Fractal Properties of Perfusion Heterogeneity in Optimized Arterial Trees

Regional blood flows in the heart muscle are remarkably heterogeneous. It is very likely that the most important factor for this heterogeneity is the metabolic need of the tissue rather than flow dispersion by the branching network of the coronary vasculature. To model the contribution of tissue needs to the observed flow heterogeneities we use arterial trees generated on the computer by constrained constructive optimization. This method allows to prescribe terminal flows as independent boundary conditions, rather than obtaining these flows by the dispersive effects of the tree structure. We study two specific cases: equal terminal flows (model 1) and terminal flows set proportional to the volumes of Voronoi polyhedra used as a model for blood supply regions of terminal segments (model 2). Model 1 predicts, depending on the number Nterm of end-points, fractal dimensions D of perfusion heterogeneities in the range 1.20 to 1.40 and positively correlated nearest-neighbor regional flows, in good agreement with experimental data of the normal heart. Although model 2 yields reasonable terminal flows well approximated by a lognormal distribution, it fails to predict D and nearest-neighbor correlation coefficients r1 of regional flows under normal physiologic conditions: model 2 gives D = 1.69 ± 0.02 and r1 = −0.18 ± 0.03 (n = 5), independent of Nterm and consistent with experimental data observed under coronary stenosis and under the reduction of coronary perfusion pressure. In conclusion, flow heterogeneity can be modeled by terminal positions compatible with an existing tree structure without resorting to the flow-dispersive effects of a specific branching tree model to assign terminal flows.

Download Full-text

High correlation of fractals for regional blood flows among resting and exercising skeletal muscles

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.1995.269.1.h7 ◽

1995 ◽

Vol 269 (1) ◽

pp. H7-H13 ◽

Cited By ~ 1

Author(s):

P. O. Iversen ◽

G. Nicolaysen

Keyword(s):

Blood Flow ◽

Skeletal Muscles ◽

Regional Blood Flow ◽

Fractal Dimensions ◽

Strongly Correlated ◽

Blood Flows ◽

Exercise Hyperemia ◽

Regional Blood Flows ◽

Resting Muscle ◽

Surprising Finding

The regional blood flow distributions within single skeletal muscles are markedly uneven both at rest and during exercise hyperemia. Fractals adequately describe this perfusion heterogeneity in the resting lateral head of the gastrocnemius muscle as well as in the myocardium. Recently, we provided evidence that the fractal dimension for the blood flow distributions in this resting muscle was strongly correlated with that of the myocardium in the same rabbit. Prompted by this hitherto unknown observation, we have now examined 1) whether fractals also describe perfusion distributions within muscles with a varying metabolic activity, and 2) whether the fractal dimensions for blood flow distributions to these muscles were correlated. We used pentobarbital-anesthetized rabbits and cats. The regional distributions of blood flow within various skeletal muscles were estimated by microsphere trapping. The data unequivocally showed that the perfusion distributions could be described with fractals both in resting and in exercising muscle in both species, the corresponding fractal dimensions ranging from 1.36 to 1.41. The fractal dimensions were markedly correlated (r2 ranged from 0.82 to 0.88) when both various resting and resting plus exercising muscles were compared in the same animal. This surprising finding of high correlations for the fractal dimensions among various muscles within one animal provides a novel characteristic of blood flow heterogeneity.

Download Full-text

The effect of adrenomedullin, amylin fragment 8-37 and calcitonin generelated peptide on contractile force, heart rate and coronary perfusion pressure in isolated rat hearts

Acta Physiologica Hungarica ◽

10.1556/aphysiol.90.2003.2.6 ◽

2003 ◽

Vol 90 (2) ◽

pp. 133-146 ◽

Cited By ~ 10

Author(s):

Z Kaygısız ◽

N Erkasap ◽

R Uyar ◽

S Kabadere ◽

TE Kabadere ◽

...

Keyword(s):

Heart Rate ◽

Perfusion Pressure ◽

Coronary Perfusion Pressure ◽

Contractile Force ◽

Coronary Perfusion ◽

Rat Hearts ◽

Isolated Rat

Download Full-text

Contribution of extravascular compression to reduction of maximal coronary blood flow

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.1992.262.1.h68 ◽

1992 ◽

Vol 262 (1) ◽

pp. H68-H77

Author(s):

F. L. Abel ◽

R. R. Zhao ◽

R. F. Bond

Keyword(s):

Blood Flow ◽

Coronary Blood Flow ◽

Coronary Flow ◽

Perfusion Pressure ◽

Left Ventricular Pressure ◽

Coronary Perfusion Pressure ◽

Left Ventricular ◽

Ventricular Pressure ◽

Coronary Perfusion ◽

Storage Site

Effects of ventricular compression on maximally dilated left circumflex coronary blood flow were investigated in seven mongrel dogs under pentobarbital anesthesia. The left circumflex artery was perfused with the animals' own blood at a constant pressure (63 mmHg) while left ventricular pressure was experimentally altered. Adenosine was infused to produce maximal vasodilation, verified by the hyperemic response to coronary occlusion. Alterations of peak left ventricular pressure from 50 to 250 mmHg resulted in a linear decrease in total circumflex flow of 1.10 ml.min-1 x 100 g heart wt-1 for each 10 mmHg of peak ventricular to coronary perfusion pressure gradient; a 2.6% decrease from control levels. Similar slopes were obtained for systolic and diastolic flows as for total mean flow, implying equal compressive forces in systole as in diastole. Increases in left ventricular end-diastolic pressure accounted for 29% of the flow changes associated with an increase in peak ventricular pressure. Doubling circumferential wall tension had a minimal effect on total circumflex flow. When the slopes were extrapolated to zero, assuming linearity, a peak left ventricular pressure of 385 mmHg greater than coronary perfusion pressure would be required to reduce coronary flow to zero. The experiments were repeated in five additional animals but at different perfusion pressures from 40 to 160 mmHg. Higher perfusion pressures gave similar results but with even less effect of ventricular pressure on coronary flow or coronary conductance. These results argue for an active storage site for systolic arterial flow in the dilated coronary system.

Download Full-text

3D ultrasound coronarography: first proof of concept study on isolated beating rat hearts

European Heart Journal - Cardiovascular Imaging ◽

10.1093/ehjci/jeaa356.011 ◽

2021 ◽

Vol 22 (Supplement_1) ◽

Author(s):

O Demeulenaere ◽

P Mateo ◽

P Sandoval ◽

O Villemain ◽

M Tanter ◽

...

Keyword(s):

Contrast Agents ◽

Flow Velocity ◽

Coronary Flow ◽

3D Ultrasound ◽

Frame Rate ◽

Doppler Imaging ◽

Coronary Perfusion ◽

Blood Flows ◽

Flow Reserve ◽

Rat Hearts

Abstract Funding Acknowledgements Type of funding sources: Foundation. Main funding source(s): Bettencourt Foundation Background/Introduction We demonstrated recently that Ultrafast ultrasound Doppler imaging can image the intramyocardial coronary circulation in beating hearts of large animals and patients [1]. Yet, ultrasound spatial resolution remains limited by wave physics and coronaries smaller than ∼100 µm could not be imaged. Ultrasound Localization Microscopy (ULM) [2] was recently introduced to tackle this issue and exploit the micrometric localization of microbubble contrast agents at ultrafast frame rate in order to image blood flows in micrometer vessels. Purpose The objective of this work was to demonstrate that 3D ultrafast ultrasound with contrast agents can provide the full 3D mapping of the coronary microcirculation with quantitative flow velocity on a beating rat heart. Methods Acquisitions were performed on ex vivo rat hearts (n = 5) with retrograde perfusion (Langendorff model). A flow of a Krebs–Henseleit solution mixed with a diluted microbubbles solution (0.22%) was perfused at controlled pressure into the coronary arteries (between 5 and 15 mL/min). We used a 32 × 32 elements, 8-MHz matrix-array ultrasound transducer connected to a 1024-channel programmable ultrasound scanner. An ultrafast Doppler imaging sequence consisting of 9 plane waves was transmitted at a PRF of 20 kHz during 270 ms and repeated 40 times. After beamforming and SVD clutter filtering, the microbubbles were localized and tracked in 3D. Flow velocity were mapped at baseline and after infusion of Adenosine (10e-5 µMol) at constant coronary perfusion pressure (120 mm Hg). Eventually, the hearts were fixed using formaldehyde perfusion and imaged by µCT after injection of radio opaque agent. Results We successfully imaged the coronary blood flows of entire rat hearts. It revealed the entire vasculature from large main coronaries arteries (cross section up to 1 mm) to small arterioles (smaller than 40 µm). Coronary flow velocities ranged from [1 – 50] cm/s depending on the arteries diameter. Velocity estimates were validated in vitro in tubes of Ø0.58mm and were in good agreement with theoretical values of a Poiseuille’s flow (relative ratio of 10% for maximum velocities). After Adenosine infusion, perfusion flow rates increased 102% ± 50% (p < 0.05) on average. Eventually, anatomy revealed by 3D ultrasound coronarography was in accordance with the anatomy revealed by the µCT. Conclusion(s) We demonstrated the feasibility of 3D ultrasound coronarography on isolated beating rat hearts. This technique has the potential to become a novel imaging tool to investigate the coronary micro-circulation and quantify non-invasively the Coronary Flow Reserve (CFR). Abstract Figure. Ultrasound coronarography

Download Full-text

Cardiac arrest complicating cardiogenic shock: from pathophysiological insights to Impella-assisted cardiopulmonary resuscitation in a pheochromocytoma-induced Takotsubo cardiomyopathy—a case report

European Heart Journal - Case Reports ◽

10.1093/ehjcr/ytab092 ◽

2021 ◽

Vol 5 (3) ◽

Author(s):

Filippo Zilio ◽

Simone Muraglia ◽

Roberto Bonmassari

Keyword(s):

Cardiac Arrest ◽

Cardiopulmonary Resuscitation ◽

Left Ventricle ◽

Cardiogenic Shock ◽

Takotsubo Cardiomyopathy ◽

Perfusion Pressure ◽

Coronary Perfusion Pressure ◽

Left Ventricular ◽

Coronary Perfusion ◽

Refractory Cardiac Arrest

Abstract Background A ‘catecholamine storm’ in a case of pheochromocytoma can lead to a transient left ventricular dysfunction similar to Takotsubo cardiomyopathy. A cardiogenic shock can thus develop, with high left ventricular end-diastolic pressure and a reduction in coronary perfusion pressure. This scenario can ultimately lead to a cardiac arrest, in which unloading the left ventricle with a peripheral left ventricular assist device (Impella®) could help in achieving the return of spontaneous circulation (ROSC). Case summary A patient affected by Takotsubo cardiomyopathy caused by a pheochromocytoma presented with cardiogenic shock that finally evolved into refractory cardiac arrest. Cardiopulmonary resuscitation was performed but ROSC was achieved only after Impella® placement. Discussion In the clinical scenario of Takotsubo cardiomyopathy due to pheochromocytoma, when cardiogenic shock develops treatment is difficult because exogenous catecholamines, required to maintain organ perfusion, could exacerbate hypertension and deteriorate the cardiomyopathy. Moreover, as the coronary perfusion pressure is critically reduced, refractory cardiac arrest could develop. Although veno-arterial extra-corporeal membrane oxygenation (va-ECMO) has been advocated as the treatment of choice for in-hospital refractory cardiac arrest, in the presence of left ventricular overload a device like Impella®, which carries fewer complications as compared to ECMO, could be effective in obtaining the ROSC by unloading the left ventricle.

Download Full-text

Esmolol during cardiopulmonary resuscitation reduces neurological injury in a porcine model of cardiac arrest

Scientific Reports ◽

10.1038/s41598-021-90202-w ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Laura Ruggeri ◽

Francesca Nespoli ◽

Giuseppe Ristagno ◽

Francesca Fumagalli ◽

Antonio Boccardo ◽

...

Keyword(s):

Cardiopulmonary Resuscitation ◽

Porcine Model ◽

Neuronal Degeneration ◽

Neuron Specific Enolase ◽

Coronary Perfusion Pressure ◽

Neurological Injury ◽

Saline Control ◽

Preclinical Model ◽

Coronary Perfusion ◽

To Receive

AbstractPrimary vasopressor efficacy of epinephrine during cardiopulmonary resuscitation (CPR) is due to its α-adrenergic effects. However, epinephrine plays β1-adrenergic actions, which increasing myocardial oxygen consumption may lead to refractory ventricular fibrillation (VF) and poor outcome. Effects of a single dose of esmolol in addition to epinephrine during CPR were investigated in a porcine model of VF with an underlying acute myocardial infarction. VF was ischemically induced in 16 pigs and left untreated for 12 min. During CPR, animals were randomized to receive epinephrine (30 µg/kg) with either esmolol (0.5 mg/kg) or saline (control). Pigs were then observed up to 96 h. Coronary perfusion pressure increased during CPR in the esmolol group compared to control (47 ± 21 vs. 24 ± 10 mmHg at min 5, p < 0.05). In both groups, 7 animals were successfully resuscitated and 4 survived up to 96 h. No significant differences were observed between groups in the total number of defibrillations delivered prior to final resuscitation. Brain histology demonstrated reductions in cortical neuronal degeneration/necrosis (score 0.3 ± 0.5 vs. 1.3 ± 0.5, p < 0.05) and hippocampal microglial activation (6 ± 3 vs. 22 ± 4%, p < 0.01) in the esmolol group compared to control. Lower circulating levels of neuron specific enolase were measured in esmolol animals compared to controls (2[1–3] vs. 21[16–52] ng/mL, p < 0.01). In this preclinical model, β1-blockade during CPR did not facilitate VF termination but provided neuroprotection.

Download Full-text

Low Cost Automatic Reconstruction of Tree Structure by AdQSM with Terrestrial Close-Range Photogrammetry

Forests ◽

10.3390/f12081020 ◽

2021 ◽

Vol 12 (8) ◽

pp. 1020

Author(s):

Yanqi Dong ◽

Guangpeng Fan ◽

Zhiwu Zhou ◽

Jincheng Liu ◽

Yongguo Wang ◽

...

Keyword(s):

Root Mean Square Error ◽

Mean Square Error ◽

Root Mean Square ◽

Low Cost ◽

Reference Value ◽

Tree Height ◽

Point Clouds ◽

Tree Structure ◽

Mean Square ◽

Tree Model

The quantitative structure model (QSM) contains the branch geometry and attributes of the tree. AdQSM is a new, accurate, and detailed tree QSM. In this paper, an automatic modeling method based on AdQSM is developed, and a low-cost technical scheme of tree structure modeling is provided, so that AdQSM can be freely used by more people. First, we used two digital cameras to collect two-dimensional (2D) photos of trees and generated three-dimensional (3D) point clouds of plot and segmented individual tree from the plot point clouds. Then a new QSM-AdQSM was used to construct tree model from point clouds of 44 trees. Finally, to verify the effectiveness of our method, the diameter at breast height (DBH), tree height, and trunk volume were derived from the reconstructed tree model. These parameters extracted from AdQSM were compared with the reference values from forest inventory. For the DBH, the relative bias (rBias), root mean square error (RMSE), and coefficient of variation of root mean square error (rRMSE) were 4.26%, 1.93 cm, and 6.60%. For the tree height, the rBias, RMSE, and rRMSE were—10.86%, 1.67 m, and 12.34%. The determination coefficient (R2) of DBH and tree height estimated by AdQSM and the reference value were 0.94 and 0.86. We used the trunk volume calculated by the allometric equation as a reference value to test the accuracy of AdQSM. The trunk volume was estimated based on AdQSM, and its bias was 0.07066 m3, rBias was 18.73%, RMSE was 0.12369 m3, rRMSE was 32.78%. To better evaluate the accuracy of QSM’s reconstruction of the trunk volume, we compared AdQSM and TreeQSM in the same dataset. The bias of the trunk volume estimated based on TreeQSM was −0.05071 m3, and the rBias was −13.44%, RMSE was 0.13267 m3, rRMSE was 35.16%. At 95% confidence interval level, the concordance correlation coefficient (CCC = 0.77) of the agreement between the estimated tree trunk volume of AdQSM and the reference value was greater than that of TreeQSM (CCC = 0.60). The significance of this research is as follows: (1) The automatic modeling method based on AdQSM is developed, which expands the application scope of AdQSM; (2) provide low-cost photogrammetric point cloud as the input data of AdQSM; (3) explore the potential of AdQSM to reconstruct forest terrestrial photogrammetric point clouds.

Download Full-text

LATTICE DYNAMICS OF THE BINARY APERIODIC CHAINS OF ATOMS I: FRACTAL DIMENSION OF PHONON SPECTRA

International Journal of Modern Physics B ◽

10.1142/s0217979295000628 ◽

1995 ◽

Vol 09 (12) ◽

pp. 1429-1451 ◽

Cited By ~ 4

Author(s):

WŁODZIMIERZ SALEJDA

Keyword(s):

Fractal Dimension ◽

Lattice Dynamics ◽

Nearest Neighbor ◽

Average Distance ◽

Local Maximum ◽

Fractal Dimensions ◽

Dimension Formula ◽

Phonon Spectra ◽

Wide Range ◽

Silver Mean

The microscopic harmonic model of lattice dynamics of the binary chains of atoms is formulated and studied numerically. The dependence of spring constants of the nearest-neighbor (NN) interactions on the average distance between atoms are taken into account. The covering fractal dimensions [Formula: see text] of the Cantor-set-like phonon spec-tra (PS) of generalized Fibonacci and non-Fibonaccian aperiodic chains containing of 16384≤N≤33461 atoms are determined numerically. The dependence of [Formula: see text] on the strength Q of NN interactions and on R=mH/mL, where mH and mL denotes the mass of heavy and light atoms, respectively, are calculated for a wide range of Q and R. In particular we found: (1) The fractal dimension [Formula: see text] of the PS for the so-called goldenmean, silver-mean, bronze-mean, dodecagonal and Severin chain shows a local maximum at increasing magnitude of Q and R>1; (2) At sufficiently large Q we observe power-like diminishing of [Formula: see text] i.e. [Formula: see text], where α=−0.14±0.02 and α=−0.10±0.02 for the above specified chains and so-called octagonal, copper-mean, nickel-mean, Thue-Morse, Rudin-Shapiro chain, respectively.

Download Full-text