Fractal analysis of vascular networks: Insights from morphogenesis

Graph analysis of cell clusters forming vascular networks

This manuscript describes the experimental observation of vasculogenesis in chick embryos by means of network analysis. The formation of the vascular network was observed in the area opaca of embryos from 40 to 55 h of development. In the area opaca endothelial cell clusters self-organize as a primitive and approximately regular network of capillaries. The process was observed by bright-field microscopy in control embryos and in embryos treated with Bevacizumab (Avastin^®), an antibody that inhibits the signalling of the vascular endothelial growth factor (VEGF). The sequence of images of the vascular growth were thresholded, and used to quantify the forming network in control and Avastin-treated embryos. This characterization is made by measuring vessels density, number of cell clusters and the largest cluster density. From the original images, the topology of the vascular network was extracted and characterized by means of the usual network metrics such as: the degree distribution, average clustering coefficient, average short path length and assortativity, among others. This analysis allows to monitor how the largest connected cluster of the vascular network evolves in time and provides with quantitative evidence of the disruptive effects that Avastin has on the tree structure of vascular networks.

Deciphering microvascular changes after myocardial infarction through 3D fully automated image analysis

The microvasculature continuously adapts in response to pathophysiological conditions to meet tissue demands. Quantitative assessment of the dynamic changes in the coronary microvasculature is therefore crucial in enhancing our knowledge regarding the impact of cardiovascular diseases in tissue perfusion and in developing efficient angiotherapies. Using confocal microscopy and thick tissue sections, we developed a 3D fully automated pipeline that allows to precisely reconstruct the microvasculature and to extract parameters that quantify all its major features, its relation to smooth muscle actin positive cells and capillary diffusion regions. The novel pipeline was applied in the analysis of the coronary microvasculature from healthy tissue and tissue at various stages after myocardial infarction (MI) in the pig model, whose coronary vasculature closely resembles that of human tissue. We unravelled alterations in the microvasculature, particularly structural changes and angioadaptation in the aftermath of MI. In addition, we evaluated the extracted knowledge's potential for the prediction of pathophysiological conditions in tissue, using different classification schemes. The high accuracy achieved in this respect, demonstrates the ability of our approach not only to quantify and identify pathology-related changes of microvascular beds, but also to predict complex and dynamic microvascular patterns.

Multiscale modelling of blood flow in cerebral microcirculation: Details at capillary scale control accuracy at the level of the cortex

Aging or cerebral diseases may induce architectural modifications in human brain microvascular networks, such as capillary rarefaction. Such modifications limit blood and oxygen supply to the cortex, possibly resulting in energy failure and neuronal death. Modelling is key in understanding how these architectural modifications affect blood flow and mass transfers in such complex networks. However, the huge number of vessels in the human brain—tens of billions—prevents any modelling approach with an explicit architectural representation down to the scale of the capillaries. Here, we introduce a hybrid approach to model blood flow at larger scale in the brain microcirculation, based on its multiscale architecture. The capillary bed, which is a space-filling network, is treated as a porous medium and modelled using a homogenized continuum approach. The larger arteriolar and venular trees, which cannot be homogenized because of their fractal-like nature, are treated as a network of interconnected tubes with a detailed representation of their spatial organization. The main contribution of this work is to devise a proper coupling model at the interface between these two components. This model is based on analytical approximations of the pressure field that capture the strong pressure gradients building up in the capillaries connected to arterioles or venules. We evaluate the accuracy of this model for both very simple architectures with one arteriole and/or one venule and for more complex ones, with anatomically realistic tree-like vessels displaying a large number of coupling sites. We show that the hybrid model is very accurate in describing blood flow at large scales and further yields a significant computational gain by comparison with a classical network approach. It is therefore an important step towards large scale simulations of cerebral blood flow and lays the groundwork for introducing additional levels of complexity in the future.

Fundamental principles of vascular network topology

The vascular system is arguably the most important biological system in many organisms. Although the general principles of its architecture are simple, the growth of blood vessels occurs under extreme physical conditions. Optimization is an important aspect of the development of computational models of the vascular branching structures. This review surveys the approaches used to optimize the topology and estimate different geometrical parameters of the vascular system. The review is focused on optimizations using complex cost functions based on the minimum total energy principle and the relationship between the laws of growth and precise vascular network topology. Experimental studies of vascular networks in different species are also discussed.

The role of vascular resistance in BOLD responses to progressive hypercapnia

The ability of the cerebral vasculature to regulate vascular diameter, hence resistance and cerebral blood flow (CBF), in response to metabolic demands (neurovascular coupling), and perfusion pressure changes (autoregulation) may be assessed by measuring the CBF response to carbon dioxide (CO₂ ). In healthy individuals, the CBF response to a ramp CO₂ stimulus from hypocapnia to hypercapnia is assumed sigmoidal or linear. However, other response patterns commonly occur, especially in individuals with cerebrovascular disease, and these remain unexplained. CBF responses to CO₂ in a vascular region are determined by the combined effects of the innate vascular responses to CO₂ and the local perfusion pressure; the latter ensuing from pressure-flow interactions within the cerebral vascular network. We modeled this situation as two vascular beds perfused in parallel from a fixed resistance source. Our premise is that all vascular beds have a sigmoidal reduction of resistance in response to a progressive rise in CO₂ . Surrogate CBF data to test the model was provided by magnetic resonance imaging of blood oxygen level-dependent (BOLD) signals. The model successfully generated all the various BOLD-CO₂ response patterns, providing a physiological explanation of CBF distribution as relative differences in the network of vascular bed resistance responses to CO₂ . Hum Brain Mapp 38:5590-5602, 2017. © 2017 Wiley Periodicals, Inc.

Computational modelling of the cerebral cortical microvasculature: effect of x-ray microbeams versus broad beam irradiation

Microbeam Radiation Therapy is an innovative pre-clinical strategy which uses arrays of parallel, tens of micrometres wide kilo-voltage photon beams to treat tumours. These x-ray beams are typically generated on a synchrotron source. It was shown that these beam geometries allow exceptional normal tissue sparing from radiation damage while still being effective in tumour ablation. A final biological explanation for this enhanced therapeutic ratio has still not been found, some experimental data support an important role of the vasculature. In this work, the effect of microbeams on a normal microvascular network of the cerebral cortex was assessed in computer simulations and compared to the effect of homogeneous, seamless exposures at equal energy absorption. The anatomy of a cerebral microvascular network and the inflicted radiation damage were simulated to closely mimic experimental data using a novel probabilistic model of radiation damage to blood vessels. It was found that the spatial dose fractionation by microbeam arrays significantly decreased the vascular damage. The higher the peak-to-valley dose ratio, the more pronounced the sparing effect. Simulations of the radiation damage as a function of morphological parameters of the vascular network demonstrated that the distribution of blood vessel radii is a key parameter determining both the overall radiation damage of the vasculature and the dose-dependent differential effect of microbeam irradiation.

Traumatic brain injury results in acute rarefication of the vascular network

The role of the cerebrovascular network and its acute response to TBI is poorly defined and emerging evidence suggests that cerebrovascular reactivity is altered. We explored how cortical vessels are physically altered following TBI using a newly developed technique, vessel painting. We tested our hypothesis that a focal moderate TBI results in global decrements to structural aspects of the vasculature. Rats (naïve, sham-operated, TBI) underwent a moderate controlled cortical impact. Animals underwent vessel painting perfusion to label the entire cortex at 1 day post TBI followed by whole brain axial and coronal images using a wide-field fluorescence microscope. Cortical vessel network characteristics were analyzed for classical angiographic features (junctions, lengths) wherein we observed significant global (both hemispheres) reductions in vessel junctions and vessel lengths of 33% and 22%, respectively. Biological complexity can be quantified using fractal geometric features where we observed that fractal measures were also reduced significantly by 33%, 16% and 13% for kurtosis, peak value frequency and skewness, respectively. Acutely after TBI there is a reduction in vascular network and vascular complexity that are exacerbated at the lesion site and provide structural evidence for the bilateral hemodynamic alterations that have been reported in patients after TBI.

Planar cell polarity genes frizzled4 and frizzled6 exert patterning influence on arterial vessel morphogenesis

Quantitative analysis of the vascular network anatomy is critical for the understanding of the vasculature structure and function. In this study, we have combined microcomputed tomography (microCT) and computational analysis to provide quantitative three-dimensional geometrical and topological characterization of the normal kidney vasculature, and to investigate how 2 core genes of the Wnt/planar cell polarity, Frizzled4 and Frizzled6, affect vascular network morphogenesis. Experiments were performed on frizzled4 (Fzd4^-/-) and frizzled6 (Fzd6^-/-) deleted mice and littermate controls (WT) perfused with a contrast medium after euthanasia and exsanguination. The kidneys were scanned with a high-resolution (16 μm) microCT imaging system, followed by 3D reconstruction of the arterial vasculature. Computational treatment includes decomposition of 3D networks based on Diameter-Defined Strahler Order (DDSO). We have calculated quantitative (i) Global scale parameters, such as the volume of the vasculature and its fractal dimension (ii) Structural parameters depending on the DDSO hierarchical levels such as hierarchical ordering, diameter, length and branching angles of the vessel segments, and (iii) Functional parameters such as estimated resistance to blood flow alongside the vascular tree and average density of terminal arterioles. In normal kidneys, fractal dimension was 2.07±0.11 (n = 7), and was significantly lower in Fzd4^-/- (1.71±0.04; n = 4), and Fzd6^-/- (1.54±0.09; n = 3) kidneys. The DDSO number was 5 in WT and Fzd4^-/-, and only 4 in Fzd6^-/-. Scaling characteristics such as diameter and length of vessel segments were altered in mutants, whereas bifurcation angles were not different from WT. Fzd4 and Fzd6 deletion increased vessel resistance, calculated using the Hagen-Poiseuille equation, for each DDSO, and decreased the density and the homogeneity of the distal vessel segments. Our results show that our methodology is suitable for 3D quantitative characterization of vascular networks, and that Fzd4 and Fzd6 genes have a deep patterning effect on arterial vessel morphogenesis that may determine its functional efficiency.

Theoretical principles for biology: Variation

Darwin introduced the concept that random variation generates new living forms. In this paper, we elaborate on Darwin's notion of random variation to propose that biological variation should be given the status of a fundamental theoretical principle in biology. We state that biological objects such as organisms are specific objects. Specific objects are special in that they are qualitatively different from each other. They can undergo unpredictable qualitative changes, some of which are not defined before they happen. We express the principle of variation in terms of symmetry changes, where symmetries underlie the theoretical determination of the object. We contrast the biological situation with the physical situation, where objects are generic (that is, different objects can be assumed to be identical) and evolve in well-defined state spaces. We derive several implications of the principle of variation, in particular, biological objects show randomness, historicity and contextuality. We elaborate on the articulation between this principle and the two other principles proposed in this special issue: the principle of default state and the principle of organization.

Toward an optimal design principle in symmetric and asymmetric tree flow networks

Fluid flow in tree-shaped networks plays an important role in both natural and engineered systems. This paper focuses on laminar flows of Newtonian and non-Newtonian power law fluids in symmetric and asymmetric bifurcating trees. Based on the constructal law, we predict the tree-shaped architecture that provides greater access to the flow subjected to the total network volume constraint. The relationships between the sizes of parent and daughter tubes are presented both for symmetric and asymmetric branching tubes. We also approach the wall-shear stresses and the flow resistance in terms of first tube size, degree of asymmetry between daughter branches, and rheological behavior of the fluid. The influence of tubes obstructing the fluid flow is also accounted for. The predictions obtained by our theory-driven approach find clear support in the findings of previous experimental studies.

Impedance boundary conditions for general transient hemodynamics

We discuss the implementation and calibration of a new generalized structured tree boundary condition for hemodynamics. The main idea is to approximate the impedance corresponding to the vessels downstream from a specific outlet. Unlike previous impedance conditions, the one considered here is applicable to general transient flows as opposed to periodic ones only. The physiological character of the approach significantly simplifies calibration. We also describe a novel way to incorporate autoregulation mechanisms in structured arterial trees at minimal computational cost. The strength of the approach is illustrated and validated on several examples through comparison with clinical data.

Blood tracer kinetics in the arterial tree

Evaluation of blood supply of different organs relies on labeling blood with a suitable tracer. The tracer kinetics is linear: Tracer concentration at an observation site is a linear response to an input somewhere upstream the arterial flow. The corresponding impulse response functions are currently treated empirically without incorporating the relation to the vascular morphology of an organ. In this work we address this relation for the first time. We demonstrate that the form of the response function in the entire arterial tree is reduced to that of individual vessel segments under approximation of good blood mixing at vessel bifurcations. The resulting expression simplifies significantly when the geometric scaling of the vascular tree is taken into account. This suggests a new way to access the vascular morphology in vivo using experimentally determined response functions. However, it is an ill-posed inverse problem as demonstrated by an example using measured arterial spin labeling in large brain arteries. We further analyze transport in individual vessel segments and demonstrate that experimentally accessible tracer concentration in vessel segments depends on the measurement principle. Explicit expressions for the response functions are obtained for the major middle part of the arterial tree in which the blood flow in individual vessel segments can be treated as laminar. When applied to the analysis of regional cerebral blood flow measurements for which the necessary arterial input is evaluated in the carotid arteries, present theory predicts about 20% underestimation, which is in agreement with recent experimental data.

Kinetic modeling in the context of cerebral blood flow quantification by H2(15)O positron emission tomography: the meaning of the permeability coefficient in Renkin-Crone׳s model revisited at capillary scale

One the one hand, capillary permeability to water is a well-defined concept in microvascular physiology, and linearly relates the net convective or diffusive mass fluxes (by unit area) to the differences in pressure or concentration, respectively, that drive them through the vessel wall. On the other hand, the permeability coefficient is a central parameter introduced when modeling diffusible tracers transfer from blood vessels to tissue in the framework of compartmental models, in such a way that it is implicitly considered as being identical to the capillary permeability. Despite their simplifying assumptions, such models are at the basis of blood flow quantification by H2(15)O Positron Emission Tomgraphy. In the present paper, we use fluid dynamic modeling to compute the transfers of H2(15)O between the blood and brain parenchyma at capillary scale. The analysis of the so-obtained kinetic data by the Renkin-Crone model, the archetypal compartmental model, demonstrates that, in this framework, the permeability coefficient is highly dependent on both flow rate and capillary radius, contrarily to the central hypothesis of the model which states that it is a physiological constant. Thus, the permeability coefficient in Renkin-Crone׳s model is not conceptually identical to the physiologic permeability as implicitly stated in the model. If a permeability coefficient is nevertheless arbitrarily chosen in the computed range, the flow rate determined by the Renkin-Crone model can take highly inaccurate quantitative values. The reasons for this failure of compartmental approaches in the framework of brain blood flow quantification are discussed, highlighting the need for a novel approach enabling to fully exploit the wealth of information available from PET data.

Cerebral malaria in children: using the retina to study the brain

Cerebral malaria is a dangerous complication of Plasmodium falciparum infection, which takes a devastating toll on children in sub-Saharan Africa. Although autopsy studies have improved understanding of cerebral malaria pathology in fatal cases, information about in vivo neurovascular pathogenesis is scarce because brain tissue is inaccessible in life. Surrogate markers may provide insight into pathogenesis and thereby facilitate clinical studies with the ultimate aim of improving the treatment and prognosis of cerebral malaria. The retina is an attractive source of potential surrogate markers for paediatric cerebral malaria because, in this condition, the retina seems to sustain microvascular damage similar to that of the brain. In paediatric cerebral malaria a combination of retinal signs correlates, in fatal cases, with the severity of brain pathology, and has diagnostic and prognostic significance. Unlike the brain, the retina is accessible to high-resolution, non-invasive imaging. We aimed to determine the extent to which paediatric malarial retinopathy reflects cerebrovascular damage by reviewing the literature to compare retinal and cerebral manifestations of retinopathy-positive paediatric cerebral malaria. We then compared retina and brain in terms of anatomical and physiological features that could help to account for similarities and differences in vascular pathology. These comparisons address the question of whether it is biologically plausible to draw conclusions about unseen cerebral vascular pathogenesis from the visible retinal vasculature in retinopathy-positive paediatric cerebral malaria. Our work addresses an important cause of death and neurodisability in sub-Saharan Africa. We critically appraise evidence for associations between retina and brain neurovasculature in health and disease, and in the process we develop new hypotheses about why these vascular beds are susceptible to sequestration of parasitized erythrocytes.

Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review

OBJECTIVES

To provide an overview of recent research in fractal analysis of tissue perfusion imaging, using standard radiological and nuclear medicine imaging techniques including computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, positron emission tomography (PET) and single-photon emission computed tomography (SPECT) and to discuss implications for different fields of application.

METHODS

A systematic review of fractal analysis for tissue perfusion imaging was performed by searching the databases MEDLINE (via PubMed), EMBASE (via Ovid) and ISI Web of Science.

RESULTS

Thirty-seven eligible studies were identified. Fractal analysis was performed on perfusion imaging of tumours, lung, myocardium, kidney, skeletal muscle and cerebral diseases. Clinically, different aspects of tumour perfusion and cerebral diseases were successfully evaluated including detection and classification. In physiological settings, it was shown that perfusion under different conditions and in various organs can be properly described using fractal analysis.

CONCLUSIONS

Fractal analysis is a suitable method for quantifying heterogeneity from radiological and nuclear medicine perfusion images under a variety of conditions and in different organs. Further research is required to exploit physiologically proven fractal behaviour in the clinical setting.

KEY POINTS

• Fractal analysis of perfusion images can be successfully performed. • Tumour, pulmonary, myocardial, renal, skeletal muscle and cerebral perfusion have already been examined. • Clinical applications of fractal analysis include tumour and brain perfusion assessment. • Fractal analysis is a suitable method for quantifying perfusion heterogeneity. • Fractal analysis requires further research concerning the development of clinical applications.

Cerebral microcirculation and oxygen tension in the human secondary cortex

The three-dimensional spatial arrangement of the cortical microcirculatory system is critical for understanding oxygen exchange between blood vessels and brain cells. A three-dimensional computer model of a 3 × 3 × 3 mm(3) subsection of the human secondary cortex was constructed to quantify oxygen advection in the microcirculation, tissue oxygen perfusion, and consumption in the human cortex. This computer model accounts for all arterial, capillary and venous blood vessels of the cerebral microvascular bed as well as brain tissue occupying the extravascular space. Microvessels were assembled with optimization algorithms emulating angiogenic growth; a realistic capillary bed was built with space filling procedures. The extravascular tissue was modeled as a porous medium supplied with oxygen by advection-diffusion to match normal metabolic oxygen demand. The resulting synthetic computer generated network matches prior measured morphometrics and fractal patterns of the cortical microvasculature. This morphologically accurate, physiologically consistent, multi-scale computer network of the cerebral microcirculation predicts the oxygen exchange of cortical blood vessels with the surrounding gray matter. Oxygen tension subject to blood pressure and flow conditions were computed and validated for the blood as well as brain tissue. Oxygen gradients along arterioles, capillaries and veins agreed with in vivo trends observed recently in imaging studies within experimental tolerances and uncertainty.

Age-related reduction of structural complexity in spleen hematopoietic tissue architecture in mice

The effects of aging on structural complexity in hematopoietic tissue are unknown. In this work, in a mouse experimental model, we report the age-related reduction of spleen hematopoietic tissue (SHT) complexity. Spleen tissue was obtained from the total of 64 male Swiss albino mice divided into 8 age groups: newborns (0 days old), 10 days, 20 days, 30 days, 120 days, 210 days, 300 and 390 days old. SHT was stained using conventional hematoxylin/eosin, and DNA-binding toluidine blue dyes. Fractal dimension as an indicator of cellular complexity, and lacunarity as indicator of tissue heterogeneity were determined based on the binarized SHT micrographs. Results indicate that fractal dimension of mice spleen hematopoietic tissue decreases with age, while lacunarity increases. These changes/trends have been detected in SHT stained both with toluidine blue and conventional hematoxylin/eosin. Fractal dimension was negatively correlated with lacunarity. The detected reduction in complexity suggests that age-related structural changes are present in mouse SHT both in general tissue architecture and progenitor cell DNA.

Correlations between the dielectric properties and exterior morphology of cells revealed by dielectrophoretic field-flow fractionation

Although dielectrophoresis (DEP) has great potential for addressing clinical cell isolation problems based on cell dielectric differences, a biological basis for predicting the DEP behavior of cells has been lacking. Here, the dielectric properties of the NCI-60 panel of tumor cell types have been measured by dielectrophoretic (DEP) field-flow fractionation, correlated with the exterior morphologies of the cells during growth, and compared with the dielectric and morphological characteristics of the subpopulations of peripheral blood. In agreement with earlier findings, cell total capacitance varied with both cell size and plasma membrane folding and the dielectric properties of the NCI-60 cell types in suspension reflected the plasma membrane area and volume of the cells at their growth sites. Therefore, the behavior of cells in DEP-based manipulations is largely determined by their exterior morphological characteristics prior to release into suspension. As a consequence, DEP is able to discriminate between cells of similar size having different morphological origins, offering a significant advantage over size-based filtering for isolating circulating tumor cells, for example. The findings provide a framework for anticipating cell dielectric behavior on the basis of structure-function relationships and suggest that DEP should be widely applicable as a surface marker-independent method for sorting cells.

A mathematical and numerical investigation of the hemodynamical origins of oscillations in microvascular networks

Evidence is presented to show that self-sustained oscillations of purely hemodynamical origin are possible in some arcade-type microvascular networks supplied with steady boundary conditions, but that in others the oscillations disappear with sufficient reduction of the time step Δt, showing them to be numerical artefacts. In an attempt to elucidate the mechanisms involved in the onset of fluctuations, we proceed to perform a linear stability analysis for the convective model of Kiani et al. (Microvasc. Res. 45:219-232, 1993; Am. J. Physiol. 266(35):H1822-H1828, 1994), and show that this leads via a system of delay differential equations to a nonlinear eigenvalue problem. This result generalises the characteristic equation obtained by Carr et al. (Ann. Biomed. Eng. 33:764-771, 2005) and Geddes et al. (SIAM J. Appl. Dyn. Syst. 6(4):694-727, 2007) who solved a special case in a two node network. An implicit numerical method is proposed for the computation of blood flows in networks using the convective model. In a moderate size subnetwork of one of the networks chosen by Kiani et al. (Am. J. Physiol. 266(35):H1822-H1828, 1994), the topology, vessel lengths, and diameters of which were based on microvascular networks in the rat mesentery, we compare results generated using the original explicit numerical method of Kiani et al. (Am. J. Physiol. 266(35):H1822-H1828, 1994) with those from our implicit scheme. From the linear stability theory, a critical value D RBC,crit of a red blood cell diameter parameter D RBC in the plasma skimming model of Fenton et al. (Pflügers Arch. 403:396-401, 1985b) is identified for the onset of oscillations about steady state and both the explicit and implicit methods are used to calculate the inflow hematocrit solutions in all vessels of the subnetwork at the critical parameter value, subject to perturbed initial conditions. The results of the implicit method are demonstrated to be in excellent and superior agreement with the predictions of the linear analysis in this case. For values of D RBC slightly larger than D RBC,crit the bifurcating periodic solutions calculated using either the explicit or implicit schemes are characteristic of those of a supercritical Hopf bifurcation and the graphs of D RBC vs. oscillation amplitude would seem to converge as Δt→0.

Dynamic adaption of vascular morphology

The structure of vascular networks adapts continuously to meet changes in demand of the surrounding tissue. Most of the known vascular adaptation mechanisms are based on local reactions to local stimuli such as pressure and flow, which in turn reflects influence from the surrounding tissue. Here we present a simple two-dimensional model in which, as an alternative approach, the tissue is modeled as a porous medium with intervening sharply defined flow channels. Based on simple, physiologically realistic assumptions, flow-channel structure adapts so as to reach a configuration in which all parts of the tissue are supplied. A set of model parameters uniquely determine the model dynamics, and we have identified the region of the best-performing model parameters (a global optimum). This region is surrounded in parameter space by less optimal model parameter values, and this separation is characterized by steep gradients in the related fitness landscape. Hence it appears that the optimal set of parameters tends to localize close to critical transition zones. Consequently, while the optimal solution is stable for modest parameter perturbations, larger perturbations may cause a profound and permanent shift in systems characteristics. We suggest that the system is driven toward a critical state as a consequence of the ongoing parameter optimization, mimicking an evolutionary pressure on the system.

Quantifying tissue microvasculature with speckle variance optical coherence tomography

In this Letter, we demonstrate high resolution, three-dimensional optical imaging of in vivo blood vessel networks using speckle variance optical coherence tomography, and the quantification of these images through the development of biologically relevant metrics using image processing and segmentation techniques. Extracted three-dimensional metrics include vascular density, vessel tortuosity, vascular network fractal dimension, and tissue vascularity. We demonstrate the ability of this quantitative imaging approach to characterize normal and tumor vascular networks in a preclinical animal model and the potential for quantitative, longitudinal vascular treatment response monitoring.

Topology and hemodynamics of the cortical cerebrovascular system

The cerebrovascular system continuously delivers oxygen and energy substrates to the brain, which is one of the organs with the highest basal energy requirement in mammals. Discontinuities in the delivery lead to fatal consequences for the brain tissue. A detailed understanding of the structure of the cerebrovascular system is important for a multitude of (patho-)physiological cerebral processes and many noninvasive functional imaging methods rely on a signal that originates from the vasculature. Furthermore, neurodegenerative diseases often involve the cerebrovascular system and could contribute to neuronal loss. In this review, we focus on the cortical vascular system. In the first part, we present the current knowledge of the vascular anatomy. This is followed by a theory of topology and its application to vascular biology. We then discuss possible interactions between cerebral blood flow and vascular topology, before summarizing the existing body of the literature on quantitative cerebrovascular topology.

Fractal characteristics of May-Grünwald-Giemsa stained chromatin are independent prognostic factors for survival in multiple myeloma

BACKGROUND

The use of computerized image analysis for the study of nuclear texture features has provided important prognostic information for several neoplasias. Recently fractal characteristics of the chromatin structure in routinely stained smears have shown to be independent prognostic factors in acute leukemia. In the present study we investigated the influence of the fractal dimension (FD) of chromatin on survival of patients with multiple myeloma.

METHODOLOGY

We analyzed 67 newly diagnosed patients from our Institution treated in the Brazilian Multiple Myeloma Study Group. Diagnostic work-up consisted of peripheral blood counts, bone marrow cytology, bone radiograms, serum biochemistry and cytogenetics. The International Staging System (ISS) was used. In every patient, at least 40 digital nuclear images from diagnostic May-Grünwald-Giemsa stained bone marrow smears were acquired and transformed into pseudo-3D images. FD was determined by the Minkowski-Bouligand method extended to three dimensions. Goodness-of-fit of FD was estimated by the R(2) values in the log-log plots. The influence of diagnostic features on overall survival was analyzed in Cox regressions. Patients that underwent autologous bone marrow transplantation were censored at the day of transplantation.

PRINCIPAL FINDINGS

Median age was 56 years. According to ISS, 14% of the patients were stage I, 39% were stage II and 47% were stage III. Additional features of a bad prognosis were observed in 46% of the cases. When stratifying for ISS, both FD and its goodness-of-fit were significant prognostic factors in univariate analyses. Patients with higher FD values or lower goodness-of-fit showed a worse outcome. In the multivariate Cox-regression, FD, R(2), and ISS stage entered the final model, which showed to be stable in a bootstrap resampling study.

CONCLUSIONS

Fractal characteristics of the chromatin texture in routine cytological preparations revealed relevant prognostic information in patients with multiple myeloma.

The "self-similarity logic" applied to the development of the vascular system

From a structural standpoint, living systems exhibit a hierarchical pattern of organization in which structures are nested within one another. From a temporal point of view, this type of organization is the outcome of a 'history' resulting from a set of developmental steps. Recently, it has been suggested that some auto similarity prevails at each nested level or time step and a principle of "self-similarity logic" has been proposed to convey the concept of a multi-level organization in which very similar rules (logic) apply at each level. In this study, the hypothesis is put forward that such a principle is particularly apparent in many morphological and developmental aspects of the vascular system. In fact, not only the morphology of the vascular system exhibits a high degree of geometrical self-similarity, but its remodelling processes also seem to be characterized by the application of almost the same rules, from the macroscopic to the endothelial cell to the sub-cellular levels, potentially allowing a unitary description of features such as sprouting and intussusceptive angiogenesis, and phenotypic differences of endothelial cells. The influence of the "self-similarity logic" shaping the vascular system on the organogenesis has been also discussed.

Langmuir-Blodgett films of fluorinated glycolipids and polymerizable lipids and their phase separating behavior

This paper describes the phase separating behavior of Langmuir monolayers from mixtures of different lipids that (i) either carry already a glycopeptide recognition site or can be easily modified to carry one and (ii) polymerizable lipids. To ensure demixing during compression, we used fluorinated lipids for the biological headgroups and hydrocarbon based lipids as polymerizable lipids. As a representative for a lipid monomer, which can be polymerized in the hydrophilic headgroup, a methacrylic monomer was used. As a monomer, which can be polymerized in the hydrophobic tail, a lipid with a diacetylene unit was used (pentacosadiynoic acid, PDA). The fluorinated lipids were on the one hand a perfluorinated lipid with three chains and on the other hand a partially fluorinated lipid with a T(N)-antigen headgroup. The macroscopic phase separation was observed by Brewster angle microscopy, whereas the phase separation on the nanoscale level was observed by atomic force microscopy. It turned out that all lipid mixtures showed (at least) a partial miscibility of the hydrocarbon compounds in the fluorinated compounds. This is positive for pattern formation, as it allows the formation of small demixed 2D patterned structures during crystallization from the homogeneous phase. For miscibility especially a liquid analogue phase proved to be advantageous. As lipid 3 with three fluorinated lipid chains (very stable monolayer) is miscible with the polymerizable lipids 1 and 2, it was mostly used for further investigations. For all three lipid mixtures, a phase separation on both the micrometer and the nanometer level was observed. The size of the crystalline domains could be controlled not only by varying the surface pressure but also by varying the molar composition of the mixtures. Furthermore, we showed that the binary mixture can be stabilized via UV polymerization. After polymerization and subsequent expansion of the barriers, the locked-in polymerized structures are stable even at low surface pressures (10 mN/m), where the unpolymerized mixture did not show any segregation.

Simulation study of brain blood flow regulation by intra-cortical arterioles in an anatomically accurate large human vascular network. Part II: flow variations induced by global or localized modifications of arteriolar diameters

In a companion paper (Lorthois et al., Neuroimage, in press), we perform the first simulations of blood flow in an anatomically accurate large human intra-cortical vascular network (~10000 segments), using a 1D non-linear model taking into account the complex rheological properties of blood flow in microcirculation. This model predicts blood pressure, blood flow and hematocrit distributions, volumes of functional vascular territories, regional flow at voxel and network scales, etc. Using the same approach, we study flow reorganizations induced by global arteriolar vasodilations (an isometabolic global increase in cerebral blood flow). For small to moderate global vasodilations, the relationship between changes in volume and changes in flow is in close agreement with Grubb's law, providing a quantitative tool for studying the variations of its exponent with underlying vascular architecture. A significant correlation between blood flow and vascular structure at the voxel scale, practically unchanged with respect to baseline, is demonstrated. Furthermore, the effects of localized arteriolar vasodilations, representative of a local increase in metabolic demand, are analyzed. In particular, localized vasodilations induce flow changes, including vascular steal, in the neighboring arteriolar trunks at small distances (<300 μm), while their influence in the neighboring veins is much larger (about 1 mm), which provides an estimate of the vascular point spread function. More generally, for the first time, the hemodynamic component of various functional neuroimaging techniques has been isolated from metabolic and neuronal components, and a direct relationship with several known characteristics of the BOLD signal has been demonstrated.

Simulation study of brain blood flow regulation by intra-cortical arterioles in an anatomically accurate large human vascular network: Part I: methodology and baseline flow

Hemodynamically based functional neuroimaging techniques, such as BOLD fMRI and PET, provide indirect measures of neuronal activity. The quantitative relationship between neuronal activity and the measured signals is not yet precisely known, with uncertainties remaining about the relative contribution by their metabolic and hemodynamic components. Empirical observations have demonstrated the importance of the latter component and suggested that micro-vascular anatomy has a potential influence. The recent development of a 3D computer-assisted method for micro-vascular cerebral network analysis has produced a large quantitative library on the microcirculation of the human cerebral cortex (Cassot et al., 2006), which can be used to investigate the hemodynamic component of brain activation through fluid dynamic modeling. For this purpose, we perform the first simulations of blood flow in an anatomically accurate large human intra-cortical vascular network (~10000 segments), using a 1D non-linear model taking account of the complex rheological properties of blood flow in microcirculation. This model predicts blood pressure, blood flow and hematocrit distributions, as well as volumes of functional vascular territories, and regional flow at voxel and network scales. First, the influence of the prescribed boundary conditions (BCs) on the baseline flow structure is investigated, highlighting relevant lower- and upper-bound BCs. Independent of these BCs, large heterogeneities of baseline flow from vessel to vessel and from voxel to voxel, are demonstrated. These heterogeneities are controlled by the architecture of the intra-cortical vascular network. In particular, a correlation between the blood flow and the proportion of vascular volume occupied by arterioles or venules, at voxel scale, is highlighted. Then, the extent of venous contamination downstream to the sites of neuronal activation is investigated, demonstrating a linear relationship between the catchment surface of the activated area and the diameter of the intra-cortical draining vein.