Amplitude-modulated Pulses Research Articles

Analysis of Magnetic Resonance Imaging Acoustic Noise Generated by a 4.7 T Experimental System

High intensity acoustic noise is an undesirable side-effect in magnetic resonance imaging (MRI) that can cause discomfort and hearing loss in patients and may be an impediment in functional MRI (fMRI) studies of the auditory system. Experimental MRI systems with high magnetic field strengths may generate acoustic noise of higher sound pressure levels (SPLs) than conventional 1.0 and 1.5 T clinical systems. We measured the SPL and spectral content of the acoustic noise generated by the Bruker Biospect 47/40 4.7 T experimental MRI system during scanning sequences commonly used in animal testing. Each sequence generated acoustic noise of high SPL, rapid pulse rates, amplitude-modulated pulse envelopes and multi-peaked spectra. The rapid acquisition with enhancement sequence with a 0.25 mm slice thickness generated SPLs of up to 129 dB peak SPL and 130 dB (A). Fourier analysis of the spectral content of the acoustic noise generated by each MRI sequence showed a wide band of acoustic energy with spectral peaks from 0.2-5 kHz. The intense MRI acoustic impulse noise generated by the 4.7 T system may cause masking of stimuli used in fMRI of the auditory cortex, reduce the hearing acuity of experimental animals and present a risk for unprotected human ears.

Response characteristics of neurons in the medial geniculate body of the little brown bat to simple and temporally-patterned sounds.

We examined the auditory response properties of neurons in the medial geniculate body of unanesthetized little brown bats (Myotis lucifugus). The units' selectivities to stimulus frequency, amplitude and duration were not significantly different from those of neurons in the inferior colliculus (Condon et al. 1994), which provides the primary excitatory input to the medial geniculate body, or in the auditory cortex (Condon et al. 1997) which receives primary input from the medial geniculate body. However, in response to trains of unmodulated tone pulses, the upper cutoff frequency for time-locked discharges (64 +/- 46.9 pulses per second or pps) and the mean number of spikes per pulse (19.2 +/- 12.2 pps), were intermediate to those for the inferior colliculus and auditory cortex. Further, in response to amplitude-modulated pulse trains, medial geniculate body units displayed a degree of response facilitation that was intermediate to that of the inferior colliculus and auditory cortex inferior colliculus: 1.32 +/- 0.33; medial geniculate body: 1.75 +/- 0.26; auditory cortex: 2.52 +/- 0.96, P < 0.01). These data suggest that the representation of isolated tone pulses is not significantly altered along the colliculothalamo-cortical axis, but that the fidelity of representation of temporally patterned signals progressively degrades along this axis. The degradation in response fidelity allows the system to better extract the salient feature in complex amplitude-modulated signals.

Search for anomalous production of di-lepton events with missing transverse momentum in e $^+$ e $^-$ collisions at $\sqrt{s} = 161$ and 172 GeV

We discuss stimulated Raman adiabatic passage (STIRAP) for pulses whose amplitude is modulated with constant frequency. We discuss in detail the case of a Lambda (Raman) system driven by two amplitude-modulated pulses. We present a variety of numerical solutions to the relevant Schrodinger equation, which we interpret using the Floquet theorem for the solution of systems of linear equations with periodic coefficients, the concept of quasienergies, and the assumption of adiabatic evolution. We find thresholds for successful population transfer and show that some peculiarities of the depicted efficiency of population transfer can be interpreted as pairs of Landau-Zener transitions in the areas of avoided crossings of quasienergies. We provide an analytic expression for the transfer efficiency in these cases. We show that the efficiency of population transfer is much more sensitive to the population decay from the upper level than in the case of smooth (non modulated) laser pulses. We note the applicability of the results to cases beyond the rotating wave approximation.

Second harmonic generation: the solution for an amplitude-modulated initial pulse

We address the initial value problem for one-dimensional second harmonic generation starting from a purely amplitude-modulated fundamental wave. A general method to solve the problem in terms of a Schrödinger equation is presented, in which the initial pulse-shape is taken as a potential. Several examples with the complete solution given in analytical form are discussed. A much broader class of solutions can be found with the help of a single numerical integration. In particular, solutions with incident pulses approximating a sech 2-shape have been obtained.

Time symmetry: an application to shaped pulse excitation of spin-1 systems

The role of time symmetry in the design of amplitude-modulated (shaped) pulses for spin-1 excitation is examined. The quaternion calculus is used to calculate the quaternion elements (Euler–Rodrigues parameters) of each shaped pulse. In this manner, it is shown how the simplicity and compactness of the Euler–Rodrigues parametrization can be used to significantly expedite a computer search for optimal time-symmetric shaped pulses. Theoretical and experimental tests of a new class of symmetric quadrupole-shaped (SQUASH) pulses identified by this procedure show a significant improvement in both excitation bandwidth and efficiency in comparison to the time-asymmetric QUASH shaped pulse previously identified.

Reduction in excitability of the auditory nerve following electrical stimulation at high stimulus rates. II. Comparison of fixed amplitude with amplitude modulated stimuli

We have previously shown that acute electrical stimulation of the auditory nerve using charge-balanced biphasic current pulses presented continuously can lead to a prolonged decrement in auditory nerve excitability (Tykocinski et al., Hear. Res. 88 (1995), 124–142). This work also demonstrated a reduction in electrically evoked auditory brainstem response (EABR) amplitude decrement when using an otherwise equivalent pulse train with a 50% duty cycle. In the present study we have extended this work in order to compare the effects of electrical stimulation using both fixed amplitude electrical pulse trains and amplitude modulated (AM) pulse trains that more accurately model the dynamic stimulus paradigms used in cochlear implants. EABRs were recorded from guinea pigs following acute stimulation using AM trains of charge-balanced biphasic current pulses. The extent of stimulus-induced reductions in the EABR were compared with our previous results using either fixed amplitude continuous, or 50% duty cycle pulse trains operating at 0.34 μC/phase (2 mA, 170 μs/phase) at 400 or 1000 pulses/s (Tykocinski et al., Hear. Res. 88 (1995) 124–142). The AM pulse train, operating at the same rates, was based on a 1-s sequence of the most extensively activated electrode of a Nucleus Mini-22 cochlear implant using the SPEAK speech processing strategy exposed to 4-talker babble, and delivered the same total charge as the fixed amplitude 50% duty cycle pulse train. Two hours of continuous stimulation induced a significant, rate-dependent reduction in auditory nerve excitability, and showed only a slight post-stimulus recovery for monitoring periods of up to 6 hours. Following 2 or 4 h of stimulation using an otherwise equivalent pulse train with a 50% duty cycle or the AM pulse train, significantly less reduction in the EABR was observed, and recovery to pre-stimulus levels was generally rapid and complete. These differences in the extent of the recovery between the continuous waveform and both the 50% duty cycle and AM waveforms were statistically significant for both 400 and 1000 pulses/s stimuli. Consistent with our previous results, the stimulus changes observed using AM pulse trains were rate dependent, with higher rate stimuli evoking more extensive stimulus-induced changes. The present findings show that while stimulus-induced reductions in neural excitability are dependent on the extent of stimulus-induced neuronal activity, the use of an AM stimulus paradigm further reduces post-stimulus neural fatigue.

MRI acoustic noise: sound pressure and frequency analysis.

The large gradient coils used in MRI generate, simultaneously with the pulsed radiofrequency (RF) wave, acoustic noise of high intensity that has raised concern regarding hearing safety. The sound pressure levels (SPLs) and power spectra of MRI acoustic noise were measured at the position of the human head in the isocenter of five MRI systems and with 10 different pulse sequences used in clinical MR scanning. Each protocol, including magnetization-prepared rapid gradient echo (MP-RAGE; 113 dB SPL linear), fast gradient echo turbo (114 dB SPL linear), and spin echo T1/2 mm (117 dB SPL linear), was found to have the high SPLs, rapid pulse rates, amplitude-modulated pulse envelopes, and multipeaked spectra. Since thickness and SPL were inversely related, the T1-weighted images generated more intense acoustic noise than the proton-dense T2-weighted measures. The unfiltered linear peak values provided more accurate measurements of the SPL and spectral content of the MRI acoustic noise than the commonly used dB A-weighted scale, which filters out the predominant low frequency components. Fourier analysis revealed predominantly low frequency energy peaks ranging from .05 to approximately 1 kHz, with a steep high frequency cutoff for each pulse sequence. Ear protectors of known attenuation ratings are recommended for all patients during MRI testing.

Long-pulse, amplitude-modulated optical parametric oscillator

A singly resonant optical parametric oscillator (OPO) based on periodically poled LiNbO(3) is pumped by a Nd:YAG-based oscillator-modulator-amplifier source. This pump source, operating at 1.064 μm, provides the ability to control the temporal characteristics of the OPO waveform. We illustrate pulse tailoring by demonstrating three pulse formats: a pulse with a sharply rising edge, a square pulse, and an amplitude-modulated square pulse. The OPO output is tuned over 1.45-1.67-μm (signal) and 2.9-4.0-μm (idler). We demonstrate a 7-μJ, 2-μs square pulse with 5-MHz sinusoidal amplitude modulation.

Degenerate two-photon propagation and the oscillating two-stream instability: The general solution for amplitude-modulated pulses

Abstract Coherent propagation of an optical pulse in a medium with a second-order resonance is investigated when we include both the dynamical Stark effect and a population-dependent refraction index. We show how to obtain the general solution when the incident pulse has no phase-modulation. The amplitude-modulation of the incident pulse can be arbitrary as can be the initial state of the medium. This general solution is reduced to obtaining the solution of an ordinary differential equation and quadratures. For an initially de-excited medium, the solution reduces to that given by Poluektov et al. {I. A. Poluektov, Yu. M. Popov and V. S. Roitberg, 1975, Kvant. Elektron. (Moscow), 2, 1147 [1975, Sov. J. Quant. Electron., 5, 620]}. We give some illustrative examples of solutions for various initial profiles. It is also shown that the oscillating two-stream instability (OTSI) from plasma physics is equivalent to the Maxwell-Bloch equations for degenerate two-photon propagation. We give a solution for the OTSI which contains five arbitrary real functions.

Degenerate two-photon propagation and the oscillating two-stream instability: The general solution for amplitude-modulated pulses

Abstract Coherent propagation of an optical pulse in a medium with a second-order resonance is investigated when we include both the dynamical Stark effect and a population-dependent refraction index. We show how to obtain the general solution when the incident pulse has no phase-modulation. The amplitude-modulation of the incident pulse can be arbitrary as can be the initial state of the medium. This general solution is reduced to obtaining the solution of an ordinary differential equation and quadratures. For an initially de-excited medium, the solution reduces to that given by Poluektov et al. {I. A. Poluektov, Yu. M. Popov and V. S. Roitberg, 1975, Kvant. Elektron. (Moscow), 2, 1147 [1975, Sov. J. Quant. Electron., 5, 620]}. We give some illustrative examples of solutions for various initial profiles. It is also shown that the oscillating two-stream instability (OTSI) from plasma physics is equivalent to the Maxwell-Bloch equations for degenerate two-photon propagation. We give a solution for the OTSI...

Theoretical design of amplitude-modulated pulses for spin decoupling in nuclear magnetic resonance

The problem of low-power spin decoupling over a broad range of chemical shifts in liquid-state nuclear magnetic resonance (NMR) is addressed through the design of periodic amplitude-modulated irradiation schemes. A principal feature of these is the composition of each decoupling period which contains a single modulated pulse in place of a composite-pulse train of the kind used traditionally. To satisfy the theoretical criterion for decoupling, the pulse amplitude is shaped such that the propagator is made cyclic and broadband, meaning here that it equals the identity matrix over a frequency range which is broad compared to the root-mean-square (RMS) pulse amplitude. The method of design is based on the use of the Floquet formalism to provide insight into the influence of the modulation on the dynamics of the irradiated spin-. Modulation functions formed from simple Fourier series are derived in the first instance using perturbation theory to impose the required cyclicity on the propagator. Broader bandwidth solutions are then obtained by the addition of higher-order Fourier components. Finally, numerical refinement of a selected solution is shown to raise the decoupling quality to the standards acceptable in routine high-resolution NMR.

Tailored Excitation of AX 3-Type Nuclear Spin Systems by Amplitude-Modulated RF Pulses. A Valuable Tool for Coupled Relaxation Studies

Tailored Excitation of AX 3-Type Nuclear Spin Systems by Amplitude-Modulated RF Pulses. A Valuable Tool for Coupled Relaxation Studies

Selective excitation of vibrational overtones in an anharmonic ladder with frequency- and amplitude-modulated laser pulses.

We show numerically that the complex hyperbolic secant pulse provides robust selective inversion of vibrational overtones. A density-matrix analysis is performed for a ten-level Morse-oscillator approximation of a diatomic molecule. We also show that in the limit of adiabatic excitation the complex-hyperbolic-secant pulse yields an inversion spectrum that is narrower than its spectral bandwidth.

Selective on-Resonance Double Pulses Applied to an IS Spin System

The case of two weakly coupled spins selectively irradiated by amplitude-modulated on-resonance pulses is discussed. Since the Hamiltonian of the case considered is a sum of two mutually commuting, time-dependent operators, it is possible to find a transformation matrix describing the net effect of the Hamiltonian in terms of certain rotation operators in an analytical form. The derived transformation matrix [formula] is utilized to analyze a particular case of the double pulse. The treatment generalizes the validity of some literature results and indicates the possibility of designing selective pulses which would invert only mutually coupled spins while leaving noncoupled spins unaffected.

Pitch percepts associated with amplitude-modulated current pulse trains in cochlear implantees.

The percepts elicited by electrical stimulation of auditory neurons by trains of amplitude-modulated current pulses were studied in a group of six cochlear implant users. Modulation frequencies of 100, 150, and 200 Hz were studied, with a range of carrier rates up to 1200 Hz. It was found that all but one subject could consistently rank 150- and 200-Hz modulated stimuli by modulation frequency when the carrier rate was more than 800 Hz, but for lower carrier rates the ranking was greatly affected by the harmonic relationship between carrier and modulation frequency. Pitch matching experiments showed that the subjects generally considered the modulated stimuli to be equal in pitch to unmodulated stimuli with rates the same as, or somewhat higher than, the modulation frequency. The results showed that the "pitch" of pulsatile electrical stimulation resulting from periodicities in the time structure of the electrical stimulus has similarities to the "pitch" observed for temporal patterns in acoustic stimulation such as amplitude-modulated noise. There were some differences, however, which may be attributable at least in part to the physiological response differences for electric and acoustic stimulation.

Time-frequency analysis of model based pulse scattering from a rough fluid-elastic interface

A null field T-matrix formalism for plane-wave scattering from a doubly infinite fluid–solid interface with doubly periodic surface roughness [Bishop and Smith, J. Acoust. Soc. Am. 94, 1560–1583 (1993)] is extended to include scattering of broadband acoustic pulses. The scattered pressure field is expressed in terms of a Fourier integral over the spectra of the incident pulse and the T matrix. Time series are calculated for the scatter of a Gaussian amplitude-modulated linear frequency-modulated pulse from a fluid–elastic interface with sinusoidal and triangular roughness. The time series are analyzed using short time Fourier, Wigner, wavelet packet, and local cosine T-F transforms. The results are displayed graphically in a T-F plot in which the T-F plane is covered by rectangular boxes of dimensions Δt×Δω. These results are used to evaluate the ability of each of the transforms to address inverse scattering and identification problems. It is shown that the T-F analysis provided by the wavelet packet may be used to distinguish between the scatter from surfaces of different roughness and is superior to the T-F analysis provided by both the short time Fourier and Wigner transforms.

Amplitude-Modulated Pulse Shapes for the Elimination of Cross Relaxation during Multiple-Pulse NMR Experiments

Abstract New amplitude-modulated windowless multiple-pulse sequences for the elimination of cross-relaxation effects in 2D NMR spectroscopy of macromolecules are described. The sequences remove cross-relaxation responses near resonance by continuous rapid averaging of the transverse and longitudinal cross-relaxation rates, which have opposite signs for large molecules. Experimental results for an application to chemical-exchange spectroscopy, in which both cross-relaxation and J-coupling responses are removed, are presented. Within the working bandwidth, the spins are effectively spin locked along the y axis of the rotating frame, resulting in 2D spectra that are easily phased. For strictly positive wave forms, variational methods are used to obtain analytical solutions for minimum energy deposition per pulse under the additional constraints of minimum dynamic range, specified minimum field, or specified 90° pulse length.

Synchronously pumped gigahertz modulated optical parametric oscillator

We report parametric generation of gigahertz modulated pulses in the visible and near infrared by use of a synchronously pumped optical parametric oscillator (OPO) based on potassium titanyl phosphate (KTP) pumped with the second harmonic of a modulated Nd:YAG laser at 0.532 μm. We modulated the pump laser by splitting the beam into two, shifting the frequency of one beam by focusing it into a stimulated Brillouin scattering cell, and then heterodyning the shifted and the unshifted beams. The resultant amplitude-modulated pulse was then doubled in a KD*P crystal. The OPO output pulse maintains the modulation depth of the pump pulse if the cavity length is close to an integer multiple of the pulse-to-pulse separation. Overall performance was characterized by use of a simple linear confguration over a wide range of input energies to yield signal efficiencies of greater than 10% in the 0.69–0.71-μm range.

Specific Spin-State Transformations Induced by Amplitude-Modulated RF Pulses

Abstract It is shown both by simulation and by experiment that amplitude-modulated soft pulses (RF pulses with low amplitude) can be designed in order to induce well-defined transformations of spin states, be it in a symmetrical or antisymmetrical manner. A theoretical description, using single-transition operators, is given. By way of example, the excitation of various antiphase terms in homonuclear and heteronuclear scalar-coupled spin systems is discussed. In addition, it is demonstrated by example how these pulses can be combined to create longitudinal spin-ordered states or may be used within INEPT-type experiments.

An integrated program for amplitude-modulated RF pulse generation and re-mapping with shaped gradients

Efficient generation of amplitude modulated, frequency selective RF pulses has been demonstrated by the Shinnar-Le Roux (SLR) algorithm. In the present article, we provide an overview of a relatively comprehensive computer program that includes a version of the SLR algorithm and also incorporates an algorithm for re-mapping a selective RF pulse onto a new dwell time with modulated gradients. The re-mapping may be used to reduce SAR, or to shorten the RF pulse time by increasing the gradient and RF strength in regions where the original RF pulse amplitude was low. The program includes additional useful features including a Bloch equations algorithm, and pulse scaling, to enable examination of pulse profiles under a variety of conditions such as RF inhomogeneity and even nuclear relaxation. The program, MATPULSE, was developed with the MATLAB for Windows programming language and makes extensive use of the MATLAB graphical user interface (GUI) features to generate a userfriendly interface. A number of examples are provided to illustrate the capabilities of the MATPULSE program.