slice thickness = 5  mm ; flip angle = 30 ) were acquired for 30 time points . permeability maps were created as described in the theory and data analysis section , and the mean of k , ve , and vp was obtained for each patient in a region of interest ( roi ) within the tumor .   the patlak algorithm and the etk model were used in order to calculate different permeability parameters . the tracer concentration in tissue , ct , and the tracer concentration in arterial blood plasma , cp , are related by the differential equation 
 ( 1)dctdt = ktranscpkepct , 
 where kep = k / ve is the rate constant . the solution of ( 1 ) , using the initial conditions cp = ct = 0 at t = 0 , is 
 ( 2)ct(t)=ktranscp()exp[kep(t)]d , 
 where t represents the current time step ,  is the variable of integration , ct(t ) is the time course of the ca concentration in the tissue compartment , and cp(t ) is the time course of the ca concentration in the plasma ( aif ) [ 22 , 23 ] .   equation ( 2 ) is the standard tofts - kety model and is acceptable in tumors with no large increase in blood volume ; however , it is not valid in other contexts , for instance when blood volume can increase markedly in neoplasms . it is possible to extend ( 2 ) to include the concentration of ca in the blood plasma : 
 ( 3)ct(t)=ktranscp()exp[kep(t)]d+vpcp(t ) . 
 equation ( 3 ) is the etk model , where vp is the vascular volume fraction within the tissue . equations ( 2 ) and ( 3 ) are the basis of the most of dce - mri experiments currently being reported in the literature . the general approach is to measure cp and ct time courses and perform a nonlinear least squares fit of these equations to such data . by varying the parameters in those equations , it is possible to obtain estimates on k , ve and vp . for this study , postprocessing analysis for the etk model was performed using in - house software . this analysis assumes that the rate constant between ees and blood plasma ( kep ) in ( 3 ) can be ignored due to low permeability and short measuring time . in these cases , ( 3 ) can be reduced to 
 ( 4)ct(t)=vpcp()+ktranscp()d. 
 using the patlak analysis , it is possible to linearize ( 4 ) to obtain a graph of the ratio ct(t)/cp(t ) versus cp()d/cp(t ) in order to calculate the values of k and vp . it is useful to keep in mind that this model does not take into account the backflow and , therefore , the results could have some limitations . for this work , postprocessing analysis for the patlak algorithm was performed using toppcat ( t - one weighted perfusion imaging parameter calculation toolkit ) [ https://dblab.duhs.duke.edu/ ] , which is a free permeability analysis software available on internet . the calculation of the permeability parameters by using ( 2 ) , ( 3 ) , or ( 4 ) requires the values of s0 , the equilibrium longitudinal magnetization , and t1 pregadolinium mapping for each voxel . precontrast t1 mapping of tissue can be obtained with different approaches ; a common method employs multiple 3d gradient echo acquisitions at multiple variable flip angles . for this purpose , pulse sequence and flip angle must be chosen to maximize the sampling rate within the constraint of an adequate signal - to - noise ratio ( snr ) . another frequently used method to calculate the t1 baseline values utilizes 2d t1-weighted inversion recovery scans at various inversion times [ 27 , 28 ] . this method is considered more accurate than the variable flip angle method , but it is usually more time consuming .   in our study , we chose to use acquisitions at multiple variable flip angles to obtain s0 and t1 values . in flash mri with a complete spoiling of the transverse magnetization , the steady - state signal is given by 
 ( 5)s=s0(1exp[tr / t1])sin1cos  exp[tr / t1 ] , 
 where tr is the repetition time and  is the flip angle for tr > > t2 * . to construct the t1 and s0 maps , it is necessary to fit the data from flash sequence by a linearization of ( 5 ) . the t1 and s0 values are then utilized to estimate the voxel r1 time courses , or relaxation rates , from the acquired signal intensity time courses , 
 ( 6)r1(t )  = 1tr  ln[(1(s(t)s(0)s0sin+1m1(mcos ) ) )  (1cos(s(t)s(0)s0sin+(1m1(mcos))))1 ] , 
 where m = exp[tr / t1 ] ,  is the flip angle of the dce - mr sequence , and s(0 ) and s(t ) are the signal intensities at time t = 0 and time t , respectively . the relaxation rate r1(t ) is related to the tracer concentration ct(t ) by 
 ( 7)r1(t)=r10+r1c(t ) , 
 where r10 is the relaxation rate before tracer injection and r1 is the relaxivity of the ca , which varies with the molecule 's contrast type ( in our case r1 = 4.3  mms ) . the kolmogorov - smirnov test of normality was used to determine whether the distribution of values was normal , and comparisons between these two theoretical models were performed using the student 's t - test . a p value lower than 0.05 was considered to indicate statistical significance for all comparisons . the study group consisted of twenty - five patients , whose histological diagnoses were as follows seventeen glioblastoma multiforme ( who grade iv ) , two oligoastrocytoma ( who grade iii ) , two anaplastic astrocytomas ( who grade iii ) , one pleomorphic xanthoastrocytoma ( who grade iii ) , and three astrocytomas ( who grade ii ) . differences in permeability measurements were found between different tumor grades , with higher histological grades characterized by higher permeability values . in particular , for grade iv tumors , the mean k value calculated by using the patlak algorithm was 0.039  0.016  min , and the mean k value calculated by using the etk model was 0.051  0.015  min ( figure 1 ) . for grade iii tumors , the mean k value was 0.032  0.011  min for the patlak algorithm and 0.043  0.022 min for the etk model . in grade ii tumors , we obtained a mean k value of 0.010  0.006  min with the patlak algorithm and a mean k value of 0.011  0.007  min with the etk model . statistical analysis showed significant differences in the mean k values obtained with the patlak algorithm versus those obtained with the etk model for grade iv tumors ( p = 0.049 , t = 2.04 ) and for high grade tumors ( i.e. , who iv and who iii grouped together ) ( p = 0.031 , t = 2.02 ) . no significant differences were found between mean k values obtained with the two algorithms for grade ii tumors . in addition , we did not find significant differences in mean vp values between the two methods in both high - grade tumors and low - grade tumors . additionally , we calculated ve only for the etk model , finding for high - grade tumors ( who iv and who iii grouped together ) a mean ve of 0.15  0.05 , whilst a mean ve of 0.017  0.006 was found for low - grade tumors . the histological grade of tumors for these patients was found to have a significant correlation with k values . for the patlak algorithm , we found a pearson correlation coefficient r = 0.54  ( p = 0.004 ) , and for the etk model we found a pearson correlation coefficient = 0.58(p = 0.002 ) . over the past two decades , important progress has been made in the development of a robust method to noninvasively quantify the microvascular permeability of the bbb for clinical use . bbb can be altered in brain tumors neoangiogenesis because of new vessels , which are structurally and functionally abnormal . this abnormality impairs effective delivery of therapeutic agents to all regions of tumors , creates an abnormal microenvironment ( e.g. , hypoxia ) that reduces the effectiveness of radiation and chemotherapy , and selects for more malignant cells . bbb disruption caused by tumors is heterogeneous , thus , the permeability can vary widely in different areas of the same tumor . creation of parametric maps with a k value for each voxel can be of practical importance and useful , for instance , to guide the biopsy target . different theoretical models can be used to fit dce - mri experimental data , and the resulting permeability parameters can be influenced by the model used . in this study , 25 patients with different brain tumors underwent dce mri . the patlak algorithm , which assumes that the washout rate from the ees back into the blood plasma is small and therefore negligible , and the etk model were applied to estimate kinetic parameters . our results showed that k mean values in rois within high - grade tumors were significantly different between the two methodologies , with higher k mean values calculated with the etk model .   in many studies , k is estimated by applying the tk model or the etk model . however , the main disadvantage of the tk model is that it overestimates k in highly vascularized regions , since the contribution of intravascular ca to the signal enhancement is mistaken as tracer that enters the ees and thus appears to reflect permeability . used the tk and etk models to estimate permeability on 18 high - grade gliomas , and they found that k values calculated by using the tk model were considerably higher than the k values obtained using the etk technique . on the other hand , port et al . estimated the difference between noncompartmental , tk and etk models on 20 patients with recurrent glioblastoma , finding significant differences in the results obtained with the different models .   in our study , we found statistically different k values for high - grade tumors , but no significant difference for low - grade tumors . this result may be related to the low number of patients with grade ii tumors in this study , but biological differences between high - grade tumors and low - grade tumors can also be associated with these findings . both techniques reveal a significant correlation between the histological grade of tumors and their k values . these data are in line with other results that can be found in the literature [ 35 , 36 ] . in conclusion , we demonstrated that dce acquisition is feasible in patients with brain tumors and that the choice of the postprocessing tool can influence the permeability metrics . in particular , the use of the patlak algorithm versus the etk model can lead to statistically significant differences in the k values . in our small sample