Pulse Functions

qMRLab · May 21, 2024 · 56a86ef · 56a86ef
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diff --git a/src/Models_Functions/adiabatic_inv/pulses/AI_gauss_pulse.m b/src/Models_Functions/adiabatic_inv/pulses/AI_gauss_pulse.m
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+function [rf_pulse, omega1, A_t, Params] = AI_gauss_pulse( Trf, Params)
+
+%   gauss_pulse Adiabatic Inversion Gaussian RF pulse function.
+%   pulse = gauss_pulse(Trf, PulseOpt)
+%
+%   B1(t) = A(t) * exp( -1i *integral(omega1(t')) dt' )
+%   where A(t) is the envelope, omega1 is the frequency sweep
+%
+%   Phase modulation is found from taking the integral of omega1(t)
+%   Frequency modulation is time derivative of phi(t)
+%
+%   For the case of a Gauus pulse:
+%   A(t) = A_0 * exp((-beta^2 * t^2)/2)
+%   lambda = A0^2/(beta*Q)
+%   omega1(t) = -lamdba*(erf(beta*t)/erf(beta))
+%
+%   A0 is the peak amplitude in microTesla
+%   beta is a frequency modulation parameter in rad/s
+%
+%   The pulse is defined to be 0 outside the pulse window (before 
+%   t = 0 or after t=Trf). (HSn, n = 1-8+) 
+%
+%   --args--
+%   t: Function handle variable, represents the time.
+%   Trf: Duration of the RF pulse in seconds.
+%
+%   --optional args--
+%   PulseOpt: Struct. Contains optional parameters for pulse shapes.
+%   PulseOpt.Beta: frequency modulation parameter
+% 
+%   Reference: Matt A. Bernstein, Kevin F. Kink and Xiaohong Joe Zhou.
+%              Handbook of MRI Pulse Sequences, pp. 110, Eq. 4.10, (2004)
+%
+%              Tannús, A., & Garwood, M. (1997). Adiabatic pulses. NMR in 
+%              Biomedicine: An International Journal Devoted to the 
+%              Development and Application of Magnetic Resonance In Vivo, 
+%              10(8), 423-434. https://doi.org/10.1002/(sici)1099-1492(199712)10:8 
+%                  --> Table 1 contains all modulation functions 
+%                  --> A(t), omega1
+%                  --> Fig 5, Gaussian OIA pulse image 
+%                  --> Trf = 10 ms 
+%
+%              Kupce, E., & Freeman, R. (1996). Optimized adiabatic pulses 
+%              for wideband spin inversion. Journal of Magnetic Resonance, 
+%              118(2), 299-303. https://doi.org/https://doi.org/10.1006/jmra.1996.0042 
+%                  --> lambda equation, Eq. 10 (added to omega1 for scaling)
+%
+%              Tannús, A., & Garwood, M. (1996). Improved performance of 
+%              frequency-swept pulses using offset-independent adiabaticity. 
+%              Journal of Magnetic Resonance, 120(1), 133-137. 
+%              https://doi.org/https://doi.org/10.1006/jmra.1996.0110 
+%                   --> Fig 1a and 1b. Show how width of amplitude and
+%                   frequency vary with each pulse
+%
+% To be used with qMRlab
+% Written by Amie Demmans & Christopher Rowley 2024
+
+
+% Function to fill default values;
+    if ~isfield(Params, 'PulseOpt')
+        Params.PulseOpt = struct();
+    end
+
+Params.PulseOpt = AI_defaultGaussParams(Params.PulseOpt);
+Trf = Trf/1000;
+nSamples = Params.PulseOpt.nSamples;  
+t = linspace(0, Trf, nSamples);
+tau = t-Trf/2;
+
+% Amplitude 
+A_t = Params.PulseOpt.A0 .* exp(-1*(Params.PulseOpt.beta.^2 .* tau.^2)./2);
+A_t((t < 0 | t>Trf)) = 0;
+% disp( ['Average B1 of the pulse is:', num2str(mean(A_t))]) 
+
+% Scaling Factor (lambda) 
+% --> Setting Q = 0 allows for viewing of RF pulse 
+if Params.PulseOpt.Q == 0 
+    lambda = 0;
+else 
+    lambda = (Params.PulseOpt.A0)^2 ./ (Params.PulseOpt.beta.*Params.PulseOpt.Q);
+end 
+
+% Frequency modulation function 
+% Carrier frequency modulation function w(t):  
+omega1 = -lambda*erf(Params.PulseOpt.beta.*tau)./erf(Params.PulseOpt.beta);
+
+% Phase modulation function phi(t):
+phi1num = lambda.*tau.*erf(Params.PulseOpt.beta.*tau);
+phi1denom = erf(Params.PulseOpt.beta);
+phi1 = phi1num/phi1denom;
+phi2num = lambda*exp(-Params.PulseOpt.beta.^2 .* tau.^2);
+phi2denom = sqrt(pi)*Params.PulseOpt.beta*erf(Params.PulseOpt.beta);  
+phi2 = phi2num/phi2denom;
+phi = phi1+phi2;
+
+% Put together complex RF pulse waveform:
+rf_pulse = A_t .* exp(1i .* phi);
+
+
+
+
diff --git a/src/Models_Functions/adiabatic_inv/pulses/AI_hanning_pulse.m b/src/Models_Functions/adiabatic_inv/pulses/AI_hanning_pulse.m
@@ -0,0 +1,98 @@
+function [rf_pulse, omega1, A_t, Params] = AI_hanning_pulse( Trf, Params)
+
+%   hanning_pulse Adiabatic Inversion Hanning RF pulse function.
+%   pulse = hanning_pulse(Trf, PulseOpt)
+%
+%   B1(t) = A(t) * exp( -1i *integral(omega1(t')) dt' )
+%   where A(t) is the envelope, omega1 is the frequency sweep
+%
+%   Phase modulation is found from taking the integral of omega1(t)
+%   Frequency modulation is time derivative of phi(t)
+%
+%   For the case of a Hanning pulse:
+%   A(t) = A_0 * ((1 + cos(beta*pi*t))/2)
+%   lambda = A0^2/(beta*Q)
+%   omega1(t) = -lambda ((beta*t)+((4/3)*pi)*sin(beta*pi*t)*(1 +1/4*cos(beta*pi*t)))
+%
+%   A0 is the peak amplitude in microTesla
+%   beta is a frequency modulation parameter in rad/s
+%
+%   The pulse is defined to be 0 outside the pulse window (before 
+%   t = 0 or after t=Trf). (HSn, n = 1-8+) 
+%
+%   --args--
+%   t: Function handle variable, represents the time.
+%   Trf: Duration of the RF pulse in seconds.
+%
+%   --optional args--
+%   PulseOpt: Struct. Contains optional parameters for pulse shapes.
+% 
+%   Reference: Matt A. Bernstein, Kevin F. Kink and Xiaohong Joe Zhou.
+%              Handbook of MRI Pulse Sequences, pp. 110, Eq. 4.10, (2004)
+%
+%              Tannús, A., & Garwood, M. (1997). Adiabatic pulses. NMR in 
+%              Biomedicine: An International Journal Devoted to the 
+%              Development and Application of Magnetic Resonance In Vivo, 
+%              10(8), 423-434. https://doi.org/10.1002/(sici)1099-1492(199712)10:8 
+%                  --> Table 1 contains all modulation functions 
+%                  --> A(t), omega1 
+%                  --> Trf = 10ms
+%
+%              Kupce, E., & Freeman, R. (1996). Optimized adiabatic pulses 
+%              for wideband spin inversion. Journal of Magnetic Resonance, 
+%              118(2), 299-303. https://doi.org/https://doi.org/10.1006/jmra.1996.0042 
+%                  --> lambda equation, Eq. 10 (added to omega1 for scaling)
+%                  --> Added beta for everywhere theres tau to follow
+%                  trends in Table 1
+%
+% To be used with qMRlab
+% Written by Amie Demmans & Christopher Rowley 2024
+
+
+% Function to fill default values;
+    if ~isfield(Params, 'PulseOpt')
+        Params.PulseOpt = struct();
+    end
+
+Params.PulseOpt = AI_defaultHanningParams(Params.PulseOpt);
+Trf = Trf/1000;
+nSamples = Params.PulseOpt.nSamples;  
+t = linspace(0, Trf, nSamples);
+tau = t-Trf/2;
+
+% Amplitude
+A_t = Params.PulseOpt.A0*((1+cos(pi.*tau.*Params.PulseOpt.beta))./2);
+A_t((t < 0 | t>Trf)) = 0;
+% disp( ['Average B1 of the pulse is:', num2str(mean(A_t))]) 
+
+% Scaling Factor (lambda) 
+% --> Setting Q = 0 allows for viewing of RF pulse 
+if Params.PulseOpt.Q == 0 
+    lambda = 0;
+else 
+    lambda = (Params.PulseOpt.A0)^2 ./ (Params.PulseOpt.beta.*Params.PulseOpt.Q);
+end 
+
+% Frequency modulation function 
+% Carrier frequency modulation function w(t):
+omegaterm1 = Params.PulseOpt.beta.*tau;
+omegaterm2 = (4/(3*pi)*sin(pi.*tau.*Params.PulseOpt.beta));
+omegaterm3 = 1+1/4*cos(pi.*tau.*Params.PulseOpt.beta);
+omega1 = -lambda.*(omegaterm1+(omegaterm2.*omegaterm3));
+
+
+% Phase modulation function phi(t):
+phiterm1 = (Params.PulseOpt.beta*lambda.*tau.^2)./2;
+phiterm2num = lambda*(cos(pi.*tau.*Params.PulseOpt.beta)+4).^2;
+phiterm2denom = 6*Params.PulseOpt.beta*pi^2;
+phi = phiterm1 - (phiterm2num/phiterm2denom);
+
+% Put together complex RF pulse waveform:
+rf_pulse = A_t .* exp(1i .* phi);
+
+
+
+
+
+
+
diff --git a/src/Models_Functions/adiabatic_inv/pulses/AI_hs1_pulse.m b/src/Models_Functions/adiabatic_inv/pulses/AI_hs1_pulse.m
@@ -0,0 +1,126 @@
+function [rf_pulse, omega1, A_t, Params] = AI_hs1_pulse(Trf, Params)
+
+%   hyperbolicSecant_pulse Adiabatic Inversion hyperbolic secant RF pulse function.
+%   pulse = hyperbolicSecant_pulse(t, Trf, PulseOpt)
+%
+%   B1(t) = A(t) * exp( -1i *integral(omega1(t')) dt' )
+%   where A(t) is the envelope, omega1 is the frequency sweep
+%
+%   Phase modulation is found from taking the integral of omega1(t)
+%   Frequency modulation is time derivative of phi(t)
+%
+%   For the case of a hyperbolic secant pulse:
+%   A(t) = A0 * sech(Beta*t)
+%   omega1(t) = -mu*Beta*tanh(Beta*t)
+%
+%   A0 is the peak amplitude in microTesla
+%   Beta is a frequency modulation parameter in rad/s
+%   mu is a phase modulation parameter (dimensionless)
+%
+%   The pulse is defined to be 0 outside the pulse window (before 
+%   t = 0 or after t=Trf). (HSn, n = 1-8+) 
+%
+%   --args--
+%   t: Function handle variable, represents the time.
+%   Trf: Duration of the RF pulse in seconds.
+%
+%   --optional args--
+%   PulseOpt: Struct. Contains optional parameters for pulse shapes.
+%   PulseOpt.Beta: frequency modulation parameter
+%   PulseOpt.n: time modulation - Typical 4 for non-selective, 1 for slab
+%   Reference: Matt A. Bernstein, Kevin F. Kink and Xiaohong Joe Zhou.
+%              Handbook of MRI Pulse Sequences, pp. 110, Eq. 4.10, (2004)
+%
+%              Tannús, A., & Garwood, M. (1997). Adiabatic pulses. NMR in 
+%              Biomedicine: An International Journal Devoted to the 
+%              Development and Application of Magnetic Resonance In Vivo, 
+%              10(8), 423-434. https://doi.org/10.1002/(sici)1099-1492(199712)10:8 
+%                   --> Table 1 contains all modulation functions 
+%
+%              Garwood, M., & DelaBarre, L. (2001). The return of the frequency
+%              sweep: designing adiabatic pulses for contemporary NMR. Journal
+%              of Magnetic Resonance, 153(2), 155-177. 
+%              https://doi.org/10.1006/jmre.2001.2340 
+%                   --> A(t), omega1, mu(phase modulation parameter)
+%
+%              Tannús, A., & Garwood, M. (1996). Improved performance of 
+%              frequency-swept pulses using offset-independent adiabaticity. 
+%              Journal of Magnetic Resonance, 120(1), 133-137. 
+%              https://doi.org/https://doi.org/10.1006/jmra.1996.0110 
+%                   --> Fig 1a and 1b. Show how width of amplitude and
+%                   frequency vary with each pulse
+%
+%
+% To be used with qMRlab
+% Written by Christopher Rowley 2023 & Amie Demmans 2024
+
+
+% Function to fill default values;
+    if ~isfield(Params, 'PulseOpt')
+        Params.PulseOpt = struct();
+    end
+
+Params.PulseOpt = AI_defaultHs1Params(Params.PulseOpt);
+Trf = Trf/1000;
+nSamples = Params.PulseOpt.nSamples;  
+t = linspace(0, Trf, nSamples);
+tau = t-Trf/2;
+
+% Amplitude
+A_t =  Params.PulseOpt.A0* sech(Params.PulseOpt.beta* ( (tau)).^Params.PulseOpt.n);
+A_t((t < 0 | t>Trf)) = 0;
+% disp( ['Average B1 of the pulse is:', num2str(mean(A_t))]) 
+
+% Frequency modulation function 
+% Carrier frequency modulation function w(t):
+% NOTE: Q in Hs1 is NOT the same as in the other pulses, Q = mu
+omega1 = -Params.PulseOpt.Q.*Params.PulseOpt.beta .* ...
+            tanh(Params.PulseOpt.beta .* (tau))./(2*pi); % 2pi to convert from rad/s to Hz
+
+% Phase modulation function phi(t):
+phi = Params.PulseOpt.Q .* log(sech(Params.PulseOpt.beta .* (tau)) );
+
+% Put together complex RF pulse waveform:
+rf_pulse = A_t .* exp(1i .* phi);
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