Ultrasound Notes 4: Doppler

Transcription

1 Noll (24) US Notes 4: page 1 Ultrasound Notes 4: Doppler Imaging o Blood Flow with US One o the more interesting and useul appliations o US is or the imaging o low in the body. One way to do this is trak spekle patterns oer time using a ross-orrelation tehnique. Another way to do this is take adantage o the Doppler eet. This is disussed below. The Doppler Eet In US, the Doppler eet has two omponents. We look irst at the eetie requeny seen by a reletor traeling towards the transmitter at eloity. During an interal o duration T, the number o yles reeied will be T plus the number o yles that reletor ame aross due to its moement. The reletor traeled a distane T, and thus ame aross T/ additional yles: T # o yles in T T + and thus the eetie requeny and requeny shit seen by the reletor is: e + ; shit For positie (moing towards the transmitter) the requeny shits upwards, or negatie downwards. We now look the omplimentary ase o a soure moing towards the reeier. Here the emitted waeronts are ompressed due to the moement o the soure:

2 Noll (24) US Notes 4: page 2 The displaement o the soure in 1 yle is / and thus the new waelength is short by that amount: new and the eetie requeny and requeny shit are: ; e shit new Again, or positie the requeny shits upwards, or negatie downwards. In US, the reletor is both a listener and a soure and so we hae both shits ouring. The net requeny shit is: net shit + 2 or << Comments: - Obsere that the size o the requeny shit is proportional to. - For physiologial blood eloities in the body: 5 m/s 5x1-4 mm/µs in major essels. 1.5 mm/µs relatie shit 2/ 6.7x1-4 and or 5 MHz, shit 3.3 khz - All Doppler measurements only aount or eloities towards/away rom the transduer. CW Doppler US One method or doing doppler US measurements is ontinuous wae (CW) doppler US. In CW imaging, the US signal is transmitted ontinuously and thus pulsing annot be

3 Noll (24) US Notes 4: page 3 used to get depth resolution. This also means that the reeier must be a dierent transduer than the transmitter. Typially, one uses the intersetion o two beams to reate an area o loalization: The reeied signal will hae omponents related to stati reletors at and perhaps a ull spetrum o other signals related to omponents at dierent eloities: In order to distinguish between and shited omponents at e, the reeied signal needs to be obsered or a long enough interal, T obs. The requeny resolution will be 1/T obs and the eloity resolution will be: 2Tobs For example, we want eloity resolution o 5 m/s 5x1-5 mm/µs and or 5 MHz, T obs must be at least 3 ms. This is muh longer than the round trip delay or a pulse (whih is typially on the order o 1-2 µs). Comments: - CW Doppler has exellent eloity resolution and is apable o measuring an entire eloity spetrum rom the region o loalization - CW Doppler has ery poor range resolution (no pulsing) - It requires separate transmit and reeie transduers - It is ery slow or sanning a large spae

4 Noll (24) US Notes 4: page 4 Pulsed Doppler In pulsed Doppler imaging, a train o pulses is sent along a single beam repeatedly. Only one pulse is propagating through the body at any point in time so that maximum rate or pulsing is limited by the roundtrip time or the pulses. For example, i r max 15 m, then the pulse repetition time is T PR 2r max / 2 µs. Thus the pulse repetition requeny is PR 5 khz. In pulsed Doppler, the pulses are sampling the eloity shits and thus, any requeny shits larger than PR /2 will be aliased (e.g. to negatie requenies or equialently, negatie eloities). Another major onsideration or pulsed Doppler relates to eloity resolution. Veloities are mapped to requeny shits and in order to detet small requeny shits, we need to 1 obsere in time or a long period o time, so Tobs. The total des 2 des obseration time, T obs, must also be long enough so that the astest moing satterer interats with the pulse or that length o time. Sine Dopper detets eloities towards and away rom the detetor only, we need satterers to remain within the depth resolution element (point spread untion) long enough to establish the desired eloity resolution. z T So, i the resolution element is z T / 2, then T obs. Equating these two expressions or T obs, we get T max max 2 max, that is, the number o yles or the length o the pulse must be larger than the number o eloity steps that one wishes to resole. Thereore, pulsed Dopper US uses muh longer pulses than imaging US and thus, has poorer spatial (depth) resolution. Likewise, the requeny is also limited by the desired depth resolution, and this, o ourse, aets lateral resolution. Another way to think about this is to reognize that one has to hae a narrow spetrum pulse in order to detet small shits in requeny and long pulses hae a narrow spetrum.

5 Noll (24) US Notes 4: page 5 - Depth o region o interest, r max determines PR and thus the requeny shit (eloity) at whih aliasing ours - Maximum eloity determines requeny - and T, determine the maximum requeny shit, - e.g. or max depth 9.6 m and maximum eloity PR 8 khz ( 1.54 mm/ms) maximum shit will be 4 khz or max 5 m/s, this sets,max 6.1 MHz or a eloity resolution o 2 m/s, we then need a pulse length T 4.1 ms this orresponds to a depth resolution o z 6.25 m. The aboe are only approximate relationships. There is also some leer signal proessing that an be done to improe the aboe relationships i we restrit our region o interest to a limited range o depths. For more ino on Doppler, please examine proessor O Donnell s Doppler notes at: