Review of tracer kinetic models in evaluation of gliomas using dynamic contrast-enhanced imaging

Glioma is the most common type of primary malignant tumor of the central nervous system (CNS), and is characterized by high malignancy, high recurrence rate and poor survival. Conventional imaging techniques only provide information regarding the anatomical location, morphological characteristics, and enhancement patterns. In contrast, advanced imaging techniques such as dynamic contrast-enhanced (DCE) MRI or DCE CT can reflect tissue microcirculation, including tumor vascular hyperplasia and vessel permeability. Although several studies have used DCE imaging to evaluate gliomas, the results of data analysis using conventional tracer kinetic models (TKMs) such as Tofts or extended-Tofts model (ETM) have been ambiguous. More advanced models such as Brix’s conventional two-compartment model (Brix), tissue homogeneity model (TH) and distributed parameter (DP) model have been developed, but their application in clinical trials has been limited. This review attempts to appraise issues on glioma studies using conventional TKMs, such as Tofts or ETM model, highlight advancement of DCE imaging techniques and provides insights on the clinical value of glioma management using more advanced TKMs.


Introduction
Glioma originates from the neurostromal cells and is the most common primary tumor of the central nervous system (CNS) (1).It is characterized by wide-spread invasion and angiogenesis, with short median survival duration and high recurrence rate (2).Firstline therapy for gliomas consists of radiotherapy, surgery, concomitant chemoradiotherapy and adjuvant chemotherapy with temozolomide (3), while immunotherapies are currently in the preclinical and clinical stages of testing (4).The treatment response of glioma is primarily evaluated on the basis of contrast enhanced T1weighted magnetic resonance imaging (MRI).However, the correlation between changes in enhancement and the treatment response is often confounded by the presence of radiation necrosis, pseudoprogression or pseudoresponse (5-7) (Figures 1 and 2 for example), thereby warranting more advanced imaging techniques for accurate assessment.
Dynamic contrast enhancement (DCE) imaging is a noninvasive approach that can provide in vivo physiological and metabolic information of tissues, and assess microvascular features such as the degree of vascularity and disruption of vascular wall permeability (8)(9)(10)(11).DCE imaging data can be analyzed in terms of both semi-quantitative and quantitative parameters.The former includes time-intensity curve (TIC) parameters, such as initial area under the curve (IAUC) and time to peak, which are easy to derive (12) but challenging to reproduce across studies due to differences in data acquisition and subject conditions.DCE imaging data can be quantitatively analyzed using a tracer kinetic model (TKM), a mathematical description of tracer molecular transport within the tissue microenvironment that derives quantitative values of various model parameters pertaining to the tissue status.Several clinical studies have tested DCE imaging for various applications, including glioma assessment (13)(14)(15)(16)(17).Most of these studies used Tofts or extended-Tofts model (ETM), which represents early development in DCE imaging.More advanced TKMs have been developed (18, 19), but have received less attention in clinical studies.
In this review, the evaluation of glioma using conventional TKMs, advances in DCE imaging techniques, and the clinical potential of advanced TKMs in glioma management have been discussed.

Literature search and selection strategy
We searched for candidate articles describing the different TKMs for gliomas in PubMed and Science Direct databases published between January 1950 and May 2024.The search strategy of key terms used was "((tracer kinetic model OR pharmacokinetic model) OR (Tofts OR generalized kinetic model) OR extended Tofts model OR (two-compartment model OR two-compartment exchange model) OR tissue homogeneity model OR distributed parameter model)) AND (glioma OR glioblastoma) AND (dynamic contrast-enhanced OR DCE)".The studies were included based on the following inclusion criteria: (1) clinical studies that employed DCE data in patients with gliomas, or experimental animal studies that refer to pathophysiological mechanism of microenvironment; (2) original research published in English with the full text available; and (3) the theoretical basis of tracer kinetic model and its application in glioma diagnosis and evaluation after treatment.The following types of studies were excluded: (1) unrelated or irrelevant studies, such as those that did not employ DCE techniques to investigated gliomas; and (2) studies focusing on other topics that are irrelevant to our research purpose.After a detailed evaluation and screening,105 studies that met our criteria were included and reviewed.The article selection process is shown as a flowchart in Figure 3.

Fundamental concepts and primary tracer kinetic models
Tracer kinetic models describe the transport of tracer molecular within the tissue microenvironment.The physical space of the movement of tracer molecules in the tissue is termed as compartment.Typically, there are two well-defined compartments

A B C
A 59-year-old female with glioma of the left parieto-occipital lobe, treated with surgery and radiation therapy. in the field, namely, the compartment of intravascular plasma space (IVPS), and the compartment of extravascular extracellular space (EES).Furthermore, based on the distribution of the tracer, a compartment in TKMs can be categorized as homogeneous or nonhomogeneous.For a homogeneous compartment, diffusive resistances are assumed to be zero and the tracer is assumed to move fast and distribute instantaneously and evenly upon arrival in the compartment, which is also termed as a well-mixed compartment.
Since the distribution of the tracer is uniform in a well-mixed or homogeneous compartment, the tracer concentration is constant in space and only changes with time (18).TKMs with assumptions on homogeneous or well-mixed compartment are often named as lumped parameter models.In contrast, the tracer concentration varies in a non-homogeneous compartment, and is therefore a function of both space and time.In general, a homogeneous or well-mixed compartment would simplify the modeling process and computation.Thus, the early TKMs were developed based on this assumption.However, the uniform distribution of a tracer in the compartment would depend on rapid movement of tracer molecules or sufficiently long measurement time, neither of which is viable in clinical practice.Therefore, subsequent TKMs introduced a concentration gradient in space to account for the variation in tracer distribution, leading to the assumption of non-homogeneous compartment.Nevertheless, tracer concentration in these models is homogeneous in the radial direction and variable in the axial direction.The meaning of these terms has been summarized in Table 1.
Primary tracer kinetic models, including Tofts, ETM, Brix's conventional two-compartment model (Brix), tissue homogeneity model (TH), and distributed parameter model (DP), have been listed in Table 2.It is worth pointing out that the notation of a TKM could be different in different studies, and what is introduced here follows largely the notations in earlier review papers on technical aspects of tracer kinetic modeling (18,19).Tofts model was also named as generalized kinetic (GK) model in (18).The model developed by Brix and coauthors (24,25) has been denoted as two-compartment exchange model (2CXM) in some literature (19,35,36).However, this notation reflects also the fundamental features of other models such as TH and DP, likely leading to confusion in understanding the connection and the difference among these TKMs.To emphasize that the exchange between two-compartments is the common feature of these models, the notation of the model proposed by Brix and coauthors is denoted as A 67-year-old male with WHO grade 2 glioma of the left basal ganglia and posterior horn of lateral ventricle, treated with surgery, radiotherapy plus concomitant and adjuvant temozolomide.Flowchart of the literature screening process.
where u(t) denotes the Heaviside unit-step function and I 1 is the modified Bessel function.
Tissue homogeneity (TH) model, Equation 3C tiss (t) = AIF ⊗ Tofts assumes that IVPS is significantly smaller than EES, and thus only involves EES.All other models are two-compartment models.The movement of tracer molecules in tissue generally involves intravascular transport and exchange between intravascular and interstitial space.The former reflects blood flow (CBF) and the latter indicates permeability of endothelial wall (PS).Tofts and ETM utilize one parameter (K trans ) to describe both movements, whereas Brix, TH and DP differentiate between the two and model them separately (24).Tofts, ETM and Brix models assume the compartment to be well-mixed.In the TH model, EES is well-mixed but IVPS is non-homogenous.On the other hand, both compartments are non-homogenous in the DP model.The parameters derived from these models are listed in Table 2.The technical details pertaining to these models have been comprehensively discussed in previous reviews (18,19).The kinetic parameters were graphically presented in Figure 4.

Comparison between DCE MRI and DCE CT
As a well-established imaging technique, DCE can be performed by data acquisition on either MRI or CT scanners, followed by image analysis using TKMs (39).Each imaging modality has its merits and demerits.CT is fast in scanning and allows acquisition of images with high resolution in both spatial and temporal space, but at cost of X-ray radiation.MRI is advantageous in better contrast in soft tissue and radiation-free.To reduce radiation in DCE CT, non-uniform acquisition strategy can be adopted to decrease the number of X-ray exposure in the design of DCE CT protocol, with frequent scans during artery phase and less frequent scans during delayed phase.A key difference in terms of DCE language between two modalities lies in the calculation of contrast concentration.Contrast concentration in DCE CT follows simply a linear relationship with CT image signal, whereas the relationship between contrast concentration in DCE MRI with MRI signal is much more complicated, which relates to changes in T1 values of tissue before and after contrast injection.A practical approach to estimating T1 value of tissue is the method of variable flip angles and the computation involves several MR scanning factors such as time of repetition (TR), time of echo (TE), flip angle, homogeneity of B1 field.After deriving contrast concentration from either CT or MR image signals, the analytical process of concentration-time curve will be exactly the same between DCE CT and DCE MRI.For a good appraisal on DCE CT and DCE MRI, interested readers can refer to the review paper (39), where it was shown that data acquisition and analysis were well comparable despite inherent differences in signal production and mechanism of tissue contrast enhancement.
3 Application of conventional tracer kinetic models in glioma evaluation

Application in glioma grading
Various studies have analyzed the relationship between DCE imaging parameters and glioma grading (40)(41)(42)(43)(44)(45)(46)(47)(48)(49).Santarosa et al. (50) used ETM of DCE MRI in a cohort of 26 glioma patients and demonstrated that V p and K trans differed significantly between lowgrade and high-grade gliomas.Using the same model, Zhang et al. (51) found that K trans and V e values calculated in 28 glioma patients based on DCE MRI increased with advanced tumor grade, and significant differences were observed between the low (I and II) and high (III and IV) grade gliomas, as well as between grades II and III.Awasthi et al. (52) applied Tofts model of DCE MRI to 76 glioma patients and showed that K ep and V e could differentiate low-grade from high-grade tumors, although there was no significant correlation between K trans and the expression of MMP-9, which plays a key role in the disruption of the blood-brain barrier (BBB) by degrading extracellular matrix in order to facilitate tumor cell infiltration and metastasis.In contrast, other studies (53, 54) based on DCE MRI have shown that K trans is the most effective parameter for differentiating between glioma grades.These contradictory findings can be attributed to the differences in the extent of BBB disruption among different tumor grades, as well as the different mechanisms underlying BBB disruption in infectious and neoplastic pathologies.

Correlation with immunohistochemical markers
Since the 2021 World Health Organization (WHO) guidelines on the histological classification of central nervous system tumors were published (55), molecular markers have been instrumental in the diagnosis of gliomas.For instance, IDH mutation, 1p/19q codeletion, TERT promoter mutation, and EGFR gene amplification are key biomarkers used for the classification of diffuse gliomas in FIGURE 4 The graphic illustration of various kinetic parameters in tracer kinetic models.IVPS, intravascular compartment (intravascular plasma space); EES, interstitial compartment (extravascular extracellular space); K trans , transfer constant; K ep , washout rate; CBF, tumor blood flow; V e , interstitial volume; V p , blood volume; PS, permeability-surface area product.IDH mutation is associated with a survival benefit in glioma patients (64).Wang et al. (65) retrospectively studied the IDH mutation status of 30 patients with low grade gliomas (LGGs) using ETM of DCE MRI, and showed that K trans , V e and V p were higher values in the IDH wild-type compared to the IDH mutant LGGs.In contrast, Brendle et al. (66) reported that DCE MRI kinetic parameters derived using the same model did not distinguish between IDH mutant and wild-type astrocytomas.Ahn et al. (67) retrospectively studied the molecular markers in 132 LGG patients using ETM of DCE MRI, and found no significant difference in the DCE kinetic parameters between the IDH mutant and wildtype gliomas.
MGMT promoter methylation predicts favorable prognosis after alkylating drug-based chemotherapy in patients with IDHwild-type glioblastomas (68).Several studies have evaluated the correlation between MGMT promoter methylation and DCE kinetic parameters in gliomas (69-71).Ahn et al. (67) showed that K trans , V e and V p values derived using ETM of DCE MRI were significantly lower in MGMT methylated LGGs than in the unmethylated counterparts.Another study (70) using the Tofts model of DCE MRI showed that K trans values were significantly higher in the MGMT methylated tumors, while K ep and V e showed no significant difference between gliomas with methylated and unmethylated MGMT.Hilario et al. (69) analyzed 49 glioma patients using ETM of DCE MRI, and did not detect any significant differences in the DCE kinetic parameters of the MGMT methylated and non-methylated tumors.Zhang et al. (71) further showed that gliomas with non-methylated MGMT had higher V e and K trans values with ETM of DCE MRI than those with methylated MGMT.

Differential diagnosis of glioma, PCNSL, and metastasis
Due to differences in clinical treatment and prognosis, it is critical to distinguish between primary central nervous system lymphoma (PCNSL), high-grade gliomas (HGGs), and metastatic glioma (72-79).Xi et al. (80) used Tofts model of DCE MRI to retrospectively analyze 8 cases of PCNSL, 21 cases of HGGs and 6 cases of metastasis, and detected significantly higher K trans and V e in the PCNSL tumors compared to HGGs and metastatic tumors.However, Kickingereder et al. (81) did not observe any significant difference in the V e values of PCNSL and GBM using ETM of DCE MRI.Lin et al. (82) showed that PCNSL had higher values of K trans using ETM of DCE MRI compared to GBM, although the difference was not statistically significant.Jin et al. (83) used ETM of DCE MRI to show that K trans had the highest specificity and sensitivity in differentiating between GBM, PCNSL, and metastasis.Kang et al. (84) calculated the V p in glioblastomas and PCNSL through ETM of DCE MRI, and found that the values were significantly higher in the former.In contrast, Abe et al. (43) used ETM of DCE MRI to analyze 29 lesions (including glioma, metastatic tumor and lymphoma) and found that V p was not helpful in differentiating PCNSL from GBM.

Evaluation of treatment response
All patients with glioblastoma eventually relapse.It is challenging to differentiate relapsed tumor from other treatmentrelated changes during the follow-up of glioma patients (85)(86)(87)(88)(89)(90)(91)(92).Thomas et al. (93) found that V p and K trans measurements were lower in glioblastoma patients with pseudoprogression compared to those with relapsed lesions using ETM of DCE MRI.Yun et al. (94) also applied ETM of DCE MRI to differentiate false progression from true progression, and found that K trans and V e were significantly higher in the latter, whereas V p value was similar for both types of lesions.Jing et al. (95) applied the Tofts model of DCE MRI to a retrospective analysis of 51 patients with new enhancement lesions after standard radiotherapy and chemotherapy after surgical resection, and found no significant difference in V e and K ep between the pseudoprogression group and the recurrence group.
4 Assessment of gliomas using advanced tracer kinetic models 4.1 Glioma grading Jain et al. (96,97) investigated glioma grading using perfusion CT (PCT) with the TH model (27) to estimate permeability and blood volume.While the rCBV increased more than the PS in LGGs, grade 3 and especially grade 4 gliomas showed a greater increase in PS compared to rCBV.The rate of change in the rCBV/ PS ratio may correlate to changes occurring at the tumor microvasculature level.Both PS and CBV were higher in the HGGs compared to the LGGs.Furthermore, PS can also be used to differentiate WHO grade 3 glioma from grade 4 glioma.Tietze et al. (35) presented a Bayesian framework for parameter optimization of tracer kinetic modeling and compared the Brix model and ETM in the grading of 42 untreated glioma patients.Brix-derived V p showed the best diagnostic performance with AUC of 0.97, followed by ETM-derived K trans with an AUC of 0.92.However, the diagnostic performance of permeability parameter was low, with AUC of 0.57.

Monitoring of treatment response 4.2.1 In vivo human studies
Jensen et al. (98) correlated parameters derived from a gamma capillary transit time model of DCE MRI, which is based on the distributed capillary approximated TH model (99,100), with molecular markers of hypoxia, vascularity, proliferation, and progression-free and overall survival (OS) in a cohort of 18 glioma patients.The derived parameters included tumor blood flow (CBF), extraction fraction (E), permeability-surface area product (PS), transfer constant (K trans ), washout rate (K ep ), interstitial volume (V e ), blood volume (V p ), capillary transit time (tc), and capillary heterogeneity (a −1 ).The study showed that a −1 , tc, K ep , and V p were correlated with HIF-1a and VEGF expression, whereas V e and a −1 were correlated with OS.The other imaging markers were not helpful in predicting OS.In particular, none of the blood flow and permeability parameters (K trans , CBF, E, PS) showed any correlation with patient outcome.
Lundemann et al. (101) explored the feasibility of predicting tumor recurrence using multi-modal imaging based on DCE MRI at the pre-radiotherapy stage in a cohort of 16 glioblastoma patients using Brix-derived DCE parameters.The median MTT, V p , V e and PS derived from scans prior to chemoradiotherapy showed differences between recurring and non-recurring voxels.Henriksen et al. ( 102) investigated the diagnostic value of Brixderived parameters of DCE MRI for short-term disease progression in 60 anaplastic astrocytoma and glioblastoma patients with suspected recurrence and evaluable outcome within 6 months of follow-up as determined by histopathology, MRI findings or clinical decision.The blood volume and vascular permeability were significantly higher in the progressive lesions compared to the non-progressive lesions.ROC analysis showed that blood flow and blood volume had AUC values of 0.76 and 0.78 respectively, which were higher than that of vascular permeability (0.68).
Larsen et al. ( 103) utilized Brix of DCE MRI to differentiate tumor recurrence from radiation necrosis in 19 glioma patients following surgery and radiation therapy, and demonstrated that an empirical threshold of 2 ml/100 g for blood volume allowed detection of regressing lesions with sensitivity and specificity of 100% each.In comparison, neither blood flow nor permeability parameter could discriminate between regressing and progressing lesions.

Ex vivo animal studies
Kiser et al. (36) applied the Brix model of DCE MRI to evaluate test-retest repeatability and tumor response of a murine glioblastoma model at 7 T to a combination therapy of bevacizumab and fluorouracil.Test-retest experiments demonstrated that there was no significant difference between the scans in terms of the median values of parameters, except for K trans .The compartmental volume fractions (V e and V p ) remained more consistent between scans while the vascular functional parameters (CBF and PS) showed noticeable increase in values, likely due to physiological changes in the tumor between scans.The tumor volume in the control and treated groups did not differ significantly at any time point, which corresponded to similar tracer kinetic parameters in both groups.
Yeung et al. ( 104) investigated the efficacy of CT perfusion imaging as an early biomarker of the response to stereotactic radiosurgery in a rat glioma model using the TH model (27).Rats with orthotopic C6 glioma tumors received either mock irradiation or stereotactic radiosurgery delivered by Helical Tomotherapy.The responders to stereotactic radiosurgery showed lower relative CBV, and PS on day 7 post-stereotactic radiosurgery when compared to controls and non-responders.Relative CBV and PS on day 7 were correlated with the OS, and predicted survival with 92% accuracy.

Correlation to immunohistochemical markers
Li et al. ( 105) applied the DP model of DCE MRI to a dataset consisting of 55 glioma patients to assess glioma isocitrate dehydrogenase (IDH) mutation.The IDH-mutant gliomas showed significantly lower CBF, PS, V p , E and V e compared to the IDH-wildtype gliomas.V p exhibited the best performance in differentiating between IDH-mutant and IDH-wildtype gliomas (AUC=0.92),followed by PS (AUC=0.82)and E (AUC=0.8).Furthermore, the Tofts parameters K trans and V e were lower for the IDH-mutant gliomas, and no significant difference was observed in K ep .The AUCs of K trans , V e , and K ep were 0.69, 0.79, and 0.55 respectively.These findings suggested that IDH-mutant gliomas have lower vascularity, vessel permeability and blood flow compared to IDH-wildtype gliomas, which may explain the better outcomes in patients with IDH-mutated versus IDHwildtype gliomas.

Advantage of advanced TKMs over conventional ones
The fifth edition of the WHO Classification of CNS Tumors (WHO CNS5), published in 2021, builds on the fourth edition updated in 2016 and the work of the Consortium to Inform Molecular and Practical Approaches to CNS Tumor Taxonomy, further advancing the role of molecular diagnostics in the classification of CNS tumors, but remains rooted in other established methods for assessing tumor characteristics, including histology and immunohistochemistry (55).Besides, the existing evaluation of glioma features is still based on pathological biopsy as the gold standard.Due to the high heterogeneity of gliomas and the influence of non-uniform sampling error of tumors, the diagnostic accuracy is limited by the subjective judgment of pathologists.In 2021 WHO CNS5, EGFR amplification is commonly seen in IDH wild-type gliomas.EGFR is a tyrosine kinase receptor regulating cell proliferation and differentiation by interacting with epidermal growth factor (EGF) and tumor growth factor-a (TGF-a), and can reflect microvascular proliferation in tumors (106).With the development of MRI technologies, more abundant characteristics of tumor microenvironment have been provided for the non-invasive diagnosis of gliomas.DCE MRI is sensitive to the destruction of the blood-brain barrier (BBB) and is closely related to microvascular proliferation and vascular wall permeability, which can effectively evaluate tumor angiogenesis and obtain various kinetic parameters reflecting tissue microcirculation function (9).
The focus of this review was to reveal the characteristics of the immune microenvironment of gliomas based on the conventional and advanced TKMs of DCE imaging, and to provide a noninvasive method for the diagnosis and treatment response evaluation of gliomas.Most studies on glioma assessment with DCE imaging have used Tofts or ETM for image postprocessing and data analysis, and the results show considerable variability.For instance, some studies (50,107) have reported that ETM-derived V p is a useful imaging parameter that can discriminate between LGG and HGG, whereas one study (51) showed that V e and not V p differed significantly between LGG and HGG.Likewise, Arevalo-Perez et al. (42) showed that V p had the best discriminatory power in glioma grading, whereas Jung et al. (44) reported that K trans was the most significant pharmacokinetic parameter.ETM-derived parameters can also distinguish IDH-mutant gliomas from IDH wildtype gliomas (65), although some studies (66, 67) have reported contradictory findings.While ETM_V p was reported to be significantly higher for glioblastomas compared to PCNSL in one study (84), another study (43) showed that it could not differentiate between the two lesions.Furthermore, K trans derived from the Tofts model was demonstrated to be a promising discriminatory biomarker for LGG relative to HGG (41, 108), although Awasthi et al. (52) found that K trans was not significantly different between LGG and HGG.The variations in the results across the different studies using Tofts or ETM, and the inconsistent performance of K trans in particular, have been reported in earlier reviews (13,14).
Quantitative imaging biomarkers alliance (QIBA) has recommended ETM for analyzing brain tumors through DCE imaging (109).Both imaging hardware and DCE tracer kinetic modeling have undergone significant advances over the years, thereby allowing acquisition of DCE images with higher temporal resolution, better signal-to-noise ratio, wider brain coverage and increased spatial resolution, and enabling separate quantification of CBF and PS.The advantages of a DP model over the Tofts model have been demonstrated in the assessment of the IDH mutation status in glioma (105).Recent test-retest experiments using Brix (36) showed that only the median K trans was significantly different between scans, which might justify the separate modeling of intravascular transport and exchange between intra-and extravascular space in Brix, instead of mixed modeling using one transport rate parameter (K trans ).HIF-1a expression is significantly associated with HGGs (110) and is an excellent biomarker for glioma grading (111).Furthermore, gliomas are typically characterized by a marked increase in the formation of blood vessels with abnormal blood flow and increased vessel permeability.In fact, blood volume is a promising imaging biomarker for glioma grading (42,50,107).As expected, V p derived using a DP model showed good correlation with HIF-1a expression (r= 0.747, P=0.043) (108).However, low correlation was observed between HIF-1a expression and ETM-derived V p (r= 0.149, P=0.219) in another study (111).
Physiological interpretation of K trans has been ambiguous in clinical trials using Tofts or ETM, and is generally described as a volume transfer constant that reflects vessel wall permeability (13,14).Several theoretical descriptions have been provided to interpret K trans as a combination of blood flow and vessel wall permeability (112,113).Separate measurement of CBF and PS has been well addressed in nuclear medicine (114), which is crucial to the understanding of tissue hemodynamics, and has spurned the development of more advanced DCE TKMs.In Figure 5, the parametric maps of ETM and DP for a glioblastoma (GBM) patient after surgery have been compared.The follow-up MR images in Row 1 demonstrated the evolution of enhancing lesion.DP-derived parameters in Row 2 showed that the enhancing lesion was characterized by reduced blood flow, increase in PS and marginal increase in V e compared to the contralateral tissue.ETM-derived parameters in Row 2 manifested as reduced K trans , marginal increase in V p , and increase in V e .As previously reported (24), V e in the brain tumor reflects the transfer of tracer molecules between intravascular and interstitial space due to insufficient leakage from the intravascular space and attainment of steady levels in the interstitial space during the insufficient scanning period.Hence, ETM and DP illustrated similar pattern in vessel wall permeability in this case.Nonetheless, the lower value of K trans , which is generally explained as reduced vessel wall permeability, may be indicative of reduced blood flow for this case.
The MR images of WHO grade 4 glioma at the right frontal lobe treated with surgery and chemoradiotherapy are shown in Figure 6.Small enhancing lesions appeared in the 31 th month of follow-up after surgery and continued to grow.DCE scan was performed in the 37 th month of follow-up, and analyzed using the distributed parameter model.The parametric maps are shown in the second row, which indicate reduced blood flow and increased vessel permeability in the lesion compared to the contralateral tissue.The patient underwent a second surgery, and histopathological analysis revealed necrotic foci with no evidence of recurrent tumor.
In the traditional WHO classification of tumors, each tumor type has a unique WHO grading, such as anaplastic astrocytoma, which is automatically assigned to WHO grade III.The latest 2021 WHO Classification of CNS Tumors emphasizes the combination of histological grades and molecular markers, such as Glioblastoma, IDH-wild type; Astrocytoma, IDH-mutant; or Oligodendroglioma, IDH-mutant & 1p/19q codeleted.IDH mutant astrocytoma expands from the CNS in WHO grade 2-4.However, most of the current studies are based on the 2016 WHO Classification, lacking specific tumor pathological classification diagnosis (Table 3).Therefore, future studies need to use more advanced MRI technologies for further comprehensive diagnosis and stratified reporting of gliomas.

Standardization of DCE data acquisition and postprocessing
Despite limited research on advanced DCE imaging TKMs for glioma, the differences across studies are obvious.Brix-derived blood volume has shown high discriminatory ability for regressing lesions, whereas blood flow and permeability parameters showed fairly low discriminating power in the differential diagnosis of tumor recurrence (103).In contrast, a recent study (102) demonstrated similar ability of blood flow and blood volume in differentiating progressive lesions from nonprogressive lesions, and significantly higher permeability in the former.Multiple factors can contribute to these discrepancies, such as DCE imaging protocols, data post-processing, scanners, operators in data processing, sample size and patient characteristics, etc. QIBA has made the following recommendations to standardize DCE MR imaging protocol ( 115): (1) 3D T1-weighted GRE sequence, (2) variable flip angle (VFA) method to estimate T1 map and contrast agent concentration, (3) same sequence for precontrast VFA scan and post-contrast dynamic scan, (4) temporal resolution not lower than 4 s in most cases, (5) sufficiently long scanning duration of about 6 min for permeability measurement.The DCE protocols used in earlier studies often deviated from QIBA recommendations, whereas the more recent studies (102) have protocols closer to QIBA guidelines.DCE imaging data is largely analyzed using commercial software programs that differ in algorithm implementation, which may result in significant differences in the estimated DCE parameters (116).When analyzing DCE images, it is critical to accurately determine the contrast concentration from image intensities.The relationship FIGURE 5 59-year-old male with glioblastoma of the left temporal lobe.Row 1: follow-up MR examinations after surgery showed the evolution of enhancing lesion.Row 2: parametric maps of blood flow CBF, vessel permeability PS and fractional volume of interstitial space V e as derived using DP.Parametric maps of volume transfer constant K trans , V p and V e as derived using ETM. between image intensity and concentration can be non-linear, particular for MRI.In some software programs, linear assumption between change in signal intensity and gadolinium concentration is used to directly derive the contrast concentration-time curve from signal intensity-time curve (42).The choice of vascular input function (VIF) also affects the estimated values of DCE parameters.It would be ideal to select VIF from DCE images for each patient.Some software programs use population VIF or empirical VIF, as summarized in the QIBA profile (109).Standardization of imaging protocol and postprocessing procedure is crucial in making DCE reproducible and bringing forward the technology into clinical practice.

Cross-validation in DCE studies
ROC curve analysis is a useful tool for characterizing the differential diagnostic ability of potential biomarkers, which can be quantified by calculating the area under the ROC curve (AUC), or by finding an optimal threshold from the ROC curve and determining the associated sensitivity, specificity and accuracy.Most studies on DCE imaging-based glioma assessment directly applied the ROC curve method to the total data, and reported the performance of DCE parameters.In clinical practice, however, the imaging data is invariably subjected to different sources of perturbations.Therefore, the resulting diagnostic metrics could be biased towards best matching pattern in the current data, and their performance could be significantly different when applied to new data.This phenomenon is called overfitting in machine learning (117) and is particularly acute when the sample size is small, which is often the case in glioma studies.This issue is commonly resolved by cross-validation, which is typically performed by dividing data into the training set and validation set, and applying the information derived from the former to the latter.K-fold cross-validation is the most frequently used cross-validation method in machine learning.However, the leave-one-out cross-validation method is recommended for glioma studies since the cohort size is usually small.Shao et al. (38) used this method to assess the parameters of DCE imaging in a small cohort of cervical cancer patients.The following steps were used: (1) one data was left out, and the remaining data was used as the training set to build a model and make prediction on the excluded data, (2) the previous step was repeated for each data, and (3) the differential diagnostic ability was quantified by summarizing all predicted values.In the current DCE glioma studies, performance quantification without cross-validation has resulted in variation between the results of different research groups.

Conclusion
DCE imaging is effective in glioma grading and therapeutic effect monitoring, and its parameters are potential imaging markers for glioma diagnosis.However, the discrepancies between the findings in different studies warrant further improvement and validation of this technique with standardization of protocol design, and data post-processing in multi-center and large cohorts.Advanced DCE imaging techniques that allow separate modeling of blood flow and vessel permeability have advantages over conventional counterparts, although more studies are needed to ascertain the clinical value.
(A) MR image before surgery; (B) 10 months after surgery and completion of radiation therapy showed enhancing lesion; (C) follow-up MR showed resolution of the lesion.
(A) MR image before surgery; (B) MR image after surgery; (C) 1 month after surgery; (D) 10 months after surgery; (E) 13 months after surgery; (F) 15 months after surgery.Follow-up examinations demonstrated the presence of enhancing lesion in 10 months after surgery, which expanded in 13 months and reduced in 15 months.

FIGURE 3
FIGURE 3 FIGURE 6 35-year-old female with WHO grade 4 glioma of the right frontal lobe.Postoperative pathology confirmed the enhanced lesion as radiation necrosis (RN).Row 1: follow-up MR examinations after surgery showed the presence and evolution of enhancing lesion.(A) MR image after the first surgery; (B) 30 months after surgery; (C)31 months after surgery; (D)33 months after surgery; (E)35 months after surgery; (F)37 months after surgery.Row 2: parametric maps of blood flow CBF, mean transit time MTT, fractional volume of intravascular space CBV, fractional volume of interstitial space V e , vessel permeability PS, and extraction ratio E as derived using DP model.

TABLE 1
The concept and clinical significance of several terms.

TABLE 2
Summary of primary tracer kinetic models.