Single Pulsed Field Research Articles

Cations impact radical reaction dynamics in concentrated multicomponent aqueous solutions.

Ultraviolet (UV) photolysis of nitrite ions (NO2-) in aqueous solutions produces a suite of radicals, viz., NO·, O-, ·OH, and ·NO2. The O- and NO· radicals are initially formed from the dissociation of photoexcited NO2-. The O- radical undergoes reversible proton transfer with water to generate ·OH. Both ·OH and O- oxidize the NO2- to ·NO2 radicals. The reactions of ·OH occur at solution diffusion limits, which are influenced by the nature of the dissolved cations and anions. Here, we systematically varied the alkali metal cation, spanning the range from strongly to weakly hydrating ions, and measured the production of NO·, ·OH, and ·NO2 radicals during UV photolysis of alkaline nitrite solutions using electron paramagnetic resonance spectroscopy with nitromethane spin trapping. Comparing the data for the different alkali cations revealed that the nature of the cation had a significant effect on production of all three radical species. Radical production was inhibited in solutions with high charge density cations, e.g., lithium, and promoted in solutions containing low charge density cations, e.g., cesium. Through complementary investigations with multinuclear single pulse direct excitation nuclear magnetic resonance (NMR) spectroscopy and pulsed field gradient NMR diffusometry, cation-controlled solution structures and extent of NO2- solvation were determined to alter the initial yields of ·NO and ·OH radicals as well as alter the reactivity of NO2- toward ·OH, impacting the production of ·NO2. The implications of these results for the retrieval and processing of low-water, highly alkaline solutions that comprise legacy radioactive waste are discussed.

37 Short-term effects of a single pulsed electromagnetic field therapy session on lameness, gait quality, and stress in moderately exercising horses

Pulsed electromagnetic field (PEMF) therapy is applied to equids for a variety of preexisting conditions; however, research with its usage to enhance performance in the horse is limited. To test the hypothesis that a single PEMF therapy session improved stress, performance, and lameness parameters, 14 horses (11 ± 4.1 years) underwent a single 30-min whole body PEMF therapy session at 5 Hz and a single sham therapy session where horses were randomly assigned to a treatment order. A 2-week washout period was given between treatments. Resting heart rate, salivary cortisol, stride length, quality of movement, and lameness evaluation (fore limb vector sum, hip height difference, forehand stride rate, hind stride rate) on crushed gravel and loose sand surfaces were evaluated at 8 different time points: immediately before and after treatment, and at 2, 4, 8, 24, 48, and 72 h post treatment. Videos were assessed for stride length and were assessed by 3 blinded, carded judges for quality of movement. Mixed model analysis for crossover design with repeated measures was used to determine the effect of treatment, time, period, and all interactions. At 7.5 h post treatment, horses were subjected to a 30 min lunge to simulate a moderate exercise session. Post hoc multiple comparisons were performed with Tukey's adjustment (mean ± SE).Heart rate was lowered immediately following PEMF treatment (29 ± 1 BPM, P < 0.0001) when compared with all other sampling time points. For quality of movement (1 = poor, 10 = excellent), judges found walk quality to decrease immediately following PEMF treatment (5.68 ± 0.18) and at 4 h post (5.59 ± 0.16) when compared with 2 h sham (5.98 ± 0.1, P = 0.006) while trot quality did not differ. Walk stride length was affected by time but not treatment, increasing at 8 h (2.49 ± 0.03 m) post treatment when compared with pre-treatment sampling (2.43 ± 0.04 m, P = 0.03) but not the trot. Salivary cortisol concentration was unaffected by treatment but did have an effect of time (P < 0.0001) varying depending on the time of day of the sample. Forehand and hind stride rate were affected by surface (P = 0.004, P = 0.004) with sand having a slower rate than gravel and time (P < 0.0001, P < 0.0001) slowing stride rate as the day progressed. No differences were observed with fore limb vector sum and hip height difference. This study shows PEMF therapy has a relaxing effect evidenced by lowered heart rate immediately following treatment; however, more work is needed to determine the full effects of PEMF in performance horses.

PV Isolation Using a Spherical Array PFA Catheter: Application Repetition and Lesion Durability (PULSE-EU Study)

BackgroundPreclinical studies have revealed that pulsed field ablation (PFA) lesion dimensions increase with repetitive applications at a similar electric field. ObjectivesThis study investigated whether pulmonary vein isolation (PVI) durability varies with single vs repetitive pulsed field (PF) applications. MethodsAtrial fibrillation patients underwent PVI using a spherical multielectrode array PFA catheter delivered with a 19-F deflectable sheath under intracardiac echocardiographic guidance. Esophagogastroduodenoscopy and brain magnetic resonance imaging were performed within 1 to 3 days, and invasive remapping at ∼2 to 3 months. ResultsThe patient cohort (n = 21; age 63 ± 11 years; 67% women) underwent PVI in either of 2 groups: group 1 (n = 11)—single PF application/PV; and group 2 (n = 10)—3 PF applications/PV. In both groups, PVI was acutely successful in all (100%) patients. Despite significantly longer pulse delivery times (75.2 ± 7.4 s/patient vs 24.5 ± 5.5 s/patient) the procedure times (73.2 ± 13.7 minutes vs 93.7 ± 18.5 minutes) were shorter with group 2 vs group 1. There was no stroke/transient ischemic attack, pericardial effusion, phrenic nerve injury, or esophageal complications. Esophagogastroduodenoscopy was normal in both groups of patients (n = 9). Screening brain magnetic resonance imaging revealed asymptomatic cerebral lesions (diffusion weighted imaging+/fluid attenuated inversion recovery−) in 3 of 16 (18.7%) patients. PV remapping revealed durable PVI in 62.5% PVs in group 1 (n = 10), compared with all 100% PVs in group 2 (n = 9); this translates to all PVs being durably isolated in 30% vs 100% (P < 0.05) of patients in groups 1 and 2, respectively. ConclusionsIn his first-in-human trial, the “single-shot” spherical array PFA catheter was shown to safely isolate PVs. Repetitive PF application is key for lesion consolidation to maximize PVI durability.

Multidimensional Diffusion MRI Methods With Confined Subdomains

Diffusion Magnetic Resonance Imaging (dMRI) is an imaging technique with exquisite sensitivity to the microstructural properties of heterogeneous media. The conventionally adopted acquisition schemes involving single pulsed field gradients encode the random motion of water molecules into the NMR signal, however typically conflating the effects of different sources contributing to the water motion. Time-varying magnetic field gradients have recently been considered for disentangling such effects during the data encoding phase, opening to the possibility of adding specificity to the recovered information about the medium’s microstructure. Such data is typically represented via a diffusion tensor distribution (DTD) model, thus assuming the existence of several non-exchanging compartments in each of which diffusion is unrestricted. In this work, we consider a model that takes confinement into account and possesses a diffusion time-dependence closer to that of restricted diffusion, to replace the free diffusion assumption in multidimensional diffusion MRI methods. We first demonstrate how the confinement tensor model captures the relevant signal modulations impressed by water diffusing in both free and closed spaces, for data simulated with a clinically feasible protocol involving time-varying magnetic field gradients. Then, we provide the basis for incorporating this model into two multidimensional dMRI methods, and attempt to recover a confinement tensor distribution (CTD) on a human brain dataset.

Investigating the flux jump behaviour during single waveform control pulsed field magnetization of GdBaCuO superconducting bulk

We aimed to improve the trapped magnetic flux density obtained with a waveform control pulsed field magnetization (WCPM) by using a negative feedback control of the magnetic flux density on the growth sector boundary of a GdBaCuO superconducting bulk sample. The WCPM method with negative feedback control has previously shown that it could help increase the trapped magnetic flux density, compared to conventional passive pulsed flux magnetization, if the magnetic field penetrates the bulk centre substantially using a flux jump. The flux jump sometimes greatly changes the magnetic and thermal state of the bulk, which limits the maximum trapped magnetic field. The active control method of the applied magnetic field helps to overcome this limit if the control conditions are appropriate. While searching for the ideal control conditions of the WCPM, the magnetization characteristics have been investigated. We found that the flux jump, which assists the flux in penetrating the centre of the bulk, can be “slowed down” thanks to the negative-feedback WCPM. This operation helped to decrease the heat generated by the moving flux inside the bulk and reduced the temperature rise, which contributed to the increase of the trapped magnetic flux density.

Multiphysics modelling of electroporation under uni- or bipolar nanosecond pulse sequences

A nonlinear dispersive multiphysics model of single-cell electroporation was proposed in this paper. The time-domain Debye model was utilised to describe the membrane dispersion while the dynamic pore radius function was deployed to modify the plasma membrane conductivity. The dynamic spatial distributions of the ion concentration were dominated by the Nernst-Planck function. First, a single nanosecond pulsed electric field was applied to verify our model and to explore the effects of dispersion and dynamic pore radius on the redistribution of the electric field. The dispersive membrane was found to increase the transmembrane potential, expedite the electroporation process, and weaken the membrane permeability; however, adding the dynamic pore radius function had the opposite effect on transmembrane potential and membrane permeability. The responses of the cells exposed to unipolar and bipolar nanosecond pulse sequences were subsequently simulated. During the application of unipolar pulse sequences, the pore radius and perforation area showed a step-like accumulation, and significant increases in the perforation area and intracellular ion concentration were observed with higher frequency pulse sequences and wider subpulse intervals. The bipolar cancellation effect was also observed in terms of membrane permeability and pore radius.

Observation of surface deformation of tungsten exposed to single pulsed high heat flux and magnetic field for divertor design

Tungsten (W) is one of candidate surface materials for a plasma facing component (PFC) in a magnetically confinement fusion reactor such as a divertor from the perspective of its high melting point, high thermal conductivity, low tritium retention and low sputtering yield. In the fusion reactor in operating, the divertor surface is exposed by the transient heat load generated by plasma disruption or ELM. The heat load is sufficiently high to melt the W surface. Because of the repetition of melting and solidification, it is concerned that W surface deformation occurs, the droplets scatter and its heat resistance degrades. These are critical issues for developing the fusion reactor. In previous studies, the in-situ observations of the W specimen surface during irradiating by a pulsed laser simulating the heat load were conducted using a HSV camera. However, PFCs lies under intense magnetic field in the actual fusion-reactor condition. Magnetic field affects the motion of fluid by the effect of generated Lorentz force. Therefore, this study aims to clarify the melting and solidification behavior of W under the intense magnetic field. In order to simulate the heat load, the Nd/YAG laser, which has almost flatten spatial profile and rectangular temporal profile, was irradiated on a W specimen. The power density of the laser was 3.12 GW/m2 and 3.9 GW/m2 and the pulse width was 3 [ms]. Helmholtz-like electromagnetic coils were applied for generating pulsed magnetic field. The magnetic density was also changed in the range from 0 to 4 [T] in this study. From observation of the light emitted from the heated W surface using a high-speed video camera and measurement of irradiation traces, the behavior of molten W and the effect of the magnetic field will be reported and discussed.

Waveform Control Pulsed Magnetization of GdBaCuO Bulk Using Negative Feedback at 60 K

The practical use of high-temperature superconducting bulk electric rotating machines is limited, despite their increased power densities over permanent magnet machines, by the magnetization process of the bulks. A fast and effective magnetization process is needed to promote the practical application of superconducting machines. This is why we developed a method for magnetizing bulk superconductors and trapping high magnetic flux density using a single pulsed field magnetization (PFM). The method of magnetization of the superconducting bulk magnet by controlling the applied magnetic field has been tested previously at 77 K and 70 K. We tried during this study to trap high magnetic flux density in a GdBaCuO bulk at 60 K, to confirm that the method is effective at a lower temperature. Moreover, we tried to improve the method by using negative feedback of the magnetic flux density on the growth sector, to control the chopping of the current flowing through the magnetizing coils. We managed to reduce the temperature rise during the pulse by 10 K compared to a passive PFM and trapped a maximum of 2.17 T in the center of the bulk sample, the improvements compared to passive PFM at 60 K are remarkable.

Numerical and experimental studies on solidification of AZ80 magnesium alloy under out-of-phase pulsed magnetic field

For obtaining the finer grains of magnesium alloy, a novel combined pulsed magnetic field with different initial phases, also called out-of-phase pulsed magnetic field (OPPMF), was applied to study the solidification structure of AZ80 magnesium alloy. The numerical simulation was simultaneously conducted to investigate the refinement mechanisms. The experimental results showed that the macrostructure could be effectively refined by applying external magnetic field. Meanwhile, finer grains were obtained with the higher current intensity. However, the increase of current intensity could only refine the grains to about 0.5 mm. Furthermore, compared to a single pulsed magnetic field (PMF) and alternating series of OPPMF (Connection II), a finer structure was observed when the consecutive series of OPPMF (Connection I) was imposed. In contrast with a single PMF and Connection II, the numerical results showed that the greater axial Lorentz force was obtained under the Connection I, generating the stronger forced flow in the melt. It is believed that abundant nuclei could detach from the mold wall and move faster into the interior melt due to the stronger forced flow; besides, the lower superheat and greater temperature uniformity in bulk melt were realized, accounting for the finest structures under the Connection I.

Magnetizing characteristic evaluation of REBCO bulk in PFM using different yokes

A REBCO bulk magnet is able to generate a several-tesla-class magnetic field by a compact system with low power consumption. Pulsed field magnetization (PFM), which is one of major magnetization method, has the advantage that the bulk is activated using a conventional equipment in a few seconds, and, therefore, it is suitable for practical use. However, a trapped field is lower than the maximum performance of material. To increase the field, improvement of magnetization method and modification of exciting equipment are considered. We aim to improve the trapped field by changing the exciting system simply and inexpensively. In the bulk magnet system, soft-iron yokes are generally used to extend the pulse width. This paper evaluated magnetizing characteristic quantitatively. A single pulsed field was applied to a new GdBCO bulk using ϕ64-mm and ϕ80-mm soft-iron yokes. The pulse width of ϕ80-mm yoke was about 35% longer than that of ϕ64-mm yoke. When comparing the trapped flux density and total magnetic flux, these values of ϕ80-mm yoke were higher than those of ϕ64-mm yoke. Also, the temperature rise of ϕ80-mm yoke was decreased by approximately 5% as compared with ϕ64-mm yoke, implying that the same effect as the long-pulse method was achieved.

Improvement of trapped magnetic field in GdBCO by waveform control pulse magnetization at 70 K

We attempted to trap a strong magnetic field with a single pulsed magnetic field by applying waveform control pulse magnetization (WCPM) method to a high-temperature superconductor (HTS) bulk sandwiched between two vortex-type copper coils at less than 77 K. The GM cryocooler conductively cooled the GdBCO bulk to 70 K in an arrangement similar to the internal structure of our axial gap type HTS motor. The HTS bulk showed no flux jump, while the duty ratio of WCPM was small. When we increased the duty ratio, we found a flux jump without looking at any prior signs and the trapped magnetic flux density increased twice. Hence we attempted a negative feedback WCPM with the control target at the highest trapped magnetic flux density while no flux jump was found. After trial and error of control conditions, the HTS bulk sample trapped a maximum magnetic flux density of 1.79 T by a single pulse magnetic field. If the WCPM technique is used, a single pulse magnetic field will cause the HTS bulk to obtain a higher trapped field at lower temperatures.

Single pulsed electromagnetic field restores bone mass and microarchitecture in denervation/disuse osteopenic mice

Pulsed electromagnetic fields (PEMFs) have been proposed to treat bone loss. However, time-consuming is the main complaint. A time-saving and effective treatment is of expectation. Previously, we showed a 3 min daily of single pulsed electromagnetic field (SPEMF) accelerated bone formation of long bone defect in mice. Here we compared the effect of SPEMF with PEMF for treating denervation/disuse osteopenic mice.Healthy mice were divided into 3 groups: intact mice (INT), INT + PEMF, and INT + SPEMF. Induced osteopenic mice were divided to osteopenia (IOP), IOP + PEMF, and IOP + SPEMF groups. The PEMF treated groups were subjected to daily 8 h PEMF(15 Hz, 18 G) exposure, while SPEMF treated groups were daily 3 min SPEMF(0.2 Hz, 1 T) exposure. BMD was evaluated every two weeks during the 12 weeks of treatment. Microarchitecture was evaluated on week 12.SPEMF significantly reversed bone loss in IOP mice as early as 6 weeks post-treatment, while PEMF reversed bone loss after 8 weeks. Bone volume was significantly increased in the IOP + PEMF and IOP + SPEMF group. Besides, bone volume and trabecular number of IOP + SPEMF mice were restored to the levels of INT mice in 12 weeks. Our finding suggests SPEMF increased BMD and restored microarchitecture of disuse osteopenic mice to healthy level.

A single-pulsed electromagnetic field enhances collagen synthesis in tendon cells

Tendinopathy is a progressive pathology of tendon that is characteristic of imbalance between matrix synthesis and degeneration and is often caused by failure to adapt to mechanical loading. Non-steroidal anti-inflammatory medications (NSAIDS) are used as a conventional treatment to alleviate pain and swelling in the short term, but the ideal treatment for tendinopathy remains unclear. Here, we show a single pulsed electromagnetic field (SPEMF, 0.2 Hz) that up-regulated tenogenic gene expression (Col1a1, Col3a1, Scx, Dcn) and down-regulated inflammatory gene expression (Mmp1) in vitro. After five days of SPEMF stimulation (3 min/day), the collagen type I and total collagen synthesis protein levels were significantly increased. Under pro-inflammatory cytokine (IL-1β) irritation, the decreased expression of Col1a1/Col3a1 was up-regulated by SPEMF treatment, and the increased expression of Mmp1 was also reversed. From the above, it can be inferred that SPEMF that enhances matrix synthesis and reduces matrix degeneration may counteract the imbalance in tendinopathy. SPEMF application may be developed as a potential future strategy for therapeutic intervention in tendon disorders.

JEDI: Joint Estimation Diffusion Imaging of macroscopic and microscopic tissue properties.

A new method for enhancing the sensitivity of diffusion MRI (dMRI) by combining the data from single (sPFG) and double (dPFG) pulsed field gradient experiments is presented. This method uses our JESTER framework to combine microscopic anisotropy information from dFPG experiments using a new method called diffusion tensor subspace imaging (DiTSI) to augment the macroscopic anisotropy information from sPFG data analyzed using our guided by entropy spectrum pathways method. This new method, called joint estimation diffusion imaging (JEDI), combines the sensitivity to macroscopic diffusion anisotropy of sPFG with the sensitivity to microscopic diffusion anisotropy of dPFG methods. Its ability to produce significantly more detailed anisotropy maps and more complete fiber tracts than existing methods within both brain white matter (WM) and gray matter (GM) is demonstrated on normal human subjects on data collected using a novel fast, robust, and clinically feasible sPFG/dPFG acquisition. The potential utility of this method is suggested by an initial demonstration of its ability to mitigate the problem of gyral bias. The capability of more completely characterizing the tissue structure and connectivity throughout the entire brain has broad implications for the utility and scope of dMRI in a wide range of research and clinical applications.

Improvement of Trapped Magnetic Field of a REBCO Bulk Magnet Activated by Pulsed Field Magnetization in a High-Cooling Power Two-Stage GM-Type Refrigerator

We developed a high-cooling power bulk magnet system using a 12 K two-stage Gifford-McMahon (GM)-type refrigerator with a cooling ability of 12 W at 20 K in our previous study. When a single pulsed field was applied using a GdBCO bulk, the maximum trapped field of 3.59 T at the center of sample surface and the total magnetic flux of 2.89 mWb were achieved. In this paper, we aim to improve the trapped magnetic field by increasing the size of soft-iron yoke. When the same experiment was carried out using the same bulk, the trapped field was increased to 3.85 T. Moreover, the total magnetic flux reached a value of 3.97 mWb by a multipulsed field magnetization.

Magnetizing Performance Evaluation of HTS Bulk Magnet Using a 12 K Refrigerator With High Cooling Capacity

We study a high magnetic field generation using HTS bulk magnets activated by pulsed-field magnetization with the goal of their industrial application. In our previous study, a single-stage GM-type refrigerator and a two-stage GM-type refrigerator with an air-cooled-type compressor and a Stirling refrigerator were used for cooling an HTS bulk aiming at simplifying the bulk magnet system. Now, we developed a new bulk magnet system using a two-stage GM-type refrigerator with a high cooling capacity of 12 W at 20 K aiming to enhance a trapped field by improving the cooling ability. When a GdBCO bulk 60 mm in diameter and 20 mm thick was cooled from the room temperature to the lowest, the lowest temperature was 13.3 K at the sample stage and 45.5 K at the bulk surface for 3.5 h. When a single pulsed field was applied with varying the amplitude and temperature, the maximum flux densities of 3.59 T on the bulk surface and 2.34 T at the pole surface, and the total magnetic flux of 2.48 mWb were achieved at 20 K.

Comparison of Magnetizing Characteristics of Superconducting Bulk Magnet Cooled by Stirling and GM Refrigerators During Pulsed Field Magnetization

We developed several type superconducting bulk magnets with the goal of their industrial application, and study to improve a magnetic field by pulsed field magnetization. It is important to select a suitable refrigerator to cool a bulk superconductor. This paper investigates magnetizing characteristics when using different refrigerators. One is a Stirling refrigerator, in which an ultimate temperature was up to 50 K and cooling capacity was 11 W at 77 K. Another is a dual-stage GM refrigerator with an air-cooled compressor, in which an ultimate temperature was 13 K and cooling capacity was 5 W at 20 K. The other is a dual-stage GM refrigerator with a water-cooled compressor, in which an ultimate temperature was 12 K and cooling capacity was 12 W at 20 K. When a GdBCO bulk with dimensions of 60 mm in diameter and 20 mm thick was cooled by the Stirling refrigerator, the lowest temperature was approximately 55 K. Then, in the other refrigerators, the temperature was adjusted to the same value by a temperature regulator. The bulk was cooled by each refrigerator and a single pulsed field was applied while varying the amplitude of 3.1 to 7.0 T. During magnetization, time variations of magnetic flux density on the bulk surface were monitored. After magnetization, the trapped field distributions were measured on the magnetic pole surface. These data show that even the bulk magnet using the Stirling refrigerator with relatively low cooling ability could trap a high magnetic field. Consequently, the bulk magnet with high cooling capacity could not necessarily generate a high magnetic field.

Development of a Desktop-Type Superconducting Bulk Magnet

We developed a desktop-type superconducting bulk magnet using a Stirling cryocooler with the aim of miniaturizing the system. This refrigerator was compact and highly energy efficient because a compressor was not needed outside; power consumption was approximately 160 W. Moreover, the length of the magnetic pole was decreased by restricting the activation method to pulsed field magnetization. A GdBCO bulk material 45 mm in diameter and 20 mm thick was attached to the cold stage of a refrigerator and was covered with a vacuum chamber. The sample was cooled from room temperature to 52.3 K in approximately 4.5 h. When a single pulsed field was applied in amplitudes varying from 0.8 to 7.0 T, the maximum trapped field was approximately 2.8 T at the center of the bulk surface in the applied field of 7.0 T. Moreover, the maximum magnetic field on the chamber's surface was approximately 1.3 T, and the total magnetic flux was 0.94 mWb. The operational status after magnetization was good, and the operating sound was small.

Materials preparation and magnetization of Gd-Ba-Cu-O bulk high-temperature superconductors

The paper reports on recent achievements in the preparation and magnetization of bulk high-temperature superconductors (HTS). The melt-growth of HTS bulks has technically stabilized due to the use of buffer materials with a seed crystal and modified infiltration to supply a rich liquid phase during growth. This modified growth technology was adapted as our standard processing method. This paper describes some new aspects of both field cooling and pulsed field magnetization processes. Pulsed field magnetization uses waveform control that feeds back the transient flux around the top-center of the bulks and traps a field of 1.63 T, which is more than 90% of the field cooling value. This was achieved by applying a single step pulsed field at a liquid nitrogen temperature. For practical applications, the magnetization under a static magnetic field that is tilted from the crystallographic c-axis was investigated at liquid nitrogen temperature. The trapped flux component perpendicular to the bulk surface remains strong up to θ = 30° inclination, compared to the procedure along the axis. Information about HTS bulks is considered to be important for machine applications using bulk HTS as cryo-permanent magnets.

Constrained optimization of gradient waveforms for generalized diffusion encoding

Diffusion MRI is a useful probe of tissue microstructure. The conventional diffusion encoding sequence, the single pulsed field gradient, has recently been challenged as more general gradient waveforms have been introduced. Out of these, we focus on q-space trajectory imaging, which generalizes the scalar b-value to a tensor valued entity. To take full advantage of its capabilities, it is imperative to respect the constraints imposed by the hardware, while at the same time maximizing the diffusion encoding strength. We provide a tool that achieves this by solving a constrained optimization problem that accommodates constraints on maximum gradient amplitude, slew rate, coil heating and positioning of radio frequency pulses. The method’s efficacy and flexibility is demonstrated both experimentally and by comparison with previous work on optimization of isotropic diffusion sequences.