How can I constrain the Levenberg-Marquardt algorithm?

I am currently using the Levenberg-Marquardt algorithm (in lsqcurvefit.m) to fit a signal equation to some MRI data.

I need to put some boundary constraints on the output (the parameters I get as a result of the fitting) but this is not possible in lsqcurvefit when using the Levenberg-Marquardt method.

Do any of you know another function in matlab that uses the Levenberg-Marquardt algorithm and can apply constraints to it? or maybe you know how I can make a work-around and still use the lsqcurvefit?

I have pasted some of my code if that (for some reason) should be of any help.

ub = [10 1 0.1 0.001];
lb = [0 0 0 0];
constants = [t_sat,tr_p,gamma,Rb,g,Ra_obs,p1,p2];

 s_ramani_wm = @(p,M0_wm)s_ramani(p,M0_wm,constants,offset,theta);        [sign_wm,resnorm_wm,residual_wm,exflag_wm,output_wm,lambda_wm,jacobian_wm]...
     = lsqcurvefit(s_ramani_wm, p0w, M0_wm, ydata_wm, lb, ub);

Thank you for your time.

Best regards, Nanna