Abstract:
A method or apparatus for the simulation of electrical stimulations in an examination subject which are generated by rapidly switched gradient fields of an MR device, and wherein aborting of the executed measuring sequence occurs given the crossing of a threshold value in an online monitoring, wherein the crossing of the threshold value is signaled prior to the execution of the measuring sequence in a look-ahead monitoring, at least one gradient signal G(t) is determined which is defined by the time characteristic of the gradient pulses, at least one first filtered gradient signal G F1 (t) is formed by filtering the gradient signal G(t) with a first filtering function f F1 (t) a stimulation signal Stim(t) is formed which describes the stimulation of the examination subject, from the first filtered gradient signal G F1 (t), and the stimulation signal Stim(t) is compared to a definable stimulation threshold value Stim lim . If Stim lim  is exceeded an indicator indicating that a stimulation has occurred is emitted.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method for simulating the electrical stimulations which are generated in an examination subject by gradient coils of an MR device. 
     2. Description of the Prior Art 
     In the known MR devices, rapidly switched gradient fields with a high amplitude are superimposed on a basic magnetic field. 
     In MR exams, the patients can be stimulated by switching the gradient impulses (known as MR stimulation). The stimulations are caused by the effect of an electrical field on the patient. The electrical field is induced by the alteration, according to Maxwell&#39;s equations, of the magnetic flux B which is generated by each of the three gradient coils. For a given MR device, the magnitude of the electrical field that is generated by switching a gradient coil is directly proportional to the time variation of the value of the magnetic flux B, expressed by dB/dt, i.e., the time derivative of the magnitude of the magnetic field which is produced by the gradient coil. Because of the proportionality of the electrical field and dB/dt (chronological change of the magnetic flux B), it is sufficient merely to observe the time variation of the magnetic flux B. 
     On the basis of the proportionality of the magnetic flux B and the gradient field G for a given gradient coil, monitoring the time variation d/dt of the spatially dependent gradient field G (in mT/m) is equivalent to aforementioned monitoring the time variation d/dt of the spatially dependent magnetic flux B (in mT). Therefore, the following considers the time variation of the gradient signals. 
     A stimulation occurs when a characteristic threshold value of the electrical field is exceeded. The corresponding threshold value of dB/dt, or of dG/dt, depends for a fixed gradient schema on the anatomy and the physiology of the patient, his orientation in the MR device and the geometric and physical properties of the three gradient coils. The value dB/dt is defined by the amplitude of the gradient pulses and the rise times. In practice, however, the gradient profile is not constant from pulse to pulse, either with respect to the amplitudes or the timing, but rather, besides being dependent on the selection of the measuring sequence, it depends in particular on the selected measuring parameters (e.g. slice thickness, number of slices, field of view FOV, matrix size, repetition time T R , echo time T E , etc.). In this case, in addition to the aforementioned parameters, the threshold value for the stimulation particularly depends on the time configuration of the individual gradient pulses, their total number and repetition rate, and the superimposition of all three gradient coils G x , G y , and G z . 
     For whole-body gradient coils, not only the B z  component of the magnetic field, which extends in a longitudinal direction, but also its transverse components B x  and B y  are responsible for the stimulation, the B y  component being more critical with respect to stimulations, since the field lines penetrate the body frontally. Thus, given a prone or supine position of the patient, the stimulation limit value for the y-axis must be the smallest. 
     As an extreme simplification, from a physiological perspective, a consciously perceived stimulation by an external electrical field can be described in two steps. The electrical field can either act directly from outside or can be induced by a varying magnetic field. 
     In a first step, the electrical field generates an electrical potential at the cell wall of the stimulated nerve cells. The cell wall of the nerve cell can be approximately imagined as a capacitor which is charged by the electrical field. When the electrical potential exceeds a characteristic threshold, an action potential is triggered in the nerve cell and spreads over the entire nerve cell. 
     In the second step, at the connection of two nerve cells (a synapse), an action potential on the presynaptic side leads to a diffusion out of chemical messenger substances. These substances are absorbed on the postsyanptic side, i.e., they are absorbed in the nerve cell which is connected downstream, where they trigger another action potential. The stimulus spreads. The concentration of the messenger substances in the synapse is a measure of the number of postsynaptically triggered action potentials. In particular, the concentration of the messenger substances in the synapse subsides only gradually. The characteristic time constant is in the range of a few milliseconds. A more exact description of the neurophysiological processes can be found in the text  Neuro - und Sinnesphysiologie  (R. F. Schmidt, pub.; Springer, Second Edition 1995: Chapters 2 and 3). 
     In order to avoid such stimulations in the examined body given rapidly switched gradient fields of high amplitude, it is taught in German OS 42 25 592 to cover, with a closed conductor loop, those regions outside the examination region which are sensitive to stimulation. This results in a reduction of the currents induced in the covered region. This method is based on the fact that, given switched gradients, the highest current values are induced outside the examination region, so that the danger of stimulations is greatest there. The linearity of the gradients in the examination region, which is of importance for the image quality, is minimally compromised by the attachment of conductor loops outside the examination region. Given a change of examination region, however, the position of the conductor loops must also be adjusted. 
     There are also known methods which enable a prediction of magnetostimulations. One of these approaches to stimulation monitoring is what is known as the dB/dt model. This method involves checking and monitoring the pure dB/dt values that arise in a measurement. The maximum permissible dB/dt values derive from the result of a stimulation study with the corresponding gradient coil, or from the limit values which are strictly prescribed by the certification authorities. Further details can be from in the article “Peripheral Nerve Stimulation by Time-Varying Magnetic Fields” (J. Abart,  J. Computer Assisted Tomography  (1997); 21(4):532-38. The dB/dt model does not adequately consider the patient physiology; in particular, the dependency of the stimulation threshold on the timing of the gradient impulses is not taken into account. The dB/dt model is thus only a worst-case estimate, which, in many cases, allows the capability of modern gradient systems to be used only within certain limits. 
     Another known approach to stimulation monitoring is known as the “Irnich model”. This method describes the stimulation threshold value as a factor of the duration t E  of the external influence. The duration t E  is the time in which the gradient changes in one direction; i.e., dB/dt is permanently &gt;0, or &lt;0. A more detailed explanation can be found in the article “Electrostimulaticn by time-varying magnetic fields” (W. Irnich, MAGMA; 1994; 2:43-9. Represented as the dB/dt value, the threshold is therein proportional to (1+t chron /t E ), i.e. is hyperbolically dependent on the duration of effect t E . The chronaxie time t chron  is a physiologically defined characteristic time. 
     The experimental results in different studies can be described well with the Irnich model. The results of these studies are discussed in the article “Magnetostimulation in MRI” (W. Irnich, F. Schmitt; MRM; 1995;33:619-23), and in the article “Threshold and Pain Strength-Duration Curves for MRI Gradient Fields” (J. D. Bourland; Proc. SMRM; 1997:1974). Nevertheless, it is possible to apply the Irnich model with a fixed set of parameters only to one characteristic gradient pulse shape, given which the alteration of the duration of t E  is performed globally, i.e. for each individual pulse in a like manner. A discrepancy thus arises when trapezoidal pulses with a corresponding duration of effect t E  are used instead of sinusoidal pulses. The method which is based on the Irnich model is also not usable if mere single pulses within a long pulse train generate particularly high dB/dt values (e.g. blip pulses). In addition, the Irnich model does not take into account the dependency of the stimulation threshold on the number of individual pulses in a pulse train. In this respect, one can refer to FIG. 4 of the article “Physiological Effects of Fast Oscillating Magnetic Field Gradients” (Th. F. Budinger,  J. Computer Assisted Tomography,  1991;15(6):909-14. The dependency on what are known as plateau times in sinusoidal excitations is not taken into account, either, such as can be seen in FIG. 7 of the essay “Peripheral Nerve Stimulation by Time-Varying Magnetic Fields”;  J. Computer Assisted Tomography  (4):532-38. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to provide a method which avoids electrical stimulations in an examination subject who is exposed to rapidly switched gradient fields of high amplitude can be avoided. 
     This object is inventively achieved in a method wherein at least one gradient signal G(t) determined that is defined by the time characteristic of the gradient pulses, at least one first filtered gradient signal G F1 (t) is formed by filtering the gradient signal G(t) with a first filtering function f F1 (t), from the first filtered gradient signal G F1 (t), a stimulation signal Stim(t) is formed which describes the stimulation of the examination subject, and the stimulation signal Stim(t) is compared to a predetermineable stimulation threshold value Stim lim , and if the threshold value Stim lim  is exceeded, a signal is emitted. 
     The above object is also achieved in an apparatus having at least two parallel circuit paths, a first of which is a series circuit formed by it least one low pass filter followed by a rectifier and a second of which is a series circuit formed by a rectifier followed by at least one low pass filter, an input stage whose input signal is the gradient signal G(t) and whose output signal is fed to both the paths as a path input signal, and an adder which adds the output signals of the two paths, forming at least one stimulation signal Stim(t) with a predetermineable weighting, which signal describes the stimulation of the examination subject. 
     The inventive method can be applied to one, two or all three gradient coils, which represent physical gradient axes, respectively. The number of gradient coils from the total of three to which this method is applied ultimately depends on the particular MR device, on the desired pickups and on the permissible stimulation threshold values Stim lim . 
     If all three gradient coils are switched simultaneously (e.g. given tilted or rotated slices), then it can be checked for each gradient axis separately whether or not a stimulation is produced. This may not be sufficient, however, since a stimulation can be triggered, for example, by the simultaneous influence of all three gradient coils, although the stimulation threshold has not yet been exceeded for each individual coil. In an embodiment of the invention, a check as to whether stimulations can be triggered by the simultaneous influence of all three gradient coils can be realized easily, such as by combining the three ratios Stim x (t)/Stim lim,x , Stim y (t)/Stim lim,y , and Stim z (t)/Stim lim,z . 
     In a further version of this check, it can be checked whether the following condition is satisfied for each time t (the additional indices relate to the observed respective physical gradient axes x,y,z): 
     
       
         [(Stim x (t)/Stim lim,x ) 2 +(Stim y (t)/Stim lim,y ) 2 +(Stim z (t)/Stim lim,z ) 2 ] ½ &lt;Stim factor   
       
     
     wherein Stim factor  designates the stimulation factor which describes the stimulation caused by the influence of all three gradient coils (gradient axes). For the stimulation factor Stim factor , the following inequality applies: Stim factor ≦1. 
     When the aforementioned condition is satisfied, then stimulations do not arise. When this condition is not satisfied, i.e. when the sum on the left side of the inequality is greater than the stimulation factor Stim factor , then stimulations can be expected. The inclusion of the stimulation factor Stim factor  permits a greater flexibility in the adaptation of the inventive method to the device-specific data, which can be acquired experimentally. 
     A further embodiment of the device for practicing the inventive method takes into account that the simultaneous influence of at least two gradient fields can trigger a stimulation, even though the stimulation threshold for each individual gradient field has not been exceeded, and that the orthogonality of the gradient fields usually no longer exists outside the examination region. To this end, adders with predetermineable weighting add at least two stimulation signals of two gradient coils and/or at least two squared stimulation signals of two gradient coils and/or at least one stimulation signal of a gradient coil and the same signal in squared form, in order to compare the summed signals to appertaining predetermineable reference levels in a comparator unit. 
     In the inventive method according to Claim  1 , it is sufficient to observe the gradient signals G(t) without having to know their mathematical structure, which can be derived from the time characteristic and the amplitude of the gradient impulse. 
     The gradient signals G(t) are easy to measure, since they correspond (up to a scaling factor) to the current through the related gradient coil. 
     In a further embodiment of the inventive method existing voltage signals of the gradient control and amplifier unit of an MR device are used as gradient signals G(t). The current real value signals, or current target value signals and voltage signals, which are directly proportional to the first time derivative of a gradient coil current, are suitable for this. Given the use of current real value signals, an error of the gradient control and amplifier unit can also be monitored with the inventive device. The advantage of using current target value signals is that the attainment of stimulation thresholds in an online monitoring is recognized a few microseconds earlier than with current real value signals. Given the use of a voltage signal which is directly proportional to the first time derivative of a gradient coil current, the differentiation that is necessary for the current real value signals and target value signals not needed. This voltage signal is usually available as an output voltage of the gradient control and amplifier unit. 
     By filtering the differentiated gradient signal G diff  with a first filtering function f F1 (t) and with a second filtering function f F2 (t), in another embodiment of the invention, the stimulations which are induced by an external electrical field and the further conduction of these stimulations in the nervous system are approximately modeled. The first filtering function f F1 (t) describes the excitement of the action potential on the presynaptic side, which causes chemical messenger substances to be diffused out. These messenger substances are absorbed on the postsynaptic side, i.e., in a nerve cell downstream, where they trigger a further action potential. The excitation of the action potential on the postsynaptic side is described by the second filtering function f F2 (t). Since the original polarity of the excitation is no longer contained in the action potential on the postsynaptic side, in a further embodiment of the invention, the result of the first filtering function f F1 (t) is rectified to Abs (f F1 (t)), and only the rectified portion of the differentiated gradient signal G diff  is processed by the second filtering function f F2 (t). 
     Although a knowledge of the mathematical structure of the gradient signals is not necessary in the inventive method, the inventive method offers a better approximation with reference to stimulation prediction than previously known methods. This results from the fact that not only are the dependencies that are described by the Irnich model taken into account, but also the shape of the gradient impulse (e.g. trapezoidal, sinusoidal, blip impulse), the number of individual impulses generated by the NMR device, and the included plateau times are taken into account, but without observing their mathematical structure. Furthermore, the degree of accuracy can be arbitrarily improved by the use of additional filtering functions. 
     In an embodiment of the device for practicing the inventive method, a refined simulation of the processes in the relaying of stimulations in the nervous system is achieved. To this end, the low passing is carried out in the first path by a parallel arrangement of two low pass filters and an adder which is connected downstream, which adds the output signals of the two low pass filters with a specifiable weighting. In the second path, at least one additional low pass filter is connected to the originally-cited low pass filter in parallel fashion, the output signal of the additional filter also being added by the adder with a specifiable weighting. 
     The inventive method can be realized as a hardware or software solution, or as a mixed hardware-software solution. 
     Both an online monitoring and a look-ahead monitoring of the MR device are possible with the inventive method. A combination of both types of monitoring is also possible within the framework of the invention. In this context, online monitoring means monitoring during imaging. In an embodiment of the invention the measuring sequence is immediately aborted given attainment of the stimulation threshold Stim lim . In online monitoring, an erroneous behavior of the gradient amplifier can also be monitored by means of appropriate additional measures. Look-ahead monitoring means monitoring prior to the beginning of the imaging measuring sequence. Furthermore, a wide variety of imaging measuring sequences can be simulated with the inventive method. In a look-ahead monitoring and in a measuring sequence simulation, the aborting of the measuring sequence as described above is not necessary, or at least is not desirable. 
     In another embodiment of the inventive method the filtering of the differentiated gradient signal G diff  is described by a convolution:                  G   diff          (   t   )       ⊗     1   τ                 -     t   τ           =       1   τ            ∫     -   ∞       +   ∞                  G   diff          (     t   1     )       ·            (     t   -     t   1       )     τ                              t   1               ,                          
     the filter functions f F1 (t) and f F2 (t) being realized by an exponential function with a specifiable time constant τ. 
     For the case τ=τ 1 , a first e-function (filtering function f F1 (t)) results, and for the case τ=τ 2 , a second e-function (filtering function f F2 (t)) results, with which the differentiated gradient signal G diff  is respectively physically filtered, or mathematically convolved. 
     In another embodiment of the Invention the stimulation threshold value Stim lim  can also be specified for each imaging, depending on the patient. For the patient-dependent prescription of the stimulation threshold value Stim lim , it is necessary to obtain the patient&#39;s individual stimulation threshold by a suitable measurement at the patient, e.g. by an electrical conductivity measurement. Then the stimulation threshold value Stim lim  need only be scaled accordingly. 
     In a further version of the inventive method, the function of the inventive filtering method can be changed to a pure dB/dt monitoring. By the selection of a sufficiently large value for the limit frequency of the first filtering function f F1 (t), its filtering effect is nearly eliminated. By the selection of a sufficiently small value for the second weighting factor a 2  (the weighting factor for the second filtered gradient signal G F2 (t)), the filtering result of the second filtering function f F2 (t) is effectively ignored. 
     The inventive method allows for developments which take into account further parameters besides those discussed above. Among these further parameter are the orientation of the patient in the patient tube of the magnet (e.g. lying on the back or side, head or feet first) or his/her position in the z-direction (i.e. the body part onto which the positioning occurs), for example. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a flow chart of an embodiment of the inventive method. 
     FIGS. 2 through 7 respectively show the time characteristics of signals which are measured in an embodiment of the inventive method, and of signals formed according to this method. 
     FIG. 8 is a block diagram of a first embodiment of an apparatus in accordance with the invention for conducting the inventive method. 
     FIG. 9 is a block diagram of a second embodiment of an apparatus in accordance with the invention for conducting the inventive method. 
     FIGS. 10 through 19 show circuit details of various electrical circuit modules for use in the apparatus embodiments shown in FIGS. 8 and 9. 
     FIG. 20 is a more detailed circuit diagram of further embodiment of an apparatus in accordance with the invention for conducting the inventive method. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The flow chart according to FIG. 1 begins with a differentiation stage  1  to which a gradient signal G(t) is fed. The gradient signal G(t) has the time characteristic which is illustrated in FIG. 2. A preferred embodiment of the inventive method is detailed below using a trapezoidal gradient signal (trapezoidal pulse) with the amplitude B 0 =10 mT. 
     The dimension of the gradient impulse and thus of the gradient signal G(t) are mT/m. The spatial dependency of the magnetic field which is generated by the gradient coil is not considered more closely below. Rather, with G=G(t), the gradient field which is defined by the gradient coil is observed at a fixed point in space. The scaling factor in the transition from the gradient signal to the magnetic field is determined by the gradient coil that is used and the point in space that is observed. 
     In the differentiation stage  1 , a differentiated gradient signal G diff (t) is formed from the gradient signal G(t) by a first time derivative d/dt, the time characteristic of this differentiated gradient signal being illustrated in FIG.  3 . 
     The differentiated gradient signal G diff (t) is sent to a first low pass filter stage  2  and a second low pass filter stage  4 . In the illustrated exemplifying embodiment, the two low pass filter stages  2  and  4  are arranged parallel to one another and are connected downstream from the differentiation stage  1 . A rectifier stage  3  is present downstream of the first low pass filter stage  2 , and a rectifier stage  3  is present upstream of the second low pass filter stage  4 , by means of which only the rectified portion of the differentiated gradient signal G diff (t) is fed to the second low pass filter stage  4 . Thus, only the absolute value of the differentiated gradient signal G diff (t) is available for further signal processing. 
     In the first low pass filter stage  2 , the differentiated gradient signal G diff (t) is filtered with a first filtering function f F1 (t). In the second low pass filter stage  4 , the absolute value of the differentiated gradient signal G diff (t) is filtered with a second filtering function f F2 (t). 
     In the described development of the inventive method, the two filtering functions f F1 (t) and f F2 (t) are defined as follows:              f   F1          (   t   )       =         1     τ   1                 -     t     τ   1                         and                     f   F2          (   t   )         =       1     τ   2                 -     t     τ   2                 ,                          
     wherein τ 1  and τ 2  are selected time constants. 
     The stimulations caused by an external electrical field and the relay (transmission) thereof in the nervous system are approximately described by the filtering of the differentiated gradient signal G diff (t) with a first filtering function f F1 (t) and by filtering of its rectified portion Abs(G diff (t)) with a second filtering function f F2 (t). The first filtering function f F1 (t) herein describes the excitation of the action potential on the presynaptic side, which causes chemical messenger substances to be diffused out. These messenger substances are absorbed on the postsynaptic side, i.e. in nerve cells downstream, where they trigger a further action potential. The excitation of the action potential at the postsynaptic side is described by the filtering function f F2 (t). Since the original polarity of the excitation is no longer contained in the action potential at the postsynaptic side, only the rectified portion of the differentiated gradient signal G diff (t), which is designated Abs(G diff (t)), is processed in the second low pass filter stage  4 . 
     Thus, the filtering of the differentiated gradient signal G diff (t) in the first low pass filter stage  2  simulates the presynaptic behavior. Analogously, the post-synaptic behavior is mapped as a model in the second low pass filter stage  4 . 
     The time characteristic of the first filtered gradient signal            G   F1          (   t   )       =           G   diff          (   t   )       ⊗     1     τ   1                   -     t     τ   1                                    
     is illustrated in FIG. 4, with τ 1 =0.2 ms selected for the first time constant. For comparison, the differentiated gradient signal G diff (t) is also included in FIG.  4 . 
     FIG. 5 depicts the time characteristic of the second filtered gradient signal            G   F2          (   t   )       =         Abs        (       G   diff          (   t   )       )       ⊗     1     τ   2                   -     t     τ   2                                    
     whereby the second time constant τ 2 =2.0 ms has been selected. For comparison, the absolute value of the differentiated gradient signal G diff (t), designated Abs(G diff (t)), is also included in FIG.  5 . 
     The first filtered gradient signal G F1 (t) and the second filtered gradient signal G F2 (t) each undergoes a weighting in a further step. In the exemplary embodiment, this occurs by the multiplication of the rectified first filtered gradient signal Abs(G F1 (t)) by a specifiable first weighting factor a 1 , and the multiplication of the second filtered gradient signal G F2 (t) by a specifiable second weighting factor a 2 . The first filtered gradient signal G F1 (t) is fed for this purpose to a first multiplier stage  5 , and the second filtered gradient signal G F2 (t) is fed to a second multiplier stage  6 . For the weighting factors a 1  and a 2  the following equation applies: a 1 +a 2 =1. In the exemplary embodiment, a 1 =0.6 and a 2 =0.4. 
     In the first multiplication stage  5 , a first weighted and filtered gradient signal G F1g (t)=a 1 . Abs(G F1 (t)) is thus obtained. 
     Analogously, in the second multiplication stage  6 , a second weighted and filtered gradient signal G F2g (t)=a 2 ·G F2 (t) is obtained. 
     The two weighted and filtered gradient signals G F1g (t) and G F2g (t) are combined by a freely selectable logic operator into a stimulation signal Stim(t). In the present exemplary embodiment, the combining occurs by addition of the two weighted and filtered gradient signals G F1g (t) and G F2g (t). The two weighted and filtered gradient signals G F1g (t) and G F2g (t) thus are fed to an adder stage  7  for this purpose. 
     The resultant stimulation signal Stim(t) is thus as Stim(t)=G F1g (t)+G F2g (t). 
     FIG. 6 illustrates the characteristic of the stimulation signal Stim(t). For comparison, the absolute value of the differentiated gradient signal G diff (t), designated Abs(G diff (t)), is included in FIG.  6 . 
     The stimulation signal Stim(t) which is so obtained is fed to a comparator stage  8 . 
     In the comparator stage  8 , the stimulation signal Stim(t) is compared to a specifiable stimulation threshold Stim lim . If the detected stimulation signal Stim(t) attains or exceeds a characteristic limit value Stim lim  for the gradient coil, then this is an indicator of the occurrence of stimulations. In the given exemplary embodiment, the maximum stimulation value Stim max  of the stimulation signal Stim(t) is determined and is compared with the specifiable stimulation threshold value Stim lim . If the maximum stimulation value Stim max  is greater than the stimulation threshold value Stim lim , then stimulations are expected to occur; otherwise, they are not. 
     If no stimulations are to be expected, then the imaging measuring sequence is continued (as indicated by the CONTINUE block). If so desired, the maximal stimulation value Stim max  can be continuously logged. 
     In the exemplary embodiment, which involves online monitoring, if the stimulation threshold value Stim lim  is exceeded, the imaging is at least temporarily interrupted (as indicated by the STOP block). The ratio Stim lim /Stim max , which is obtained from the specifiable stimulation threshold value Stim lim  and the maximum stimulation value Stim max  (and which is &lt;1), is used directly as a scaling factor for the amplitude of the gradient signal G(t). Stimulations then no longer arise in a renewal imaging sequence. 
     In the characteristic of the stimulation signal Stim(t) illustrated in FIG. 7, Stim lim =20.1 T/s is selected for the stimulation threshold value. 
     As can be seen in FIG. 7, in this example a stimulation would be triggered by the trailing edge of the third gradient signal after some 6 ms, although the arising nominal dB/dt values are constant for all individual gradient pulses. 
     The filtering of the differentiated gradient signal G diff (t) which is to be performed in the inventive method can be easily calculated mathematically as a filtering function employing an exponential function. 
     Below, G n =G diff (n·Δt) designates the differentiated gradient signal at a time (n·Δt), and G Fn =G F (n·Δt) designates the filtered gradient signals G F1 (t) and G F2 (t) at a time (n·Δt). At represents the sampling interval. 
     With c 1 =e −Δ/     τ    and c 2 =1−c 1 , the filtered gradient signal G Fn  can then be calculated iteratively from the differentiated gradient signal G n  (input signal of the low pass filter stage  2  or  4  and the already calculated values of G Fn , according to the following relation: 
     
       
           G   Fn   =c   1   ·G   Fn-1   +c   2   ·G   n . 
       
     
     The flow chart depicted in FIG. 1 for monitoring the stimulation thresholds is realized in an exemplary electrical circuit shown in FIG.  8 . Thus, for example, convolution of the differentiated gradient signal with an e-function corresponds to the behavior of a low-pass circuit comprised of a resistor and a capacitor. 
     FIG. 8 depicts an exemplifying embodiment for realizing the flow chart which is depicted in FIG. 1 from the gradient signal G(t) to the stimulation signal Stim(t). The differentiator DIF, the low pass filters TP 1  and TP 2 , the rectifiers GR 1  and GR 2  and the adder SUM 1  are thus composed of operational amplifiers OPAMP, resistances R and capacitances C, in corresponding circuit modules according to FIG.  10  through FIG.  16 . The gradient signal G(t) is a voltage signal which is directly proportional to the current in a gradient coil, which is determined by a gradient pulse sequence. 
     In FIG. 8, the gradient signal G(t) is fed to a differentiator DIF. The output signal of the differentiator is fed to a first low pass filter TP 1 , whose output signal is fed to a first rectifier GR 1 . The output signal of the differentiator is simultaneously fed to a second rectifier GR 2 , whose output signal is fed to a second low pass filter TP 2 . The output signals of the rectifier GR 1  and of the low pass TP 2  are fed to an adder SUM 1 , wherein they are added together, with a definable weighting, the output signal of said adder being the stimulation signal Stim(t). 
     FIG. 11 depicts the differentiator DIF. The illustrated circuit is a differentiator with an integrated low pass filter with the low-pass time constant T TP . The frequency response OUT/IN=−j·ω·T DIF /(1+j·ω·T TP ), wherein, T DIF =C 1 ·R 1  is the differentiator time constant, T TP =C 1 ·R 2  is the low-pass time constant, and ω=2·π·f is the angular frequency, f being the frequency. In practice, the differentiator with the frequency response OUT/IN=−j·ω·R 1 ·C 1 , as illustrated in FIG. 10, exhibits an undesirable transient condition. This transient condition is eliminated by the integrated low pass filter. The time constant T TP  is selected on the order of magnitude of 1 to 3 μs, so that it is rather small compared to the rise time of the gradient and is therefore negligible. 
     The low pass filter TP 1  can be formed as a circuit with an operation amplifier OPAMP according to FIG.  15 . The amplification factor is −R 21 /R 20 , the time constant is R 21 ·C 10  and the frequency response OUT/IN=−(R 21 /R 20 )·(1/(1+j·ω·R 21 ·C 10 )). A passive low pass filter according to FIG. 16 can also be used, but the impedance of the subsequent circuit should be taken into account. The passive low filter pass according to FIG. 16 has the time constant R 30 ·C 30  and the frequency response OUT/IN=1/(1+j·ω·R 30 ·C 30 ). The use of a passive low pass filter conserves components although it complicates the calculation of the time constants and weighting factors. 
     The rectifier GR 1  corresponds to the circuit depicted in FIG.  12 . It delivers a negative output voltage OUT independently of the sign of the input voltage IN, i.e. OUT=−Abs(IN). The rectifier GR 2  corresponds to the circuit in FIG.  13  and always delivers a positive output voltage OUT, independent of the sign of the input voltage IN, i.e. OUT=Abs (IN). The dimensioning with the resistance values R and 2·R respectively illustrated in FIG.  12  and FIG. 13 effects a correspondence between the output voltage and the negative or positive value of the input voltage; i.e., there is a gain of one. 
     The low pass filter TP 2  corresponds to the circuit according to FIG.  15 . The adder SUM 1  is generally illustrated in FIG.  14 . The weighting of the input signals relative to one another is set by the resistors R 41  and R 42 , and the resistor R 4 xx is responsible for the total gain. Given two input voltages IN 1  and IN 2 , the following equation applies to the output voltage OUT of the adder: OUT=−(IN 1 ·R 4 xx/R 41 +IN 2 ·R 4 xx/R 24 ). It is guaranteed by the two different rectifiers (GR 1  and GR 2  that the two input voltages of the adder SUM 1  have the same sign. 
     A good dimensioning of the circuit according to FIG. 8 is achieved when the individual signal levels are high relative to disturbing influences, but an overcontrolling of individual circuit parts is avoided. It is assumed below that the supply voltage of the operation amplifier is +/−15V. 
     Taking the example of the fastest possible rise time of the gradient signal of 100 μs, the output voltage of the differentiator is 10V. The time constant T DIF =R 1 ·C 1  is thus 100 μs. If C 1  is defined as 1 nF, then R 1  becomes 100 kΩ. The resistance R 2  is determined experimentally. It is preferably under 5 kΩ. 
     In order to maintain the signal level of 10V, the two resistances R 21  and R 20  of the low pass filters are selected so as to be equally large. If the time constant of the first low pass filter TP 1  is defined as 0.2 ms and R 21  is defined as 10 kΩ, then a value of 20 nF results for C 10 . The dimensioning of the second low pass filter TP 2  with the exemplary time constant of 2 ms results in a capacitance value of 200 nF with a resistance of 10 kΩ. 
     Since the rectifiers GR 1  and GR 2  have a gain of one, the maximum level of 10 V is maintained. The adder SUM 1  weights and adds the output signals OUT(GR 1 ) and OUT(TP 2 ) of rectifier GR 1  and low pass filter TP 2 . If said signals are to be valued 0.6 and 0.4, for example, and if the 10V level is to be maintained, then the following dimensioning applies: 
     
       
         10V=−((OUT(GR 1 )·R 4 xx/R 41 )+OUT(TP 2 )·R 4 xx/R 42 )). 
       
     
     The output signal level of rectifier GR 1  and low pass filter TP 2  is −10V, resulting in R 4 xx/R 41 =0.6 and R 4 xx/R 42 =0.4. If R 4 xx is set at 10 kΩ, then R 41 =16.666 kΩ and R 42 =25 kΩ. 
     FIG. 9 depicts an exemplary embodiment for generating a stimulation signal Stim(t) by means of which a refined simulation of the nerve stimulation is achieved. To this end, the low pass filtering of the low pass filter TP 1  from FIG. 8 is implemented with two low pass filters TP 1   a  and TP 1   b,  whose output signals are weighted and added by an adder SUM 2 . The output signal of SUM 2  forms the input signal for the rectifier GR 1 . Furthermore, additional low pass filters TP 3 , etc. are arranged parallel to the low pass filter TP 2 . The output signals of the rectifier GR 1  and of the low pass filters TP 2 , TP 3 , etc. are fed to the adder SUM 1 , wherein they are weighted and added. The low pass filter (or filters) TP 3 , etc. correspond to the circuit in FIG.  15 . 
     The inventive method can be applied separately to each one of the three gradient coils, which respectively represent one physical gradient axis. If all three gradient coils are simultaneously switched (e.g. given tilted or rotated slices), however, then it can be inventively checked for each gradient axis whether or not a stimulation arises. This may not be sufficient, however, since a stimulation can be triggered, for example, by the simultaneous influence of all three gradient coils, although the stimulation threshold for each individual coil has not been exceeded. The check as to whether a stimulation can be triggered by the simultaneous influence of all three gradient coils can be easily realized with an additional step. 
     In this additional step, it is checked whether the following condition is satisfied (the additional indices relate to the observed respective physical gradient axes x,y,z): 
     
       
         [(stim x (t)/Stim lim,x ) 2 +(Stim y (t)/Stim lim,y ) 2 +(Stim z (t)Stim lim,z ) 2 ] ½ &lt;Stim factor , 
       
     
     where Stim factor  designates the stimulation factor which describes the stimulation caused by the influence of all three gradient coils. For the stimulation factor, the inequality Stim factor ≦1 applies. 
     If the preceding condition is satisfied for each time t, then stimulations do not arise. If this condition is not satisfied, i.e. if the sum on the left side of the inequality is greater than the stimulation factor Stim factor , then stimulations can be expected. The insertion of the stimulation factor Stim factor  permits a greater flexibility in the adaptation of the inventive method to experimentally obtained data, which can be different for different MR devices. 
     FIG. 20 depicts an exemplary embodiment a circuit of a device for conducting the method for three gradient coils of a gradient system. The input signals of the circuit are the gradient signals G x (t), G y (t) and G z (t) of the three physical gradient axes x, y and z. These are voltage signals. In one embodiment, these voltage signals are directly proportional to the currents in the gradient coils. The current real value signals, or target value signals, are suitable for this purpose, which signals are usually present as voltage signals in the gradient control and amplifier unit of the MR device. In another embodiment, without using the differentiator DIF in FIG.  8  and FIG. 9, voltage signals which are directly proportional to the first time derivative of a gradient coil current are used as gradient signals. As a rule, this type of signal is available as an output voltage U out (t) of the gradient control and amplifier unit. The voltage U OUT (t) is set such that the following equation applies: U OUT (t)=L·di(t)/dt+R·i(t). L is the inductance and R is the resistance of a gradient coil including its connecting cables, and i(t) is the gradient coil current. There is direct proportionality between the voltage U OUT (t) and the derivative of the gradient coil current di(t)/dt for R=0. In practice, the resistance R is not equal to zero. The error with which one is confronted when using the voltage signal U OUT (t) as the input signal is demonstrated in the following example: Given a resistance R of the gradient coil of 1 Ω, for example, which resistance has been increased by current displacement, and a current of 100 A, a voltage of 100 V drops at the resistance R. Given a total voltage of 1000 V, 900 V remain for the equation element L·di(t)/dt; the error would thus be 10%. 
     The gradient signals G x (t), G y (t) and G z (t) are fed respectively to the function blocks GSX, GSY and GSZ which correspond to the circuits, in FIG. 8 or FIG.  9 . The output signals of these function blocks GSX, GSY and GSZ are the stimulation signals Stim x (t), Stim y (t) and Stim z (t), respectively. They are respectively fed to a squarer x 2  in one path. An example of a squarer circuit is given in FIG. 17, wherein a multiplier is configured as a squarer in that two connected inputs are fed the same input signal, and the three remaining inputs are connected to ground. This results in the following equation for the output voltage OUT of the squarer: OUT=IN·IN/10V. Given an input voltage IN of 10 V, the output voltage is likewise 10V. 
     Each stimulation signal Stim x (t), Stim y (t) and Stim z (t) is fed to a logic circuit directly as well as in squared form. The logic circuit is formed by four adders SUM 2 , SUMX, SUMY and SUMZ, for example. The adder SUM 2  weights and adds the three squared stimulation signals. The combination of the three squared stimulation signals represents the stimulation in a rectangular three-dimensional coordinate system. 
     In the circuit according to FIG. 20, it is advantageous to square the stimulation signals directly, and not, as is explained in the description of the method, to first divide the stimulation signals by stimulation thresholds. 
     Since, as a rule, there is no longer rectangularity of the gradient field outside the examination region of the MR device, and the highest gradient field strength changes are achieved outside the examination region, the logic circuit contains three additional adders SUMX, SUMY and SUMZ, which respectively form the sum of all the linear and squared stimulation signals with a definable weighting. The weighting of the adder SUMX provides a high weighting of the signals related to the x-gradient-axis; the weighting of the adder SUMY provides a high weighting of the signals related to the y-gradient-axis, and the weighting of the adder SUMZ provides a high weighting of the signals related to the z-gradient-axis. 
     While the stimulation signals Stim x (t), Stim y (t) and Stim z (t) and their squared signals are always positive, their output signals are always negative, due to the sign inversion caused by the adders SUM 2 , SUMX, SUMY and SUMZ. 
     The output signals of the adders SUM 2 , SUMX, SUMY, SUMZ, are compared in a comparator circuit with storage unit COMP_S, to appertaining stored or supplied reference levels REF 2 , REFX, REFY and REFZ. If at least one reference level is exceeded, then this indicates the attainment of a stimulation threshold, and a signal is continuously emitted at the message output COMP_OUT, thereby setting the output voltage of the gradient control and amplifier unit to zero in an online monitoring, for example. The signal at the message output COMP_OUT is cleared by a reset signal at the reset input N_RESET. 
     FIG. 18 depicts the basic function of a comparator COMP which combines two input signals IN 1  and IN 2  into one output signal. The signal output is thus located at a high level as long as IN 1  is greater than IN 2 . If IN 1  is smaller than IN 2 , the signal output is located at a low level. 
     FIG. 19 depicts the comparator circuit with the storage unit COMP_S as a simple connection of comparators to a simple flip-flop consisting of two NAND gates as storage units. The comparator circuit COMP_S, contains comparators in accordance with the number of input signals. The resistance at VCC keeps the common open collector output of the comparators selected for this example at a high level. If, in one of the comparators, the input signal is more negative than the appertaining reference level, which is to be prescribed with a negative sign, then this comparator draws the common output of all comparators down to a low level and effectuates a high level at the output of the flip-flop, which leads to a stoppage of the measuring sequence, for example. This high level is maintained even if the comparator restores the common output of all comparators to the high level on the basis of the eliminated stimulation. Only a reset signal at the reset input N_RESET restores the flip-flop output to the low level again. Without the flip-flop, in an online monitoring, for example, the gradient control and amplifier unit would continue the stimulating measuring sequence subsequent to a short interruption. A time element can be used instead of the flip-flop, which element arrests the gradient control and amplifier unit until a measuring sequence break has been realized. 
     A squaring of the stimulation signals can be forgone if six sums are formed instead of the three squarers X 2  and adders SUM 2 , SUMX, SUMY and SUMZ, which sums contain the following additional weightings in addition to the scalings corresponding to their stimulation portions: 
     
       
         Σ a1 ( t )=Stim x ( t )+({square root over ( )}2−1)·Stim y ( t )+({square root over ( )}3−{square root over ( )}2)·Stim z ( t ) 
       
     
     
       
         Σ a2 ( t )=Stim x ( t )+({square root over ( )}2−1)·Stim z ( t )+({square root over ( )}3−{square root over ( )}2)·Stim y ( t ) 
       
     
     
       
         Σ b1 ( t )=Stim y ( t )+({square root over ( )}2−1)·Stim z ( t )+({square root over ( )}3−{square root over ( )}2)·Stim x ( t ) 
       
     
     
       
         Σ b2 ( t )=Stim y ( t )+({square root over ( )}2−1)·Stim x ( t )+({square root over ( )}3−{square root over ( )}2)·Stim z ( t ) 
       
     
     
       
         Σ c1 ( t )=Stim z ( t )+({square root over ( )}2−1)·Stim x ( t )+({square root over ( )}3−{square root over ( )}2)·Stim y ( t ) 
       
     
     
       
         Σ c2 ( t )=Stim z ( t )+({square root over ( )}2−1)·Stim y ( t )+({square root over ( )}3−{square root over ( )}2)·Stim x ( t ) 
       
     
     This assumes that, given equally large gradients, the resulting gradient is greater than the individual gradient by {square root over ( )}2 in the plane and by {square root over ( )}3 in space. The worst case is covered by the assumption of three equally large gradients and by the transposition of the portions in the six sums. 
     The gradient field does not dynamically correspond exactly to the gradient coil current characteristic, since it is chronologically delayed and attenuated by eddy currents. If the reference level in the dynamic gradient filed is computed experimentally, then the abovementioned condition is already taken into account in the reference levels. If instead examinations are conducted in order to obtain the reference levels at static gradient fields, it is possible to evaluate the gradient coil current characteristic with eddy currents being taken into account. An evaluated gradient coil current signal is thus obtained, the characteristic of which corresponds to the actual dynamic gradient field. 
     Although modifications and changes may be suggested by those skilled in the art, it is the intention of the inventors to embody within the patent warranted hereon all changes and modifications as reasonably and properly come within the scope of their contribution to the art.