Correlation of microvascular fractal dimension with positron emission tomography [11C]-methionine uptake in glioblastoma multiforme: Preliminary findings

Fractals, Pattern Recognition, Memetics, and AI: A Personal Journal in the Computational Neurosurgery

In this chapter, the personal journey of the author in many countries, including Italy, Germany, Austria, the United Kingdom, Switzerland, the United States, Canada, and Australia, is summarized, aimed to merge different translational fields (such as neurosurgery and the clinical neurosciences in general, biomedical engineering, mathematics, computer science, and cognitive sciences) and lay the foundations of a new field defined computational neurosurgery, with fractals, pattern recognition, memetics, and artificial intelligence as the common key words of the journey.

Computational Fractal-Based Analysis of Brain Tumor Microvascular Networks

Brain parenchyma microvasculature is set in disarray in the presence of tumors, and malignant brain tumors are among the most vascularized neoplasms in humans. As microvessels can be easily identified in histologic specimens, quantification of microvascularity can be used alone or in combination with other histological features to increase the understanding of the dynamic behavior, diagnosis, and prognosis of brain tumors. Different brain tumors, and even subtypes of the same tumor, show specific microvascular patterns, as a kind of "microvascular fingerprint," which is particular to each histotype. Reliable morphometric parameters are required for the qualitative and quantitative characterization of the neoplastic angioarchitecture, although the lack of standardization of a technique able to quantify the microvascular patterns in an objective way has limited the "morphometric approach" in neuro-oncology.In this chapter, we focus on the importance of computational-based morphometrics, for the objective description of tumoral microvascular fingerprinting. By also introducing the concept of "angio-space," which is the tumoral space occupied by the microvessels, we here present fractal analysis as the most reliable computational tool able to offer objective parameters for the description of the microvascular networks.The spectrum of different angioarchitectural configurations can be quantified by means of Euclidean and fractal-based parameters in a multiparametric analysis, aimed to offer surrogate biomarkers of cancer. Such parameters are here described from the methodological point of view (i.e., feature extraction) as well as from the clinical perspective (i.e., relation to underlying physiology), in order to offer new computational parameters to the clinicians with the final goal of improving diagnostic and prognostic power of patients affected by brain tumors.

Demystifying neuroblastoma malignancy through fractal dimension, entropy, and lacunarity

PURPOSE

Neuroblastoma is a pediatric solid tumor with a prognosis associated with histology and age of the patient, which are the parameters of the well-established current classification (Shimada classification). Despite the development of new treatment options, the prognosis of high-risk neuroblastoma patients is still poor. Therefore, there is a continuous need to stratify the children suffering from this tumor. A mathematical and computational approach is proposed to enable automatic and precise cancer diagnosis on the histological slide.

METHODS

We targeted the complexity of neuroblastoma by calculating its image entropy (S), fractal dimension (FD), and lacunarity (λ) in a combined mathematical code. First, we tested the proposed method for patient-derived glioma images. It allowed distinguishing between normal brain tissue, grade II, and grade III glioma, which harbor different outcomes.

RESULTS

In neuroblastoma, our analysis of image's FD, S, and λ combined with a machine learning algorithm automatically predicted tumor malignancy with a receiver operating characteristic curve of 0.82. FD, S, and λ distinguish between neuroblastoma and ganglioneuroma, but they only partially differentiate between the normal samples and the other classes. Ganglioneuroma, the most differentiated form, and poorly-differentiated neuroblastoma display different values of FD, S, and λ.

CONCLUSIONS

FD, S, and λ of imaging recognize groups in neuroblastic tumors. We suggest that future studies including these features may challenge the current Shimada classification of neuroblastoma with categories of favorable and unfavorable histology. It is expected that this methodology could trigger multicenter studies and potentially find practical use in the clinical setting of children's hospitals worldwide.

The Complexity and Fractal Geometry of Nuclear Medicine Images

Irregularity in shape and behavior is the main feature of every anatomical system, including human organs, tissues, cells, and sub-cellular entities. It has been shown that this property cannot be quantified by means of the classical Euclidean geometry, which is only able to describe regular geometrical objects. In contrast, fractal geometry has been widely applied in several scientific fields. This rapid growth has also produced substantial insights in the biomedical imaging. Consequently, particular attention has been given to the identification of pathognomonic patterns of "shape" in anatomical entities and their changes from natural to pathological states. Despite the advantages of fractal mathematics and several studies demonstrating its applicability to oncological research, many researchers and clinicians remain unaware of its potential. Therefore, this review aims to summarize the complexity and fractal geometry of nuclear medicine images.

Impacts on Histological Features and 11C-Methyl-L-methionine Uptake After "One-Shot" Administration with Bevacizumab Before Surgery in Newly Diagnosed Glioblastoma

BACKGROUND: Bevacizumab (BEV), an antiangiogenic agent, induces dramatic normalization of the tumor vasculature in glioblastoma. This study aimed to clarify how one-time administration of BEV changes histological features in glioblastoma and how histological changes affect the uptake of ¹¹C-methyl-L-methionine (¹¹C-met) as an amino-acid tracer. MATERIALS AND METHODS: Subjects were 18 patients with newly diagnosed glioblastoma who were assigned to two groups: BEV group, single intravenous administration of BEV before surgical tumor removal; and control group, surgical tumor removal alone. After surgery, we compared the densities of tumor cells and microvessels, and microvascular structures including vascular pericytes and L-type amino acid transporter-1 (LAT1) between the BEV and control groups. Correlations between ¹¹C-met uptake on positron emission tomography before surgery, microvascular density, and LAT1 expression were assessed in each group. RESULTS: BEV induced significant reductions in microvascular density, while tumor cell density and proliferation were retained in the BEV group. Percentages of vessels with pericytes and vascular endothelium with LAT1 expression were lower in the BEV group than in controls. Uptake of ¹¹C-met correlated significantly with microvascular density in the BEV group but not with LAT1expression. CONCLUSIONS: The present study showed that even one course of BEV administration induced reductions in microvessels, vascular pericytes, and LAT1 expression in glioblastomas. One course of BEV therapy also reduced ¹¹C-met uptake, which might have been largely attributed to reductions in microvessels rather than reductions in LAT1 expression.

Comparisons Between PET With 11C-Methyl-L-Methionine and Arterial Spin Labeling Perfusion Imaging in Recurrent Glioblastomas Treated With Bevacizumab

PURPOSE

The aim of this study was to clarify whether arterial spin labeling (ASL) perfusion imaging can assess biological effects from bevacizumab (BEV) therapy as reliably as PET with C-methyl-L-methionine (C-met-PET).

MATERIALS AND METHODS

Twenty-four patients with recurrent glioblastoma were examined using both ASL and C-met-PET before and 4 and 8 weeks after starting BEV treatment. Tumor-to-normal brain (T/N) ratios, fluctuations in T/N ratio, and tumor volumes were compared between ASL and C-met-PET. Accuracy of predicting patient with long progression-free survival (PFS) was assessed for T/N ratios and fluctuations for ASL and C-met-PET in each phase and in each period using receiver operating characteristic curves. Between 2 groups of patients assigned by cutoff values from receiver operating characteristic curves, PFS was compared in each phase or in each period.

RESULTS

T/N ratios, fluctuations in ratio, and tumor volumes correlated significantly between ASL and C-met-PET at all time points and all periods. Arterial spin labeling was eligible as a predictor for long PFS only in assessment of fluctuations in T/N ratio. However, the most accurate predictors for long PFS were T/N ratio from C-met-PET at 8 weeks and the fluctuation from baseline to 4 weeks in T/N ratio from C-met-PET.

CONCLUSIONS

Blood flows on ASL correlated with accumulations of C-met on PET in recurrent glioblastoma under BEV treatment. Although C-met-PET offered superior accuracy for predicting patients with long PFS from time points, ASL offered reliable prediction of long PFS, provided that fluctuations in T/N ratio between consecutive scans are assessed.

Microvascular fractal dimension predicts prognosis and response to chemotherapy in glioblastoma: an automatic image analysis study

The microvascular profile has been included in the WHO glioma grading criteria. Nevertheless, microvessels in gliomas of the same WHO grade, e.g., WHO IV glioblastoma (GBM), exhibit heterogeneous and polymorphic morphology, whose possible clinical significance remains to be determined. In this study, we employed a fractal geometry-derived parameter, microvascular fractal dimension (mvFD), to quantify microvessel complexity and developed a home-made macro in Image J software to automatically determine mvFD from the microvessel-stained immunohistochemical images of GBM. We found that mvFD effectively quantified the morphological complexity of GBM microvasculature. Furthermore, high mvFD favored the survival of GBM patients as an independent prognostic indicator and predicted a better response to chemotherapy of GBM patients. When investigating the underlying relations between mvFD and tumor growth by deploying Ki67/mvFD as an index for microvasculature-normalized tumor proliferation, we discovered an inverse correlation between mvFD and Ki67/mvFD. Furthermore, mvFD inversely correlated with the expressions of a glycolytic marker, LDHA, which indicated poor prognosis of GBM patients. Conclusively, we developed an automatic approach for mvFD measurement, and demonstrated that mvFD could predict the prognosis and response to chemotherapy of GBM patients.

Fractals in the Neurosciences, Part II

It has been ascertained that the human brain is a complex system studied at multiple scales, from neurons and microcircuits to macronetworks. The brain is characterized by a hierarchical organization that gives rise to its highly topological and functional complexity. Over the last decades, fractal geometry has been shown as a universal tool for the analysis and quantification of the geometric complexity of natural objects, including the brain. The fractal dimension has been identified as a quantitative parameter for the evaluation of the roughness of neural structures, the estimation of time series, and the description of patterns, thus able to discriminate different states of the brain in its entire physiopathological spectrum. Fractal-based computational analyses have been applied to the neurosciences, particularly in the field of clinical neurosciences including neuroimaging and neuroradiology, neurology and neurosurgery, psychiatry and psychology, and neuro-oncology and neuropathology. After a review of the basic concepts of fractal analysis and its main applications to the basic neurosciences in part I of this series, here, we review the main applications of fractals to the clinical neurosciences for a holistic approach towards a fractal geometry model of the brain.

Computational Fractal-Based Analysis of Brain Arteriovenous Malformation Angioarchitecture

BACKGROUND:

Neuroimaging is the gold standard for diagnosis and follow-up of brain arteriovenous malformations (bAVMs), but no objective parameter has been validated for the assessment of the nidus angioarchitecture and for prognostication following treatment. The fractal dimension (FD), which is a mathematical parameter able to quantify the space-filling properties and roughness of natural objects, may be useful in quantifying the geometrical complexity of bAVMs nidus.

OBJECTIVE:

To propose FD as a neuroimaging biomarker of the nidus angioarchitecture, which might be related to radiosurgical outcome.

METHODS:

We retrospectively analyzed 54 patients who had undergone stereotactic radiosurgery for the treatment of bAVMs. The quantification of the geometric complexity of the vessels forming the nidus, imaged in magnetic resonance imaging, was assessed by means of the box-counting method to obtain the fractal dimension.

RESULTS:

FD was found to be significantly associated with the size (P = .03) and volume (P < .001) of the nidus, in addition to several angioarchitectural parameters. A nonsignificant association between clinical outcome and FD was observed (area under the curve, 0.637 [95% confidence interval, 0.49-0.79]), indicative of a potential inverse relationship between FD and bAVM obliteration.

CONCLUSION:

In our exploratory methodological research, we showed that the FD is an objective computer-aided parameter for quantifying the geometrical complexity and roughness of the bAVM nidus. The results suggest that more complex bAVM angioarchitecture, having higher FD values, might be related to decreased response to radiosurgery and that the FD of the bAVM nidus could be used as a morphometric neuroimaging biomarker.

Comparison of 18F-FET PET and perfusion-weighted MR imaging: a PET/MR imaging hybrid study in patients with brain tumors

PET using O-(2-(18)F-fluoroethyl)-L-tyrosine ((18)F-FET) provides important diagnostic information in addition to that from conventional MR imaging on tumor extent and activity of cerebral gliomas. Recent studies suggest that perfusion-weighted MR imaging (PWI), especially maps of regional cerebral blood volume (rCBV), may provide similar diagnostic information. In this study, we directly compared (18)F-FET PET and PWI in patients with brain tumors.

METHODS

Fifty-six patients with gliomas were investigated using static (18)F-FET PET and PWI. For comparison, 8 patients with meningiomas were included. We generated a set of tumor and reference volumes of interest (VOIs) based on morphologic MR imaging and transferred these VOIs to the corresponding (18)F-FET PET scans and PWI maps. From these VOIs, tumor-to-brain ratios (TBR) were calculated, and normalized histograms were generated for (18)F-FET PET and rCBV maps. Furthermore, in rCBV maps and in (18)F-FET PET scans, tumor volumes, their spatial congruence, and the distance between the local hot spots were assessed.

RESULTS

For patients with glioma, TBR was significantly higher in (18)F-FET PET than in rCBV maps (TBR, 2.28 ± 0.99 vs. 1.62 ± 1.13; P < 0.001). Histogram analysis of the VOIs revealed that (18)F-FET scans could clearly separate tumor from background. In contrast, deriving this information from rCBV maps was difficult. Tumor volumes were significantly larger in (18)F-FET PET than in rCBV maps (tumor volume, 24.3 ± 26.5 cm(3) vs. 8.9 ± 13.9 cm(3); P < 0.001). Accordingly, spatial overlap of both imaging parameters was poor (congruence, 11.0%), and mean distance between the local hot spots was 25.4 ± 16.1 mm. In meningioma patients, TBR was higher in rCBV maps than in (18)F-FET PET (TBR, 5.33 ± 2.63 vs. 2.37 ± 0.32; P < 0.001) whereas tumor volumes were comparable.

CONCLUSION

In patients with cerebral glioma, tumor imaging with (18)F-FET PET and rCBV yields different information. (18)F-FET PET shows considerably higher TBRs and larger tumor volumes than rCBV maps. The spatial congruence of both parameters is poor. The locations of the local hot spots differ considerably. Taken together, our data show that metabolically active tumor tissue of gliomas as depicted by amino acid PET is not reflected by rCBV as measured with PWI.

Fractal dimension and vessel complexity in patients with cerebral arteriovenous malformations

The fractal dimension (FD) can be used as a measure for morphological complexity in biological systems. The aim of this study was to test the usefulness of this quantitative parameter in the context of cerebral vascular complexity. Fractal analysis was applied on ten patients with cerebral arteriovenous malformations (AVM) and ten healthy controls. Maximum intensity projections from Time-of-Flight MRI scans were analyzed using different measurements of FD, the Box-counting dimension, the Minkowski dimension and generalized dimensions evaluated by means of multifractal analysis. The physiological significance of this parameter was investigated by comparing values of FD first, with the maximum slope of contrast media transit obtained from dynamic contrast-enhanced MRI data and second, with the nidus size obtained from X-ray angiography data. We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity. Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD. The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs.

Increased tryptophan transport in epileptogenic dysembryoplastic neuroepithelial tumors

Dysembryoplastic neuroepithelial tumors (DNTs) are typically hypometabolic but can show increased amino acid uptake on positron emission tomography (PET). To better understand mechanisms of amino acid accumulation in epileptogenic DNTs, we combined quantitative α-[(11)C]methyl-L: -tryptophan (AMT) PET with tumor immunohistochemistry. Standardized uptake values (SUVs) of AMT and glucose were measured in 11 children with temporal lobe DNT. Additional quantification for AMT transport and metabolism was performed in 9 DNTs. Tumor specimens were immunostained for the L: -type amino acid transporter 1 (LAT1) and indoleamine 2,3-dioxygenase (IDO), a key enzyme of the immunomodulatory kynurenine pathway. All 11 tumors showed glucose hypometabolism, while mean AMT SUVs were higher than normal cortex in eight DNTs. Further quantification showed increased AMT transport in seven and high AMT metabolic rates in three DNTs. Two patients showing extratumoral cortical increases of AMT SUV had persistent seizures despite complete tumor resection. Resected DNTs showed moderate to strong LAT1 and mild to moderate IDO immunoreactivity, with the strongest expression in tumor vessels. These results indicate that accumulation of tryptophan in DNTs is driven by high amino acid transport, mediated by LAT1, which can provide the substrate for tumoral tryptophan metabolism through the kynurenine pathway, that can produce epileptogenic metabolites. Increased AMT uptake can extend to extratumoral cortex, and presence of such cortical regions may increase the likelihood of recurrent seizures following surgical excision of DNTs.