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1.
J Acoust Soc Am ; 151(2): 1200, 2022 02.
Artículo en Inglés | MEDLINE | ID: mdl-35232071

RESUMEN

An in vivo range verification technology for proton beam cancer therapy, preferably in real-time and with submillimeter resolution, is desired to reduce the present uncertainty in dose localization. Acoustical imaging technologies exploiting possible local interactions between protons and microbubbles or nanodroplets might be an interesting option. Unfortunately, a theoretical model capable of characterising the acoustical field generated by an individual proton on nanometer and micrometer scales is still missing. In this work, such a model is presented. The proton acoustic field is generated by the adiabatic expansion of a region that is locally heated by a passing proton. To model the proton heat deposition, secondary electron production due to protons has been quantified using a semi-empirical model based on Rutherford's scattering theory, which reproduces experimentally obtained electronic stopping power values for protons in water within 10% over the full energy range. The electrons transfer energy into heat via electron-phonon coupling to atoms along the proton track. The resulting temperature increase is calculated using an inelastic thermal spike model. Heat deposition can be regarded as instantaneous, thus, stress confinement is ensured and acoustical initial conditions are set. The resulting thermoacoustic field in the nanometer and micrometer range from the single proton track is computed by solving the thermoacoustic wave equation using k-space Green's functions, yielding the characteristic amplitudes and frequencies present in the acoustic signal generated by a single proton in an aqueous medium. Wavefield expansion and asymptotic approximations are used to extend the spatial and temporal ranges of the proton acoustic field.


Asunto(s)
Neoplasias , Terapia de Protones , Acústica , Humanos , Neoplasias/radioterapia , Terapia de Protones/métodos , Protones , Sonido , Agua
2.
J Acoust Soc Am ; 150(1): 428, 2021 07.
Artículo en Inglés | MEDLINE | ID: mdl-34340474

RESUMEN

Shear wave elastography (SWE) has the potential to determine cardiac tissue stiffness from non-invasive shear wave speed measurements, important, e.g., for predicting heart failure. Previous studies showed that waves traveling in the interventricular septum (IVS) may display Lamb-like dispersive behaviour, introducing a thickness-frequency dependency in the wave speed. However, the IVS tapers across its length, which complicates wave speed estimation by introducing an additional variable to account for. The goal of this work is to assess the impact of tapering thickness on SWE. The investigation is performed by combining in vitro experiments with acoustic radiation force (ARF) and 2D finite element simulations, to isolate the effect of the tapering curve on ARF-induced and natural waves in the heart. The experiments show a 11% deceleration during propagation from the thick to the thin end of an IVS-mimicking tapered phantom plate. The numerical analysis shows that neglecting the thickness variation in the wavenumber-frequency domain can introduce errors of more than 30% in the estimation of the shear modulus, and that the exact tapering curve, rather than the overall thickness reduction, determines the dispersive behaviour of the wave. These results suggest that septal geometry should be accounted for when deriving cardiac stiffness with SWE.


Asunto(s)
Diagnóstico por Imagen de Elasticidad , Simulación por Computador , Corazón , Fantasmas de Imagen , Ultrasonografía
3.
J Acoust Soc Am ; 147(5): 3091, 2020 05.
Artículo en Inglés | MEDLINE | ID: mdl-32486810

RESUMEN

Shear wave elastography (SWE) might allow non-invasive assessment of cardiac stiffness by relating shear wave propagation speed to material properties. However, after aortic valve closure, when natural shear waves occur in the septal wall, the stiffness of the muscle decreases significantly, and the effects of such temporal variation of medium properties on shear wave propagation have not been investigated yet. The goal of this work is to fundamentally investigate these effects. To this aim, qualitative results were first obtained experimentally using a mechanical setup, and were then combined with quantitative results from finite difference simulations. The results show that the amplitude and period of the waves increase during propagation, proportional to the relaxation of the medium, and that reflected waves can originate from the temporal stiffness variation. These general results, applied to literature data on cardiac stiffness throughout the heart cycle, predict as a major effect a period increase of 20% in waves propagating during a healthy diastolic phase, whereas only a 10% increase would result from the impaired relaxation of an infarcted heart. Therefore, cardiac relaxation can affect the propagation of waves used for SWE measurements and might even provide direct information on the correct relaxation of a heart.


Asunto(s)
Diagnóstico por Imagen de Elasticidad , Corazón/diagnóstico por imagen
4.
Phys Med Biol ; 63(7): 075015, 2018 03 29.
Artículo en Inglés | MEDLINE | ID: mdl-29508770

RESUMEN

Until now, no matrix transducer has been realized for 3D transesophageal echocardiography (TEE) in pediatric patients. In 3D TEE with a matrix transducer, the biggest challenges are to connect a large number of elements to a standard ultrasound system, and to achieve a high volume rate (>200 Hz). To address these issues, we have recently developed a prototype miniaturized matrix transducer for pediatric patients with micro-beamforming and a small central transmitter. In this paper we propose two multiline parallel 3D beamforming techniques (µBF25 and µBF169) using the micro-beamformed datasets from 25 and 169 transmit events to achieve volume rates of 300 Hz and 44 Hz, respectively. Both the realizations use angle-weighted combination of the neighboring overlapping sub-volumes to avoid artifacts due to sharp intensity changes introduced by parallel beamforming. In simulation, the image quality in terms of the width of the point spread function (PSF), lateral shift invariance and mean clutter level for volumes produced by µBF25 and µBF169 are similar to the idealized beamforming using a conventional single-line acquisition with a fully-sampled matrix transducer (FS4k, 4225 transmit events). For completeness, we also investigated a 9 transmit-scheme (3 × 3) that allows even higher frame rates but found worse B-mode image quality with our probe. The simulations were experimentally verified by acquiring the µBF datasets from the prototype using a Verasonics V1 research ultrasound system. For both µBF169 and µBF25, the experimental PSFs were similar to the simulated PSFs, but in the experimental PSFs, the clutter level was ~10 dB higher. Results indicate that the proposed multiline 3D beamforming techniques with the prototype matrix transducer are promising candidates for real-time pediatric 3D TEE.


Asunto(s)
Ecocardiografía Tridimensional/métodos , Ecocardiografía Transesofágica/métodos , Corazón/diagnóstico por imagen , Fantasmas de Imagen , Ultrasonografía/métodos , Niño , Conjuntos de Datos como Asunto , Humanos , Transductores
5.
Oncogene ; 36(6): 829-839, 2017 02 09.
Artículo en Inglés | MEDLINE | ID: mdl-27452520

RESUMEN

E2F transcription factors are important regulators of the cell cycle, and unrestrained activation of E2F-dependent transcription is considered to be an important driver of tumor formation and progression. Although highly expressed in normal skin and skin cancer, the role of the atypical E2Fs, E2F7 and E2F8, in keratinocyte homeostasis, regeneration and tumorigenesis is unknown. Surprisingly, keratinocyte-specific deletion of E2F7 and E2F8 in mice did not interfere with skin development and wound healing. However, the rate for successful isolation and establishment of E2f7/8-deficient primary keratinocyte cultures was much higher than for wild-type keratinocytes. Moreover, E2f7/8-deficient primary keratinocytes proliferate more efficiently under stress conditions, such as low/high confluence or DNA damage. Application of in vivo stress using the DMBA/TPA skin carcinogenesis protocol revealed that combined inactivation of E2f7/8 enhanced tumorigenesis and accelerated malignant progression. Loss of atypical E2Fs resulted in increased expression of E2F target genes, including E2f1. Additional loss of E2f1 did not rescue, but worsened skin tumorigenesis. We show that loss of E2F7/8 triggers apoptosis via induction of E2F1 in response to stress, indicating that the tumor-promoting effect of E2F7/8 inactivation can be partially compensated via E2F1-dependent apoptosis. Importantly, E2F7/8 repressed a large set of E2F target genes that are highly expressed in human patients with skin cancer. Together, our studies demonstrate that atypical E2Fs act as tumor suppressors, most likely via transcriptional repression of cell cycle genes in response to stress.


Asunto(s)
Factor de Transcripción E2F7/genética , Proteínas Represoras/genética , Neoplasias Cutáneas/patología , Animales , Apoptosis/fisiología , Daño del ADN , Factor de Transcripción E2F7/deficiencia , Humanos , Queratinocitos/patología , Ratones , Ratones Noqueados , Proteínas Represoras/deficiencia , Neoplasias Cutáneas/genética
6.
Eur Heart J Cardiovasc Imaging ; 17(suppl_2): ii242-ii245, 2016 Dec 01.
Artículo en Inglés | MEDLINE | ID: mdl-28415122

RESUMEN

BACKGROUND: The closure of the valves generates shear waves in the heart walls. The propagation velocity of shear waves relates to stiffness. This could potentially be used to estimate the stiffness of the myocardium, with huge potential implications in pathologies characterized by a deterioration of the diastolic properties of the left ventricle. In an earlier phantom study we already validated shear wave tracking with a clinical ultrasound system in cardiac mode. PURPOSE: In this study we aimed to measure the shear waves velocity in normal individuals. METHODS: 12 healthy volunteers, mean age=37±10, 33% females, were investigated using a clinical scanner (Philips iE33), equipped with a S5-1 probe, using a clinical tissue Doppler (TDI) application. ECG and phonocardiogram (PCG) were synchronously recorded. We achieved a TDI frame rate of >500Hz by carefully tuning normal system settings. Data were processed offline in Philips Qlab 8 to extract tissue velocity along a virtual M-mode line in the basal third of the interventricular septum, in parasternal long axis view. This tissue velocity showed a propagating wave pattern after closure of the valves. The slope of the wave front velocity in a space-time panel was measured to obtain the shear wave propagation velocity. The velocity of the shear waves induced by the closure of the mitral valve (1st heart sound) and aortic valve (2nd heart sound) was averaged over 4 heartbeats for every subject. RESULTS: Shear waves were visible after each closure of the heart valves, synchronous to the heart sounds. The figure shows one heart cycle of a subject, with the mean velocity along a virtual M-mode line in the upper panel, synchronous to the ECG signal (green line) and phonocardiogram (yellow line) in the lower panel. The slope of the shear waves is marked with dotted lines and the onset of the heart sounds with white lines. In our healthy volunteer group the mean velocity of the shear wave induced by mitral valve closure was 4.8±0.7m/s, standard error of 0.14 m/s. The mean velocity after aortic valve closure was 3.4±0.5m/s, standard error of 0.09 m/s. We consistently found that for any subject the velocity after mitral valve closure was higher than after aortic valve closure. CONCLUSION: The velocity of the shear waves generated by the closure of the heart valves can be measured in normal individuals using a clinical TDI application. The shear wave induced after mitral valve closure was consistently faster than after aortic valve closure. Abstract P1138 Figure.Abstract P1138 Figure.


Asunto(s)
Velocidad del Flujo Sanguíneo/fisiología , Ecocardiografía Doppler/métodos , Válvulas Cardíacas/diagnóstico por imagen , Válvulas Cardíacas/fisiología , Adulto , Estudios de Cohortes , Femenino , Voluntarios Sanos , Humanos , Masculino , Persona de Mediana Edad , Valores de Referencia
7.
Ultrasound Med Biol ; 34(4): 685-8, 2008 Apr.
Artículo en Inglés | MEDLINE | ID: mdl-18077080

RESUMEN

Radially oscillating microbubbles can deform when in contact with a wall. These nonspherical shapes have a preferential orientation perpendicular to the wall. Conventional microscope setups for microbubble studies have their optical axis perpendicular to the wall (top view); consequently they have a limited view of the deformation of the bubble. We developed a method to image the bubble in a side view by integrating a mirror in the microscope setup. The image was recorded at 14.5 million frames per second by a high-speed camera. When insonified by a 1-MHz, 140-kPa ultrasound pulse, a 9-microm diameter coated bubble appeared spherical in the top view, but strongly nonspherical in the side view. Its shape was alternatively oblate and prolate, with maximum second order spherical harmonic amplitude equal to the radius.


Asunto(s)
Medios de Contraste , Microburbujas , Ultrasonografía/métodos , Fluorocarburos , Humanos , Proyectos Piloto , Estrés Mecánico , Vibración
8.
Br J Math Stat Psychol ; 54(Pt 1): 139-59, 2001 May.
Artículo en Inglés | MEDLINE | ID: mdl-11393897

RESUMEN

The purpose of this paper is to derive optimal rules for sequential testing problems in psychodiagnostics. In sequential psychodiagnostic testing, each time a patient is exposed to a new treatment, the decision then is to declare this new treatment effective, ineffective, or to continue testing and exposing the new treatment to another random patient suffering from the same mental health problem. The framework of minimax sequential decision theory is proposed for solving such testing problems; that is, optimal rules are obtained by minimizing the maximum expected losses associated with all possible decision rules at each stage of testing. The main advantage of this approach is that costs of testing can be explicitly taken into account. The sequential testing procedure is applied to an empirical example for determining the effectiveness of a cognitive-analytic therapy for patients suffering from anorexia nervosa. For a given maximum number of patients to be tested, the appropriate action is indicated at each stage of testing for different numbers of positive reactions to the cognitive-analytic therapy. The paper concludes with a simulation study, in which the minimax sequential strategy is compared for the anorexia nervosa example with other procedures that exist for similar classification decision problems in the literature in terms of average number of patients to be tested, classification accuracy and average loss.


Asunto(s)
Trastornos Mentales/diagnóstico , Pruebas Psicológicas/estadística & datos numéricos , Psicometría/métodos , Anorexia Nerviosa/diagnóstico , Anorexia Nerviosa/psicología , Anorexia Nerviosa/terapia , Terapia Cognitivo-Conductual/estadística & datos numéricos , Teoría de las Decisiones , Femenino , Humanos , Trastornos Mentales/psicología , Trastornos Mentales/terapia , Método de Montecarlo , Terapia Psicoanalítica/estadística & datos numéricos , Resultado del Tratamiento
9.
Eur J Vasc Endovasc Surg ; 17(6): 486-92, 1999 Jun.
Artículo en Inglés | MEDLINE | ID: mdl-10375484

RESUMEN

OBJECTIVES: to investigate the collateral potential of the circle of Willis with transcranial colour-coded duplex ultrasonography and common carotid artery (CCA) compression. MATERIALS AND METHODS: in 46 atherosclerotic patients without cerebrovascular disease, the functional patency of the collaterals of the circle of Willis, the anterior and posterior communicating arteries, was assessed. The Peak Systolic Velocity (PSV) decrease in the middle cerebral artery (MCA) during CCA compression between complete and incomplete circles was compared. RESULTS: in 10 (22%) patients a complete and in 36 (78%) patients an incomplete circle of Willis was found, mainly due to non-functioning posterior communicating arteries. In hemispheres with collateral supply through both the anterior and the posterior communicating artery, the median PSV decrease in the MCA during CCA compression was 43%. When the posterior, anterior or both communicating arteries (1 hemisphere) were missing the PSV decrease was 58% (p =0.003), 70% (p =0.001) and 75%, respectively. CONCLUSIONS: collateral flow from the basilar to the carotid territory is often hampered by non-functioning posterior communicating arteries. A non-functioning anterior communicating artery is rare. A complete collateral circulation provides better perfusion of the MCA during carotid occlusion as compared with collateral supply through only the anterior or the posterior communicating artery in the case of an incomplete circle of Willis.


Asunto(s)
Estenosis Carotídea/diagnóstico por imagen , Círculo Arterial Cerebral/diagnóstico por imagen , Ultrasonografía Doppler Dúplex/métodos , Adulto , Anciano , Anciano de 80 o más Años , Velocidad del Flujo Sanguíneo , Estenosis Carotídea/fisiopatología , Círculo Arterial Cerebral/fisiopatología , Circulación Colateral/fisiología , Ecoencefalografía , Femenino , Humanos , Masculino , Persona de Mediana Edad
10.
Eur J Vasc Endovasc Surg ; 14(6): 462-7, 1997 Dec.
Artículo en Inglés | MEDLINE | ID: mdl-9467521

RESUMEN

OBJECTIVES: Intra-arterial pressure measurement is considered the "gold standard" for the haemodynamic evaluation of aortoiliac lesions. When compared to pressure measurement duplex scanning fails to detect some of the haemodynamically significant lesions. To improve the assessment of the haemodynamic significance of these lesions by duplex scanning, the flow-related duplex parameters delta PSV and EDV at rest and after exercise were compared with intra-arterial pressure gradients before and during increased blood flow. PATIENTS AND METHODS: Forty-five aortoiliac segments with an isolated stenosis were studied prospectively. Doppler samples were taken at the site of the stenosis both at rest and after exercise on a bicycle ergometer, followed by intraarterial pressure measurement at rest and during pharmacologically induced increased blood flow. RESULTS: At rest a delta PSV (delta PSVr) of 1.6 m/s showed a sensitivity and specificity of 85% and 88%, respectively. After exercise a delta PSV (delta PSVe) of 1.6 m/s showed a sensitivity of 100% at the cost of only a slight reduction in specificity when compared to delta PSVr. The end diastolic velocity at rest (EDVr) had only limited clinical value. The EDV after exercise (EDVe) provided important information if the velocity was 0.5 m/s or lower or if the velocity was 1.6 m/s or greater. CONCLUSION: The delta PSV and the EDV after exercise can be of value in the assessment of the haemodynamic significance of aortoiliac stenoses.


Asunto(s)
Enfermedades de la Aorta/diagnóstico por imagen , Arteriopatías Oclusivas/diagnóstico por imagen , Determinación de la Presión Sanguínea/métodos , Ultrasonografía Doppler en Color/métodos , Aorta Abdominal/diagnóstico por imagen , Enfermedades de la Aorta/diagnóstico , Arteriopatías Oclusivas/diagnóstico , Velocidad del Flujo Sanguíneo , Constricción Patológica/diagnóstico , Constricción Patológica/diagnóstico por imagen , Prueba de Esfuerzo , Arteria Femoral , Humanos , Arteria Ilíaca/diagnóstico por imagen , Claudicación Intermitente/diagnóstico , Claudicación Intermitente/diagnóstico por imagen , Valor Predictivo de las Pruebas , Estudios Prospectivos , Curva ROC , Sensibilidad y Especificidad
11.
Multivariate Behav Res ; 32(4): 403-33, 1997 Oct 01.
Artículo en Inglés | MEDLINE | ID: mdl-26777074

RESUMEN

A model for simultaneous optimization of combinations of test-based decisions in psychology and education is proposed using Bayesian decision theory. The decision problem addressed consists of a combination of a placement and a mastery decision. Weak and strong decision rules are distinguished. As opposed to strong rules, weak rules are allowed to take prior test scores in the series of decisions into account. The introduction of weak rules makes the placement-mastery problem a multivariate decision problem. Conditions for optimal rules to take monotone forms are derived. Results from an empirical example of instructional decision making are presented to illustrate the differences between a simultaneous and a separate approach.

12.
Br J Surg ; 82(5): 630-3, 1995 May.
Artículo en Inglés | MEDLINE | ID: mdl-7613933

RESUMEN

Ultrasonographic duplex scanning has become a valuable diagnostic technique in detecting and grading stenoses and occlusions of the aortoiliac and femoropopliteal arteries. However, the question remains as to whether a treatment strategy can be designed without diagnostic angiography. This prospective study evaluated the impact of duplex scanning on therapeutic decision making. Patients with intermittent claudication, rest pain or ischaemic ulceration of the lower limb who were eligible for invasive treatment were studied. If treatment was considered necessary, a duplex scan was performed instead of diagnostic angiography. The surgeon made a therapeutic decision based on clinical assessment and information obtained from the duplex scan. If it was felt that duplex scanning gave insufficient information, diagnostic angiography was then performed. A group of 112 consecutive patients were studied prospectively; 12 were excluded for logistical reasons. The 100 remaining patients (intermittent claudication in 69, rest pain in 16, ischaemic ulceration in 15) were evaluated. Based on non-invasive tests 22 patients were treated conservatively, 36 were scheduled for percutaneous transluminal angioplasty (PTA) and 32 were scheduled for surgery. Angiography was requested to determine the definitive treatment policy in 28 patients: four of the 22 were scheduled for conservative treatment and 24 of the 32 were scheduled for surgery. All PTAs were performed without prior diagnostic angiography. Angiography was considered necessary in a further ten patients to formulate a therapeutic strategy. In 62 patients the treatment strategy could be determined without diagnostic angiography. Twenty-three of the 39 angiograms performed did not give additional information on treatment strategy. Integrated use of duplex scanning for the investigation of patients with arterial occlusive disease of the lower limb can reduce the need for diagnostic angiography.


Asunto(s)
Arteriosclerosis/diagnóstico por imagen , Claudicación Intermitente/diagnóstico por imagen , Isquemia/diagnóstico por imagen , Úlcera de la Pierna/diagnóstico por imagen , Pierna/irrigación sanguínea , Anciano , Anciano de 80 o más Años , Angioplastia de Balón , Arteriosclerosis/terapia , Toma de Decisiones , Femenino , Humanos , Claudicación Intermitente/terapia , Isquemia/terapia , Úlcera de la Pierna/terapia , Masculino , Persona de Mediana Edad , Estudios Prospectivos , Ultrasonografía Doppler Dúplex
13.
Biotechnol Bioeng ; 36(4): 367-76, 1990 Aug 05.
Artículo en Inglés | MEDLINE | ID: mdl-18595090

RESUMEN

For the application of immobilized enzymes, fixed bed reactors are used almost exclusively. Fixed bed reactors have specific disadvantages, especially for processes with a deactivating catalyst. Therefore, we have studied a novel reactor type with continuous transport of the immobilized biocatalyst. Flow of biocatalyst is countercurrent to the substrate solution. Because of a stagewise reactor design, back-mixing of biocatalyst is very limited and transport is nearly plug flow. The reactor operates at a constant flow rate and conversion, due to constant holdup of catalytic activity. The reactor performance is compared with a configuration of fixed bed reactors. For reactions in the first-order regime, enzyme requirements in this new reactor are slightly less than for fixed bed processes. The multistage fluidized bed appears to be an attractive reactor design to use biocatalyst to a low residual activity. However, nonuniformity of the particles might affect plug flow transport of the biocatalyst. A laboratory scale reactor and experiments are described in Part II(1) of this series. Hydrodynamic design aspects of a multistage fluidized bed are discussed in more detail in Part III.(2).

14.
Biotechnol Bioeng ; 36(4): 377-86, 1990 Aug 05.
Artículo en Inglés | MEDLINE | ID: mdl-18595091

RESUMEN

In Part I of this series,(1) we derived a model and made simulations for a multistage fluidized bed reactor (MFBR). It was concluded that the MFBR can be an attractive alternative for a fixed bed reactor when operated with a deactivating biocatalyst. In Part II of this series, the design of a laboratory-scale MFBR and its evaluation to investigate the practical feasibility of this reactor type, will be described. Experiments with a duration as long as 10 days were carried out successfully using immobilized glucose isomerase as a model reaction system. The results predicted by the model are in good agreement with the measured glucose concentration and biocatalyst activity gradients, indicating perfect mixing of the particles in the reactor compartments.The diameters of the biocatalyst particles used in the experiments showed a large spread, with the largest being 1.7 times the smallest. Therefore, an additional check was carried out, to make sure that the particles were not segregating according to size. Particles withdrawn from the reactor compartments were investigated using an image analyzer. Histograms of particle size distribution do not indicate segregation and it is concluded that the particles used have been mixed completely within the compartments. As a result, transport of biocatalyst is nearly plug flow.

15.
Biotechnol Bioeng ; 36(4): 387-96, 1990 Aug 05.
Artículo en Inglés | MEDLINE | ID: mdl-18595092

RESUMEN

In Parts I and II of this series we described the modelling, design, and operation of a multistage fluidized bed reactor (MFBR) for immobilized biocatalysts. This article deals with those aspects of the MFBR which are different from single-stage fluidized beds which are operated in batch mode with respect to the solids. The semicontinuous transport of the particles requires perfect mixing of the particles in the reactor compartments, because particles are mainly transported from the bottom of these compartments. A large spread in the physical properties of the biocatalyst particles, especially of both size and density, may cause the particles to segregate into layers with different diameter and/or density. This affects the efficient use of the biocatalyst. The properties of the particles are dependent on the immobilization method. The suitability of different methods for possible future application in the MFBR is therefore compared. Because of segregation, successful use of a biofilm catalyst with a nonuniform thickness of the biofilm is doubtful. Experiments in a small scale reactor (+/- 0.1 m diameter) demonstrated that perfect particle mixing is possible using commercially available biocatalyst particles of uniform density. Co-immobilization of the biocatalyst with glass powder in a gel is a simple and effective method of increasing gel density. High density particles allow high liquid flow rates, and thus an improved external mass transfer can be achieved.The distributor plates, which separate the reactor compartments, must allow unhindered transport of particles. Therefore, the holes in these plates must have a diameter of at least 4.5 times that of the largest particles which are present in the particle mixture used. Furthermore, the plates must be designed such that, when scaling-up the reactor, a uniform liquid distribution over the cross-sectional area of the reactor occurs. Large-scale experiments were not carried out, but published correlations, indicate that particle mixing and a uniform liquid distribution can be accomplished in a large-scale reactor under similar flow conditions.

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