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Computertomographie

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Medizinische Physik

Zusammenfassung

Die röntgenbasierte Computertomographie (CT) ist das wichtigste diagnostische Werkzeug des Radiologen. CT-Systeme sind nahezu überall verfügbar und decken nahezu vollständig das Spektrum radiologischer diagnostischer Fragestellungen für alle menschlichen Organe ab. Dichtekontraste, materialspezifische Kontraste und funktionelle Parameter lassen sich mit CT in Scanzeiten von wenigen Sekunden mit submillimetergenauer Ortsauflösung und Subsekunden-Zeitauflösung über Scanlängen bis hin zu zwei Metern routinemäßig erfassen (Abb. 8.1) [74]. Die CT-Volumina, typischerweise bestehend aus Tausenden von Schichten, sind verzerrungsfrei, hochgenau und jederzeit reproduzierbar. Zudem stellen die Graustufen, CT-Werte genannt, ein quantitatives Maß der Dichtewerte dar. Somit ist CT, im Gegensatz zur MR, eine quantitative bildgebende Modalität.

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Notes

  1. 1.

    Der Senkrechtoperator dreht den Vektor \(\boldsymbol{v}\) um 90° gegen den Uhrzeigersinn: \(\boldsymbol{v}^{\bot}=\binom{-v_{y}}{v_{x}}\). Es gilt \(\boldsymbol{v}_{1}^{\bot}\cdot\boldsymbol{v}_{2}^{\bot}=\boldsymbol{v}_{1}\cdot\boldsymbol{v}_{2}\) und \(\boldsymbol{v}_{1}^{\bot}\cdot\boldsymbol{v}_{2}=-\boldsymbol{v}_{1}\cdot\boldsymbol{v}_{2}^{\bot}\).

  2. 2.

    Für die Fouriertransformation \(G\) einer Funktion \(g\) und für die inverse Fouriertransformation verwenden wir folgende Konvention:

    $$\begin{aligned}\displaystyle G(u)&\displaystyle=(\mathsf{F}g)(u)=\int_{-\infty}^{\infty}\mathrm{d}xg(x)\mathrm{e}^{-2\uppi\mathrm{i}ux}\\ \displaystyle g(x)&\displaystyle=(\mathsf{F}^{-1}G)(x)=\int_{-\infty}^{\infty}\mathrm{d}uG(u)\mathrm{e}^{2\uppi\mathrm{i}ux}.\end{aligned}$$
  3. 3.

    Das Faltungstheorem besagt, dass die Faltung zweier Funktionen \(g_{1}\) und \(g_{2}\)

    $$\displaystyle(g_{1}\ast g_{2})(x)=g_{1}(x)\ast g_{2}(x)=\int\mathrm{d}tg_{1}(t)g_{2}(x-t)$$

    als Multiplikation im Frequenzraum ausgeführt werden kann:

    $$\displaystyle\mathsf{F}(g_{1}\ast g_{2})=(\mathsf{F}g_{1})(\mathsf{F}g_{2})=G_{1}G_{2}.$$

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Authors and Affiliations

  1. Röntgenbildgebung und CT (E025), Deutsches Krebsforschungszentrum (DKFZ), Heidelberg, Deutschland

    Prof. Dr. Marc Kachelrieß

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Editors and Affiliations

  1. Medizinische Physik in der Strahlentherapie (E040), Deutsches Krebsforschungszentrum (DKFZ), Heidelberg, Germany

    Wolfgang Schlegel

  2. Medizinische Physik in der Strahlentherapie (E040), Deutsches Krebsforschungszentrum (DKFZ), Heidelberg, Germany

    Christian P. Karger

  3. Medizinische Physik in der Strahlentherapie (E040), Deutsches Krebsforschungszentrum (DKFZ), Heidelberg, Germany

    Oliver Jäkel

Aufgaben

Aufgaben

8.1

Welchem CT-Wert entspricht der Schwächungswert von 0,00205 mm\({}^{{-}1}\) bei 70 keV? Tipp: Rechnen Sie mit dem Schwächungswert von Wasser bei 70 keV, den Sie im Text finden. Um welches Organ handelt es sich, wenn man Tab. 8.2 zugrunde legt? Ist diese Vorgehensweise gerechtfertigt, um ein Organ zu identifizieren?

8.2

Welche Methoden zur Dosissenkung kann der Anwender selbst vornehmen?

8.3

Ein Notfallpatient wird mit starken Brustschmerzen in die Klinik eingeliefert. Zum Ausschluss eines Aortenaneurysmas wird vom behandelnden Arzt ein CT veranlasst. Der zuständige Radiologe wählt hierfür ein Thoraxprotokoll aus. Gescannt wird ein Bereich von 40 cm vom Hals an abwärts. Das verwendete Gerät akquiriert im Thoraxprotokoll 64 Schichten zu je 0,6 mm. Die Scandauer beträgt 2 s, die Rotationszeit 250 ms. Berechnen Sie den Pitchwert des Scans.

8.4

Das Gerät hat während des in Frage 3 beschriebenen Scans eine Leistung von 100 kW bei einer Röhrenspannung von 80 kV. Berechnen Sie das Röhrenstrom-Zeit-Produkt und das effektive Röhrenstrom-Zeit-Produkt. Wie hängt das effektive Röhrenstrom-Zeit-Produkt mit der Strahlendosis zusammen?

8.5

Erläutern Sie folgende Begriffe: \(\text{CTDI}_{100}\), \(\text{CTDI}_{\mathrm{w}}\), \(\text{CTDI}_{\mathrm{vol}}\), SSDE. Wie werden diese bestimmt (berechnet)?

8.6

Bei einer Untersuchung sehen Sie, wie der behandelnde Radiologe an der CT-Konsole folgende Werte setzt: „\(C=300\) HU, \(W=1600\) HU“. Welchen CT-Wertebereich deckt er damit ab? Welche Farbe hat beispielsweise ein Voxel mit 1300 HU? Sie wollen stattdessen einen Graustufenbereich von \({-}\)250 HU bis 500 HU abdecken. Wie fenstern Sie?

8.7

Wie wirkt sich die Röhrenspannung auf die Patientendosis aus? Warum ist es wichtig, bei einer Erhöhung der Röhrenspannung auch das effektive Röhrenstrom-Zeit-Produkt anzupassen? Muss dieses erhöht oder erniedrigt werden?

8.8

Welche Möglichkeiten der Dosisreduktion können hardware- und softwareseitig erreicht werden? Nennen Sie einige.

8.9

Zählen Sie einige Artefakttypen und ihre Korrekturmöglichkeiten auf.

8.10

Erklären Sie den Unterschied zwischen pixelgetriebener und strahlgetriebener Rückprojektion. Welche Rekonstruktionstechniken kennen Sie und was unterscheidet sie voneinander? Schreiben Sie die jeweiligen Lösungsansätze auf und erläutern Sie die Parameter.

8.11

Zählen Sie die Komponenten des CT-Geräts auf und beschreiben Sie jeweils die Funktionsweise der Komponenten. Wofür steht DSCT, DECT? Was sind die Vorteile?

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Kachelrieß, M. (2018). Computertomographie. In: Schlegel, W., Karger, C., Jäkel, O. (eds) Medizinische Physik. Springer Spektrum, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54801-1_8

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