Condon, Barrie

Diaz-Gomez, Manuel

Robertson, Neil

English

Mitral and aortic valve replacement is a procedure which is common in cardiac surgery. Some of these replacement valves are mechanical and contain moving metal parts in the disc or leaflets. When exposed to MRI there is a potentially hazardous interaction between the moving metal parts and the static magnetic field due to the Lenz Effect. The Lenz Effect is a result of the current (induced by the metallic component moving in a static magnetic field) changing as the valve rotates; this causes a secondary field to be set up which opposes the original field and consequently opposes the motion of the component. A simple 'worst case' analysis of the potential hazard has been performed previously (1). However the differential nature of the delaying effect of the motion of the mechanical valve on the Lenz effect itself was not assessed. In this paper a differential model of a ring-strengthener valve type has been developed to take account of the interplay between the Lenz Effect and disc motion

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    Heriot-Watt University Research Gateway                                                          Heriot-Watt UniversityEstimation of resistive pressure effects in mechanical heart valves due to MRIRobertson, Neil; Diaz-Gomez, Manuel; Condon, BarriePublished in:Proc. 9th Annual Meeting of the International Society of Magnetic Resonance in Medicine (ISMRM)Publication date:2001Link to publication in Heriot-Watt Research GatewayCitation for published version (APA):Robertson, N., Diaz-Gomez, M., & Condon, B. (2001). Estimation of resistive pressure effects in mechanicalheart valves due to MRI. In Proc. 9th Annual Meeting of the International Society of Magnetic Resonance inMedicine (ISMRM): 21-27 April 2001, Glasgow, Scotland. ISMRM.General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Proc. Intl. Soc. Mag. Reson. Med 9 (2001) 1768Proc. Intl. Soc. Mag. Reson. Med 9 (2001) 1768Estimation of resistive pressure effects in mechanical heart valves due to MRINeil Robertson1, Manuel Diaz-Gomez1, Barrie Condon Dr.11Clinical Physics, Institute of Neurological Sciences, Govan Road, Glasgow, Scotland;IntroductionMitral and aortic valve replacement is a procedure which is common incardiac surgery. Some of these replacement valves are mechanical andcontain moving metal parts in the disc or leaflets. When exposed toMRI there is a potentially hazardous interaction between the movingmetal parts and the static magnetic field due to the Lenz Effect. TheLenz Effect is a result of the current (induced by the metalliccomponent moving in a static magnetic field) changing as the valverotates; this causes a secondary field to be set up which opposes theoriginal field and consequently opposes the motion of the component.A simple 'worst case' analysis of the potential hazard has beenperformed previously (1). However the differential nature of thedelaying effect of the motion of the mechanical valve on the Lenzeffect itself was not assessed. In this paper a differential model of aring-strengthener valve type has been developed to take account of theinterplay between the Lenz Effect and disc motion.TheoryIt is straightforward to calculate the torques produced by the LenzEffect on the metallic ring strengthener type of valve for variousopening times. However, given the values of torque it is not obvioushow the normal motion of the heart is affected. The significance ofthese results cannot be fully ascertained until the forces due to theLenz Effect are placed within a suitable model where the impact canbe realised numerically. Consequently it is considered how the Lenzforce fits into the overall motion of the mechanical heart valve byconstructing a differential Newtonian model. The individual forceswhich are significant are: the Lenz Effect, blood pressure opening andclosing the single-leaflet valve, and the viscosity of the blood. Weknow:22F(Lenz)= -(B A /R). sinW(t). d(cosW(t))/dt [1]where R and A are the radius and area of the valve disc and W is theangle it makes to the field (B).The overall equation describing the motion of the disc can be shown tobe:22 2mW''(t) + ((B A /R).sin W(t)).W'(t)- F(blood).cosW(t) - (nA/l)W'(t) = 0 [2]where n is blood viscosity, l the length it is forced through and m is themass of the disc.This has no analytical solution but is solved using numerical methods.The physical parameters come from considering a titanium ringstrengthener valve, 39mm in diameter which opens 85 degrees. Afourth-order Runge-Kutta numerical method for integration is used tosolve the above equation giving the variation of the opening angle withtime. The strength of the external magnetic field can be altered to showthe delay time in opening with respect to the normal, i.e. when B=0,opening times for the valves.ResultsThe resistive pressure effects on the valve disc as a function of fieldstrength are calculated for valves in the aortic and mitral positions andthe results are summarised in Table 1.DiscussionGenerally the important data required to derive the results is not asreadily available with the same accuracy as values for resistance or thematerials of which the valves are constructed. This fact can beunderstood given the difficulty of making measurements of the actualpressure differences which instantaneously occur in a particular humanheart. This, coupled with the fact that the forces which cause the valvesto open vary constantly in one person and even more betweenindividuals means that some upper value must be used to findmeaningful results. To that end, the highest likely pressures have beendetermined from established sources giving information on typicalpressures etc. For example, it is known that the heart valves must openin a `few milliseconds´ (2); experiments performed on animals showthat the valves generally open in less than 50 ms (3).The reason no one has yet reported significant difficulty caused bythe Lenz Effect could be that the relevant factors have not been inplace. That is, no patient with a heart valve with moving metalcomponents has been imaged in an MR system with the optimally badorientation with relation to the static magnetic field. This does notseem as probable as the argument that the magnetic fields withincommercially available MR systems are not of great enough magnitudeto produce a significant torque to noticeably impede the motion of thedisc.The results of this paper are in agreement with the `worst case´model (1) in that both show that the Lenz Effect has the potential tocause the moving metallic components of mechanical heart valves toexperience a torque causing a delay in their rotation. However whilst(1) raised the possibility of significant effects at fields even as low as1.5T, the model in this paper suggests that higher fields are required.At 1.5 Tesla the effect would be less than 1% of the pressure effect formitral and aortic valves (Table 1). However, 3 to 4.7 Tesla systems arebecoming more prevalent and for such field strengths the percentageeffect would be up to 9.95% for a valve in the mitral position and up to9.91% for a valve in the aortic position. Clearly experimental studiesare required to establish appropriate maximum field levels for suchvalves, but it would seem prudent at this stage to exercise caution atfields of 3T and above. Should the torque be significant, and it shouldbe stressed that it could be significant in only the small subset ofpatients with mechanical heart valves which have moving metalcomponents (ie in the disc or leaflet but not the cage or ring), it wouldbe recognised by symptoms such as breathlessness in the patient andreduced cardiac output. That is, the Lenz Effect could make the heartbehave as though it were diseased with the resulting symptoms anddifficulties.References1.Condon B, Hadley D., JMRI 2000:12:171-1762.Guyton, A.C. Textbook of Medical Physiology, pub. W.B. SaundersCompany, 1991,3.Lynch W. 1 Implants (New York: van Vostrund Reinhold)1982Table 1. The Lenz Effect as a percentage of normal pressure effectMitral AorticField Strength(T)PercentageEffectPercentageEffect1 0.38 0.381.5 0.81 0.882.4 2.14 2.313 3.48 3.684.7 9.95 9.917 33.90 26.308 60.52 37.1710 145.10 65.03

Textbook of Medical Physiology, pub.

Estimation of resistive pressure effects in mechanical heart valves due to MRI

Proc. Intl. Soc. Mag. Reson. Med 9 (2001) 1768Proc. Intl. Soc. Mag. Reson. Med 9 (2001) 1768Estimation of resistive pressure effects in mechanical heart valves due to MRINeil Robertson1, Manuel Diaz-Gomez1, Barrie Condon Dr.11Clinical Physics, Institute of Neurological Sciences, Govan Road, Glasgow, Scotland;IntroductionMitral and aortic valve replacement is a procedure which is common incardiac surgery. Some of these replacement valves are mechanical andcontain moving metal parts in the disc or leaflets. When exposed toMRI there is a potentially hazardous interaction between the movingmetal parts and the static magnetic field due to the Lenz Effect. TheLenz Effect is a result of the current (induced by the metalliccomponent moving in a static magnetic field) changing as the valverotates; this causes a secondary field to be set up which opposes theoriginal field and consequently opposes the motion of the component.A simple 'worst case' analysis of the potential hazard has beenperformed previously (1). However the differential nature of thedelaying effect of the motion of the mechanical valve on the Lenzeffect itself was not assessed. In this paper a differential model of aring-strengthener valve type has been developed to take account of theinterplay between the Lenz Effect and disc motion.TheoryIt is straightforward to calculate the torques produced by the LenzEffect on the metallic ring strengthener type of valve for variousopening times. However, given the values of torque it is not obvioushow the normal motion of the heart is affected. The significance ofthese results cannot be fully ascertained until the forces due to theLenz Effect are placed within a suitable model where the impact canbe realised numerically. Consequently it is considered how the Lenzforce fits into the overall motion of the mechanical heart valve byconstructing a differential Newtonian model. The individual forceswhich are significant are: the Lenz Effect, blood pressure opening andclosing the single-leaflet valve, and the viscosity of the blood. Weknow:2 2F(Lenz)= -(B A /R). sinW(t). d(cosW(t))/dt [1]where R and A are the radius and area of the valve disc and W is theangle it makes to the field (B).The overall equation describing the motion of the disc can be shown tobe:2 2 2mW''(t) + ((B A /R).sin W(t)).W'(t)- F(blood).cosW(t) - (nA/l)W'(t) = 0 [2]where n is blood viscosity, l the length it is forced through and m is themass of the disc.This has no analytical solution but is solved using numerical methods.The physical parameters come from considering a titanium ringstrengthener valve, 39mm in diameter which opens 85 degrees. Afourth-order Runge-Kutta numerical method for integration is used tosolve the above equation giving the variation of the opening angle withtime. The strength of the external magnetic field can be altered to showthe delay time in opening with respect to the normal, i.e. when B=0,opening times for the valves.ResultsThe resistive pressure effects on the valve disc as a function of fieldstrength are calculated for valves in the aortic and mitral positions andthe results are summarised in Table 1.DiscussionGenerally the important data required to derive the results is not asreadily available with the same accuracy as values for resistance or thematerials of which the valves are constructed. This fact can beunderstood given the difficulty of making measurements of the actualpressure differences which instantaneously occur in a particular humanheart. This, coupled with the fact that the forces which cause the valvesto open vary constantly in one person and even more betweenindividuals means that some upper value must be used to findmeaningful results. To that end, the highest likely pressures have beendetermined from established sources giving information on typicalpressures etc. For example, it is known that the heart valves must openin a `few milliseconds´ (2); experiments performed on animals showthat the valves generally open in less than 50 ms (3).The reason no one has yet reported significant difficulty caused bythe Lenz Effect could be that the relevant factors have not been inplace. That is, no patient with a heart valve with moving metalcomponents has been imaged in an MR system with the optimally badorientation with relation to the static magnetic field. This does notseem as probable as the argument that the magnetic fields withincommercially available MR systems are not of great enough magnitudeto produce a significant torque to noticeably impede the motion of thedisc.The results of this paper are in agreement with the `worst case´model (1) in that both show that the Lenz Effect has the potential tocause the moving metallic components of mechanical heart valves toexperience a torque causing a delay in their rotation. However whilst(1) raised the possibility of significant effects at fields even as low as1.5T, the model in this paper suggests that higher fields are required.At 1.5 Tesla the effect would be less than 1% of the pressure effect formitral and aortic valves (Table 1). However, 3 to 4.7 Tesla systems arebecoming more prevalent and for such field strengths the percentageeffect would be up to 9.95% for a valve in the mitral position and up to9.91% for a valve in the aortic position. Clearly experimental studiesare required to establish appropriate maximum field levels for suchvalves, but it would seem prudent at this stage to exercise caution atfields of 3T and above. Should the torque be significant, and it shouldbe stressed that it could be significant in only the small subset ofpatients with mechanical heart valves which have moving metalcomponents (ie in the disc or leaflet but not the cage or ring), it wouldbe recognised by symptoms such as breathlessness in the patient andreduced cardiac output. That is, the Lenz Effect could make the heartbehave as though it were diseased with the resulting symptoms anddifficulties.References1.Condon B, Hadley D., JMRI 2000:12:171-1762.Guyton, A.C. Textbook of Medical Physiology, pub. W.B. SaundersCompany, 1991,3.Lynch W. 1 Implants (New York: van Vostrund Reinhold)1982Table 1. The Lenz Effect as a percentage of normal pressure effectMitral AorticField Strength(T)PercentageEffectPercentageEffect1 0.38 0.381.5 0.81 0.882.4 2.14 2.313 3.48 3.684.7 9.95 9.917 33.90 26.308 60.52 37.1710 145.10 65.03

Estimation of resistive pressure effects in mechanical heart valves due to MRI

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