Multi-branched Model Research Articles

Preparation, Two-Photon Absorption, and Bioimaging Application of a Curcumin-Based Copper(II) Complex

A new multi-branched model Cu(II) complex based on curcumin, namely CuL2(I) (НL = (1E,4Z,6E)-1,7-bis(4-(4-bromobutoxy)-3-methoxyphenyl)-5-hydroxyhepta-1,4,6-trien-3-one, C29H34O6Br2), was prepared and its two-photon absorption (TPA) properties were described in the femtosecond regime. The experimental results showed that complex I exhibited relatively strong and wide-dispersed two-photon activities in the near-infrared (NIR) regime and the calculated TPA cross section of complex I was as high as 872 GM (1 GM = 10−50 cm4 s photon−1) in DMF. Additionally, complex I revealed its potential application as a biological fluorescent probe due to its good photo-physical properties and low cytotoxicity, as well as excellent stability and specificity for optical imaging of tumors. Complex I was characterized by single crystal X-ray diffraction too (CIF file CCDC no. 1412447).

A multiscale chemomechanics theory for the solvent – Assisted recycling of covalent adaptable network polymers

Thermosetting polymers are hard to be recycled using conventional methods due to their permanently crosslinked networks. It was recently reported that covalent adaptable network (CAN) polymers could be fully decomposed in organic solvents utilizing bond-exchange reactions (BERs). Re-polymerization occurs by heating the decomposed solution to evaporate the solvent. This prominent feature of CANs provides exciting opportunities to enable the green and sustainable recycling of thermosets. In this paper, we develop a multiscale chemomechanics theory to study the re-polymerization process of CANs, where the soluble chain segments connect at the tails via BERs. At the macromolecular level, the chemical reaction rates are formulated by considering the distance and diffusivity of reactive species, which determine the average chain segment length and network degree of curing (DoC). The evolution rule of DoC is then fed into the continuum-level multi-branched model to capture the thermomechanical properties of CANs at different curing states. The established theory can predict the conversion ratio of functional groups, solution viscosity, volume shrinkage, and glass transition behaviors of re-polymerizing CANs. It also reveals the influencing mechanisms of various material and processing conditions, which paves the road for the immediate engineering applications of the green and sustainable recycling approach for thermosets and their composites.

Pulse pressure amplification and augmentation index change in opposite manner with arterial stiffness independently of systemic resistance

BackgroundPulse Pressure Amplification (PPA) is the increase in Pulse Pressure (PP) from proximal to distal arteries. The Augmentation Index (AIx) is the secondary increase in aortic pressure in systole relative to PP. With aging and increased arterial stiffness the PPA decreases while the AIx increases. Since both depend on the reflection of pressure waves, the finding that PPA and AIx change in opposite ways seems surprising.MethodsAortic PPA, AIx and Reflection Magnitude (RM = Preflected/Pforward) were determined in a multibranched model and during control and Valsalva Maneuver in the human.ResultsDuring the Valsalva Maneuver reflections decrease: the lower mean arterial pressure results in lower stiffness and Pulse Wave Velocity (PWV) while Systemic Vascular Resistance (SVR) is increased. The model confirms that SVR plays a minimal role in terms of reflections. Reflections result from many reflections sites in the larger arteries. The lower PWV implies shorter wave length and thus artery length/wave length increases. This increase makes the differences in travel times from the many reflection sites to the heart more different resulting in lower total reflection: RM and AIx decrease. The lower PWV, thus the shorter wave length, also implies an increase in travel time over the aorta, and larger amplification. (It has been shown that local reflections change little with changes in stiffness.)ConclusionsReflections are mainly determined by travel times of reflected waves of the larger arteries. Mean pressure determines arterial stiffness and the stiffness change, via PWV, results in the opposite changes in RM and PPA.

An Elaborated Multi-Branched Model of Human Arteries

Blood pressure pulse wave is propagated from heart to peripheral blood vessels with changing its waveform according to characteristics of pass way. Dynamic characteristics of total arteries have been investigated by wave equation on multi-branched arterial model. Some diseases, such as an abdominal aortic aneurysm, can be predicted by using the relation between the pulse waveform and arterial stiffness. The aim of this research is to propose a new method to detect such diseases based on the pulse wave propagation model on an arterial tree. In this paper, influences of tissue surrounding an artery, model of peripheral arteries and elasticity of arteries are investigated to elaborate a multi-branched arterial model of human body.

Two-photon absorption and optical power limiting properties in femtosecond regime of novel multi-branched chromophores based on tri-substituted olefinic scaffolds

Two new multi-branched model fluorophores based on tri-substituted olefinic skeletons had been synthesized and their degenerate two-photon absorption properties were characterized by ultra-short laser pulses in the femtosecond regime. The experimental results show that the studied chromophore structures exhibit relatively strong and wide-dispersed two-photon activities in the near infra-red (NIR) regime. It is demonstrated that molecular structures with expanded π-frameworks derived from multi-substituted olefin moieties would possess large molecular nonlinear absorptivities within the studied spectral region. Two-photon absorption based optical power limiting behaviors in the femtosecond time domain of these model compounds were also explored and the results indicate that such a structural motif could be a useful molecular design approach towards strong two-photon absorbing material systems for quick-responsive and broadband optical-suppressing related applications, especially when against ultra-short laser pulses.

A multi-segmented human bioheat model for transient and asymmetric radiative environments

This paper aims to improve the Salloum et al. multi-node multi-segmented model [M. Salloum, N. Ghaddar, K. Ghali, A new transient bio-heat model of the human body and its integration to clothing models, Int. J. Therm. Sci. 46 (4) (2007) 371–384] to accurately predict the circumferential skin temperature variation of nude and clothed human body segments when subject to complex transient and spatially non-uniform radiative environments. The passive bioheat model segments the body into the 15 cylindrical segments. Each body segment is divided into one core node, six angular skin nodes, one artery blood node, and one vein blood node. The model calculates the blood circulation using the Avolio model [A.P. Avolio, Multi-branched model of the human arterial system, Med. Biol. Eng. Comp. 18 (1980) 709–718] for arteries and arterioles up to 2 mm in diameter and the Olufsen et al., semi-analytical model [M.S. Olufsen, C.S. Peskin, W.Y. Kim, E.M. Pedersen, A. Nadim, J. Larsen, Numerical simulation and experimental validation of blood flow in arteries with structured tree outflow conditions, Ann. Biomed. Eng. 28 (11) (2000) 1281–1299] for small arteries and arterioles up to a minimum diameter of 0.3 mm; thus improving prediction of blood perfusion rates in the skin. Unsteady bioheat equations are simultaneously solved for the nodes of each body segment to predict the skin, tympanic, and core temperatures, sweat rates, and the dry and latent heat losses. The nude body thermal model is integrated to a clothing model that takes into consideration the moisture adsorption by the fibers to predict heat and mass diffusion through the clothing layers. The clothing layer is divided into six parts that are aligned to the skin sub-nodes for each clothed segment. The local and mean skin temperature can then be estimated in response to non-uniform environments. The nude body and the clothed model predictions were compared with published experimental data at a variety of ambient conditions, non-uniform conditions and activity levels. The current model agreed well with experimental data during transitions from hot to cold, dry to humid environments, and in asymmetric radiative environments. Both the nude and clothed human models have an accuracy of less than 6% for the whole-body heat gains or losses; the nude human model has an accuracy of ±0.35 °C for skin temperature values.

A new transient bioheat model of the human body and its integration to clothing models

A mathematical multi-segmented model based on an improved Stolwijk model is developed for predicting nude human thermal and regulatory responses within body segments and the environment. The passive model segments the body into the 15 cylindrical segments. Each body segment is divided into four nodes of core, skin, artery blood, and vein blood. In any body element, the blood exiting the arteries and flowing into the capillaries is divided into blood flowing in the core (exchanges heat by perfusion in the core) and blood flowing into the skin layer (exchanges heat by perfusion in the skin). The model calculates the blood circulation flow rates based on exact physiological data of Avolio [A.P. Avolio, Multi-branched model of the human arterial system, Med. Biol. Eng. Comp. 18 (1980) 709–718] and real dimensions and anatomic positions of the arteries in the body. The inclusion of calculated blood perfusion in the tissue is based on the pulsating arterial system model and the heart rate is unique for the current model. The nude body model is integrated to an existing clothing model based on heat and mass diffusion through the clothing layers and takes into consideration the moisture adsorption by the fibers. The bioheat human model is capable of predicting accurately nude human transient physiological responses such as the body's skin, tympanic, and core temperatures, sweat rates, and the dry and latent heat losses from each body segment. The nude and clothed body models predictions are compared with published experimental data at a variety of ambient conditions and activity. The current model agrees well with experimental data during transitions from hot to cold environments and during changes in metabolic rate. Both the nude and clothed human model have an accuracy of less than 8% for the whole-body heat gains or losses; the nude human model has an accuracy of ± 0.48 ° C for skin temperature values.

A method for patient-specific adjustment of the multi-branched model estimating hemodynamic parameters in the human arterial system

A method for patient-specific adjustment of the multi-branched model estimating hemodynamic parameters in the human arterial system

Pressure wave propagation in a multibranched model of the human upper limb

The influence of the large arteries and the peripheral load on pressure wave propagation in the human upper limb was investigated in an anatomically realistic multibranched model based on linear transmission theory. To mimic vascular changes seen in life, the viscoelastic properties of large arteries and the peripheral load properties (represented as modified windkessels) were altered as follows: Young's modulus (from 10.9 x 10(6) to 15.3 x 10(6) dyn/cm2) and phase (from 0 to 15 degrees) of the complex elastance, windkessel time constant (from 0 to 0.6 s), and peripheral reflection coefficient (from 0 to 0.95). The relationship between the central aortic and peripheral radial pressure waveforms was analyzed in the time and the frequency domain. Results indicate that the large arterial properties have less influence (peak systolic pressure changed by 3% and peak of transfer function changed by 29%) than the properties of the peripheral load (systolic pressure changed by 14% and peak of transfer function changed by 74%) on the pressure wave propagation in the upper limb.

Functional origin of reflected pressure waves in a multibranched model of the human arterial system

The effects of wave travel and wave reflection were simulated in a mathematical model of the whole arterial tree consisting of 142 uniform transmission line segments. The arterial model was partitioned into three separate segments: upper limbs, trunk, and lower limbs. Aging was simulated by increasing average pulse wave velocities of these segments (10.9-12.9, 8.0-11.7, and 9.0-11.3 m/s for upper limbs, trunk, and lower limbs, respectively). Reflection coefficients at the terminal elements were altered to simulate vasodilation (0.0) and vasoconstriction (0.95). The impedance patterns and spatial distribution of pressure waveforms generated by the model simulating aging and vasoconstriction were similar to in vivo measurements by other investigators. Reflected pressure waves from each segment reached the ascending aorta and contributed differently to the late systolic peak on the aortic pressure wave. Aging does not alter the origin of these reflected pressure waves in the trunk. Aortic impedance and pressure wave changes induced by simulation of dilation of splanchnic bed were similar to those observed experimentally with nitroglycerin.

Distensibility and pressure-flow relationship of the pulmonary circulation. I. Single-vessel model

To ascertain the relative contributions of vascular distensibility and nonhomogeneous behavior within the pulmonary circulation to the distinctive nonlinear relationship between inflow pressure (Pin) and flow [pressure-flow (P-F) relationship] and between Pin and outflow pressure (Pout) at constant flow (Pin-Pout relationship), we developed a multibranched model in which the elastic behavior of, and forces acting on, individual branches can be varied independently. The response of the multibranched model is described in the companion article (J. Appl. Physiol. 68: 1514-1527, 1990). Here we describe the methods used and the responses of single components of the larger model. Perivascular pressure is modeled as a function of intravascular and transpulmonary pressures (Pv and Ptp, respectively) and vessel length as a function of lung volume. These and the relationship between vascular area (A) and transmural pressure (Ptm) were modeled primarily from the dog data of Smith and Mitzner (J. Appl. Physiol. 48: 450-467, 1980). Vasomotor tone is modeled as a radial collapsing pressure (Pt) in the same plane as Ptm. In view of lack of information about the relationship between Pt and A for a given active state, different patterns were assumed that span a wide range of possible relationships. The P-F and Pin-Pout relationships of single vessels were very similar to those reported for the entire intact circulation. Of note, the slope of the Pin-Pout relationship in the low Pout range (0-5 Torr) was very low (less than 0.25) and increased gradually with Pout toward unity. Vasomotor tone caused an apparent parallel shift in the P-F relationship in the physiological flow range of the dog (2-8 l/min) regardless of the pattern used to model the Pt vs. A relationship; different patterns affected the P-F relationship only over the low flow range before the parallel shift was established.

Distensibility and pressure-flow relationship of the pulmonary circulation. II. Multibranched model

The contribution of distensibility and recruitment to the distinctive behavior of the pulmonary circulation is not known. To examine this question we developed a multibranched model in which an arterial vascular bed bifurcates sequentially up to 8 parallel channels that converge and reunite at the venous side to end in the left atrium. Eight resistors representing the capillary bed separate the arterial and venous beds. The elastic behavior of capillaries and extra-alveolar vessels was modeled after Fung and Sobin (Circ. Res. 30: 451-490, 1972) and Smith and Mitzner (J. Appl. Physiol. 48: 450-467, 1980), respectively. Forces acting on each component are modified and calculated individually, thus enabling the user to explore the effects of parallel and longitudinal heterogeneities in applied forces (e.g., gravity, vasomotor tone). Model predictions indicate that the contribution of distensibility to nonlinearities in the pressure-flow (P-F) and atrial-pulmonary arterial pressure (Pla-Ppa) relationships is substantial, whereas gravity-related recruitment contributes very little to these relationships. In addition, Pla-Ppa relationships, obtained at a constant flow, have no discriminating ability in identifying the presence or absence of a waterfall along the circulation. The P-F relationship is routinely shifted in a parallel fashion, within the physiological flow range, whenever extra forces (e.g., lung volume, tone) are applied uniformly at one or more branching levels, regardless of whether a waterfall is created. For a given applied force, the magnitude of parallel shift varies with proportion of the circulation subjected to the added force and with Pla.

Effect of glyceryl trinitrate on peripheral arteries alters left ventricular hydraulic load in man.

Effects of sublingual glyceryl trinitrate (GTN) were studied in ten patients without heart failure during diagnostic cardiac catheterisation following angiography. GTN caused substantial reduction in peak left ventricular and aortic pressure (19 mmHg) with lesser reduction in mean aortic pressure (9 mmHg) and no change in diastolic aortic pressure. Reduction in stroke volume (by 15%), associated with fall in left ventricular end diastolic pressure (by 4 mmHg) was insufficient to explain the marked (17 mmHg - 34%) reduction in pulse pressure. Decrease in pulse pressure was associated with loss of the late systolic peak on both the aortic and left ventricular pressure wave. This peak is caused by pulse wave reflection. GTN caused no change in peripheral resistance or in indices of aortic compliance (characteristic impedance, total arterial compliance) but was associated with reduction in fluctuations of both modulus and phase of aortic impedance. All these changes in pressure waves and in impedance spectra are explicable on the basis of decreased peripheral wave reflection. This can be attributed to the known vasodilatory effect of GTN on the peripheral arteries. Simulation of arterial vasodilatation in a multi-branched model of the systemic arterial system confirmed this interpretation. Dilatation of peripheral arteries explains in part the beneficial effects of GTN in adult man.

Multi-branched model of the human arterial system.

A model of the human arterial system was constructed based on the anatomical branching structure of the arterial tree. Arteries were divided into segments represented by uniform thin-walled elastic tubes with realistic arterial dimensions and wall properties. The configuration contains 128 segments accounting for all the central vessels and major peripheral arteries supplying the extremities including vessels of the order of 2·0 mm diameter. Vascular impedance and pressure and flow waveforms were determined at various locations in the system and good agreement was found with experimental measurements. Use of the model is illustrated in investigating wave propagation in the arterial system and in simulation of arterial dynamics in such pathological conditions as arteriosclerosis and presence of a stenosis in the femoral artery.

Pulsatile flow and pressure in human systemic arteries. Studies in man and in a multibranched model of the human systemic arterial tree.

Pulsatile flow and pressure in human systemic arteries. Studies in man and in a multibranched model of the human systemic arterial tree.

Beat-to-beat alterations in relationship of simultaneously recorded central and peripheral arterial pressure pulses during Valsalva maneuver and prolonged expiration in man.

ARTICLESBeat-to-Beat Alterations in Relationship of Simultaneously Recorded Central and Peripheral Arterial Pressure Pulses During Valsalva Maneuver and Prolonged Expiration in ManEdwin J. Kroeker, and Earl H. WoodEdwin J. Kroeker, and Earl H. WoodPublished Online:01 Mar 1956https://doi.org/10.1152/jappl.1956.8.5.483MoreSectionsPDF (2 MB)Download PDF ToolsExport citationAdd to favoritesGet permissionsTrack citations ShareShare onFacebookTwitterLinkedInWeChat Back to Top Next Download PDF FiguresReferencesRelatedInformation Cited ByValidation of non-invasive central blood pressure devices: ARTERY Society task force consensus statement on protocol standardization30 January 2017 | European Heart Journal, Vol. 38, No. 37Mechanism of a hypertensive response to exerciseJournal of the American College of Cardiology, Vol. 44, No. 7Reconstruction of brachial pressure from finger arterial pressure during orthostasisJournal of Hypertension, Vol. 22, No. 10Validity and Reliability of Diastolic Pulse Contour Analysis (Windkessel Model) in HumansHypertension, Vol. 39, No. 5On-line Synthesis of the Human Ascending Aortic Pressure Pulse From the Finger PulseHypertension, Vol. 30, No. 6Hemodynamic correlates of effective arterial elastance in mitral stenosis before and after balloon valvotomyPatrice Colin, Michel Slama, Alec Vahanian, Yves Lecarpentier, Gilbert Motté, and Denis Chemla1 October 1997 | Journal of Applied Physiology, Vol. 83, No. 4Regional wave travel and reflections along the human aorta: a study with six simultaneous micromanometric pressures.Circulation, Vol. 72, No. 6An approach to the noninvasive periodic assessment of arterial elasticity in the youngPreventive Medicine, Vol. 13, No. 2Valsalva maneuver and input impedance.Circulation, Vol. 64, No. 5Angiography and LMCA stenosis.Circulation, Vol. 64, No. 5Sulfinpyrazone and thromboembolism.Circulation, Vol. 64, No. 5Pulsatile flow and pressure in human systemic arteries. Studies in man and in a multibranched model of the human systemic arterial tree.Circulation Research, Vol. 46, No. 3Effect of Age, Cardiovascular Disease, and Vasomotor Changes on Transmission of Arterial Pressure Waves Through the Lower Extremities2 July 2016 | Angiology, Vol. 29, No. 8The arterial pulse— clinical manifestationsCurrent Problems in Cardiology, Vol. 2, No. 5Characteristics of Aortic Diastolic Pressure Decay with Application to the Continuous Monitoring of Changes in Peripheral Vascular ResistanceCirculation Research, Vol. 35, No. 1Delayed systolic peak of the femoral pulse from kinking of the aortic archThe American Journal of Cardiology, Vol. 33, No. 2The arterial pulse in health and diseaseAmerican Heart Journal, Vol. 82, No. 5Digital Systolic Pressures in the Lower Limb in Arterial DiseaseCirculation, Vol. 43, No. 6Dicrotic Pulse after Open Heart OperationCirculation, Vol. 42, No. 6Computer modeling of the human systemic arterial treeJournal of Biomechanics, Vol. 1, No. 4Pressure Wave Transmission along the Human AortaCirculation Research, Vol. 23, No. 4 More from this issue > Volume 8Issue 5March 1956Pages 483-494 https://doi.org/10.1152/jappl.1956.8.5.483PubMed13295161History Published online 1 March 1956 Published in print 1 March 1956 Metrics

Studies on the relations between pressure and flow in the circulation

Simple theoretical models are proposed for the study of the interdependence between cardiac contraction, arterial pressure, and capillary drainage. The relation between pressure and flow is derived for a model of branching distensible tubes taking into account the finite pulse wave velocity. Equations are derived both for the case where the pulse wave is non-distorted and for the case where the wave is damped and distorted to a limited extent. Following the model of J. W. Remington and W. F. Hamilton (1947), the former case is applied to the larger arteries. Expressions are developed for the stroke volume, cardiac ejection, and systolic arterial storage in both the steady and non-steady states. Expressions for the percentage discrepancy involved in the computation of these quantities from a single tube model as contrasted with a multi-branched model are derived. For typical cases these discrepancies are small and thus credence is lent to the further use of the simpler single tube model which requires fewer independent parameters. It is also shown that the formulae for stroke volume and arterial storage are only slightly sensitive to changes in pulse wave velocities, and that for some purposes it would seem permissible to assume an infinite velocity.