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DOI: 10.1148/radiol.2343040286
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(Radiology 2005;234:785-792.)
© RSNA, 2005


Gastrointestinal Imaging

Assessing Tumor Perfusion and Treatment Response in Rectal Cancer with Multisection CT: Initial Observations1

Dushyant V. Sahani, MD, Sanjeeva P. Kalva, MD, Leena M. Hamberg, PhD, Peter F. Hahn, MD, PhD, Christopher G. Willett, MD, Sanjay Saini, MD, Peter R. Mueller, MD and Ting-Yim Lee, PhD

1 From the Division of Abdominal Imaging and Intervention, Department of Radiology, Massachusetts General Hospital, 55 Fruit St, White 270 F, Boston, MA 02114. From the 2003 RSNA Annual Meeting. Received February 13, 2004; revision requested April 15; revision received May 13; accepted June 15. Address correspondence to D.V.S. (e-mail: dsahani@partners.org).


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
PURPOSE: To use first-pass perfusion computed tomography (CT) to prospectively investigate tumor vascularity in rectal cancer and to determine whether any of the perfusion parameters would predict tumor response to chemotherapy and radiation therapy.

MATERIALS AND METHODS: The institutional review board approved this study, and informed prior consent was obtained from participants. Perfusion CT of rectal cancer was performed with four-section multi–detector row CT in 15 patients (13 men, two women; mean age, 62.1 years; age range, 46–84 years). Five patients with prostate cancer served as controls. All patients with rectal cancer underwent 6–8 weeks of chemotherapy and radiation therapy followed by surgery. In nine patients, perfusion CT was repeated after completion of chemotherapy and radiation therapy. Contrast medium–enhanced dynamic CT was performed with a static table position for 45 seconds, and the data were analyzed by using commercial software to calculate tissue blood flow (BF), blood volume, mean transit time (MTT), and vascular permeability–surface area product. Perfusion parameters of normal rectum and tumor were compared. Perfusion parameters before and after chemotherapy and radiation therapy were compared. A tumor was considered to have responded if its stage at pathologic analysis indicated regression compared with the preoperative stage. Baseline perfusion values were compared between responders and nonresponders. Statistical analysis was performed with the Student t test.

RESULTS: Rectal cancer showed higher BF and shorter MTT compared with those of normal rectum (P ≤ .05). After chemotherapy and radiation therapy, tumors showed significant reduction in BF and increase in MTT (P ≤ .05). There was a significant difference in baseline BF and MTT values between responders and nonresponders (P ≤ .05). Tumors in three patients with high initial BF and short MTT showed poor response.

CONCLUSION: Perfusion CT of rectal cancer can enable assessment of tumor vascularity and perfusion changes that result from chemotherapy and radiation therapy. In this small patient sample, tumors with initial high BF and short MTT values tended to respond poorly to chemotherapy and radiation therapy.

© RSNA, 2005


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Colorectal cancer is the fourth most frequently diagnosed cancer in the United States and, after lung cancer, is associated with the second highest mortality (1). The 5-year survival depends on the tumor stage at patient presentation. Tumors with an advanced stage (T3 or T4, N1 or N2, or M1) at diagnosis are associated with a poor outcome (2). Accordingly, the tumor stage at diagnosis guides treatment strategies. Patients with a tumor confined to the rectal wall (stage T1 or T2) typically undergo total mesorectal fascial excision (3). In patients with a tumor of stage T3 or a more advanced stage, preoperative chemotherapy and radiation therapy are frequently administered (4). Such therapy is useful for decreasing the tumor stage to facilitate curative resection and to decrease the rate of recurrence (5). However, there are no methods for predicting which tumors will respond to chemotherapy and radiation therapy. Perfusion computed tomography (CT) is a new technology that allows measurement of tumor vascular physiology and construction of regional maps of tumor blood flow, blood volume, mean transit time, and vascular permeability–surface area product. Apart from being noninvasive and fast, this type of study can be repeated at different time periods to assess tumor response to antiangiogenic therapy or temporal changes in tumor angiogenesis. A number of articles have been published about perfusion CT for tumors in brain (6), liver (7), lung (8), pancreas (9), and head and neck (10). Most of the reported studies were focused on the detection of metastases, differentiation of benign from malignant lesions, and assessment of response to therapy. Thus, the aim of our study was to use first-pass perfusion CT (ie, dynamic CT scanning during the first circulation of an injected contrast medium through the body) to prospectively investigate tumor vascularity in rectal cancer and to determine whether any of the perfusion parameters would predict tumor response to chemotherapy and radiation therapy.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Tracer Kinetics Theory for Distribution of Contrast Medium in Tissue
The Johnson and Wilson model (6,1115) is a convenient model for this application. Details about the model are given in the Appendix. Both convective and diffusive transport of contrast medium in capillaries are modeled such that four functional parameters—blood flow, vascular blood volume, vascular mean transit time, and vascular permeability–surface area product—are simultaneously estimated from the dynamic contrast-enhanced CT data.

Patient Population
The institutional review board approved this prospective study, and informed consent was obtained from each participant prior to the study. Patients were included in this study if the tumor extended beyond the rectal wall without distant metastases. Patients were excluded from the study if the tumor was stage T1 or T2 or if the patient had renal disease that precluded contrast-enhanced CT (serum creatinine level, >1.9 mg/dL). Between July 2001 and January 2003, 15 consecutive patients who met the inclusion criteria and agreed to participate in the study were enrolled. The study cohort included 13 men and two women (mean age, 62.1 years; age range, 46–84 years) in whom pathologic analysis at biopsy confirmed a diagnosis of nonmucinous adenocarcinoma of the rectum. According to local tumor staging based on endorectal magnetic resonance (MR) imaging (n = 12) and endorectal ultrasonography (n = 3), 13 patients had stage T3 disease and two patients had stage T4 disease at the time of presentation. All patients underwent preoperative chemotherapy and radiation therapy. Three-dimensional conformal radiation therapy was given at a dose of 1.8 Gy per day, 5 days per week, for 6 weeks, with a total radiation dose of 45 Gy. In addition, 5-fluorouracil was administered via peripheral venous infusion at a dose of 225 mg/m2 per day, 5 days per week, for 6 weeks. At the end of 6 weeks, 4–5 Gy pelvic radiation was given for therapy. Total mesorectal fascial excision was finally performed within 1–3 weeks after completion of chemotherapy, and the specimen was evaluated for pathologic staging. Any tumor that showed a regression in local stage at pathologic analysis as compared with that at preoperative imaging (Table 1) was considered a responder to chemotherapy and radiation (n = 12). If there was no difference in tumor stage or if there was an increase in local tumor stage, the tumor was considered a nonresponder (n = 3).


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TABLE 1. Definitions of Response and Nonresponse to Chemo- and Radiation Therapy

 
All patients underwent perfusion CT prior to chemotherapy and radiation therapy. In nine patients, perfusion CT was performed a second time within 1–2 weeks after the completion of chemotherapy and radiation. In these patients, the time difference between baseline and posttherapeutic perfusion CT examinations was 12 weeks. Two other patients had technically inadequate perfusion CT examinations after chemotherapy and radiation therapy, and the data from these two scans were not included in the analysis. The inadequacy of these perfusion CT scans resulted from artifacts due to excessive motion during scanning. Four other patients did not undergo perfusion CT after chemotherapy and radiation therapy because they did not appear for the scheduled follow-up examination.

Five additional patients, all men (mean age, 62.6 years; age range, 55–71 years) who had no rectal disease but who had prostate cancer confined to the prostate, also underwent perfusion CT and served as controls. These patients had received no cancer-related therapy prior to CT, and they were not consecutive. These patients underwent perfusion CT for the evaluation of prostate cancer at our hospital during a pilot study that was approved by the institutional review board and for which informed consent was obtained. The same parameters were measured in the five patients with a normal rectal wall as were measured in the patients with rectal cancer. These five patients served as controls for the estimation of perfusion parameters in normal rectal wall for this age group.

Perfusion CT Technique
Perfusion CT was performed with a four-section multi–detector row CT scanner (LightSpeed QX/i; GE Medical Systems, Milwaukee, Wis). CT scanning of the pelvis was performed without oral or intravenous contrast medium to localize the tumor. The tumor was localized on the nonenhanced CT scan, and a 2-cm tumor region of interest (ROI) was selected for cine imaging. This area was chosen by an experienced gastrointestinal radiologist (D.V.S., who had 11 years of experience in radiology and 5 years of experience in gastrointestinal radiology) and on the basis of visible tumor volume. Dynamic study of this area was performed at a static table position during intravenous injection of 125 mL of iopamidol (Isovue 300; Bracco Diagnostics, Princeton, NJ) containing 300 mg of iodine per milliliter. The following parameters were used: 1-second gantry rotation time, 100–120 kVp, 200–240 mA, 10-second scanning delay from the start of injection, 45-second duration of transverse data acquisition (four sections per gantry rotation), and 5-mm reconstructed section thickness. The images were reconstructed at 1-second temporal intervals. We chose a 45-second duration of scanning for three reasons: First, it would limit the radiation dose to the subject. Second, since the patient has to keep still during scanning, the shorter time would help to prevent image artifacts caused by patient motion. Third, the level of precision with which the parameters of our tracer kinetics model were estimated was 5%–15% (13,16), which was judged acceptable.

On completion of the study, the data were transferred to an image processing workstation (Advantage Windows 4.0; GE Medical Systems) and analyzed by using software (CT Perfusion 2.0; GE Medical Systems). The analysis is based on the principles discussed in the Appendix. The parameters generated by the software are blood flow (in milliliters per 100 g of wet tissue per minute), blood volume (in milliliters per 100 g of wet tissue), mean transit time (in seconds), and permeability–surface area product (in milliliters per 100 g of wet tissue per minute). As discussed in the Appendix, for the derivation of the functional maps of blood flow, blood volume, mean transit time, and permeability–surface area product, the arterial input curve of contrast medium concentration Ca(t) is required. In all the CT scans, Ca(t) was obtained from an ROI in the right external iliac artery (area range, 18–25 mm2) by one of the authors (S.P.K., with 8 years of experience in general radiology and 1 year in gastrointestinal radiology). In addition, a second reference ROI (area range, 18–25 mm2) within a vessel large enough to be fully representative of contrast enhancement (measured in Hounsfield units) for 100% blood was identified to correct for any partial-volume averaging that may have occurred in the obtained Ca(t) (14). In our study, the left external iliac artery was used for partial-volume averaging correction. Using these reference curves, we calculated maps of blood flow, blood volume, mean transit time, and permeability–surface area product. The CT data from the five control patients were similarly analyzed. The ROI (area range, 175–676 mm2) was drawn along the rectal wall for computation of the perfusion parameters.

Statistical Analysis
The tumor ROIs (area range, 293–1300 mm2) within the rectum were hand drawn (S.P.K.) both for each map type and within each map type (blood flow, blood volume, mean transit time, and permeability–surface area product) for all four anatomic section locations available for each patient. Representative parameter values were then averaged across the four sections.

Perfusion parameters in control patients (patients with prostate cancer confined to the prostate) were similarly obtained from normal rectum and compared with the perfusion parameters in patients with rectal tumors to identify any perfusion differences between tumor and normal rectum. The perfusion parameters before and after radiation therapy were compared to investigate whether radiation therapy caused changes in the perfusion parameters. Baseline perfusion values (before initiation of chemotherapy and radiation therapy) were compared between responders and nonresponders. Statistical analysis was performed by using the Student t test for comparison of two data sets, and P values were calculated for each comparison (Excel 2000; Microsoft, Richmond, Va). P ≤ .05 was considered to indicate a statistically significant difference.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Perfusion Parameters: Rectal Cancer versus Normal Rectum
The perfusion parameters of rectal cancer in 15 patients and perfusion parameters of normal rectum in five control patients were compared. There was a significant difference in blood flow (P ≤ .05), with high blood flow in rectal tumors compared with that in normal rectum. The mean transit time was significantly shorter in rectal tumors (P ≤ .05) (Figure). There was no significant difference in blood volume or in permeability–surface area product between tumors and normal rectum (Table 2).



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Figure a. Perfusion CT scans of rectal cancer. Color maps superimposed on gray-scale images of rectum show (a) blood flow (mean, 88.7 mL/100 g wet tissue/min), (b) blood volume (mean, 6.3 mL/100 g wet tissue), (c) mean transit time (8.2 seconds), and (d) permeability-surface area product (mean, 13.4 mL/100 g wet tissue/min) in tumor.

 


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Figure b. Perfusion CT scans of rectal cancer. Color maps superimposed on gray-scale images of rectum show (a) blood flow (mean, 88.7 mL/100 g wet tissue/min), (b) blood volume (mean, 6.3 mL/100 g wet tissue), (c) mean transit time (8.2 seconds), and (d) permeability-surface area product (mean, 13.4 mL/100 g wet tissue/min) in tumor.

 


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Figure c. Perfusion CT scans of rectal cancer. Color maps superimposed on gray-scale images of rectum show (a) blood flow (mean, 88.7 mL/100 g wet tissue/min), (b) blood volume (mean, 6.3 mL/100 g wet tissue), (c) mean transit time (8.2 seconds), and (d) permeability-surface area product (mean, 13.4 mL/100 g wet tissue/min) in tumor.

 


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Figure d. Perfusion CT scans of rectal cancer. Color maps superimposed on gray-scale images of rectum show (a) blood flow (mean, 88.7 mL/100 g wet tissue/min), (b) blood volume (mean, 6.3 mL/100 g wet tissue), (c) mean transit time (8.2 seconds), and (d) permeability-surface area product (mean, 13.4 mL/100 g wet tissue/min) in tumor.

 

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TABLE 2. Perfusion Values in Rectal Tumors and in Normal Rectum

 
Perfusion Parameters of Rectal Cancer before and after Chemotherapy and Radiation Therapy
Perfusion CT was performed before and after chemotherapy and radiation therapy in nine patients. There was a significant decrease in blood flow (P ≤ .05) and increase in mean transit time (P ≤ .05) after chemotherapy and radiation therapy. Of the nine patients, seven showed decrease in blood flow and increase in mean transit time (Fig). Two patients showed a 13% increase in blood flow and a 10% increase in mean transit time. No statistically significant difference in blood volume or in permeability–surface area product was observed between CT scans obtained before and those obtained after chemotherapy and radiation therapy (Table 3).


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TABLE 3. Perfusion Values in Rectal Cancer before and after Therapy

 
Baseline Perfusion Parameters in Responders versus Nonresponders
There were significant differences in baseline blood flow and mean transit time values between responders and nonresponders on the pretreatment scans (P ≤ .05). Scans in the group of patients who had tumors with initial high blood flow and shorter mean transit time (n = 3) showed a poor response to chemotherapy and radiation therapy. Comparison of other parameters, however, did not indicate any statistically significant difference (Table 4). Tumor response and nonresponse are defined in Table 1.


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TABLE 4. Perfusion Values among Therapy Responders and Nonresponders

 

    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Physiologic Basis of Contrast Enhancement in Tumors
The enhancement of the tumor after administration of the intravenous contrast medium depends on the tumor blood flow, blood volume, and permeability of the vessels, as well as the iodine concentration (milligrams of iodine per milliliter) and volume of the contrast medium administered. After the administration of the iodinated contrast medium, the immediate or first-pass tumor enhancement is largely due to the presence of the contrast medium within the intravascular space and its first-pass extraction into the extravascular space. As time progresses, leakage of the contrast medium into the extravascular space continues, and the observed tumor enhancement is due to the presence of the contrast medium in both the intravascular and the extravascular space. The intravascular component depends on the available volume of blood space (blood vessels within the tumor), and the extravascular component depends on vascular permeability (17). During the later phases, the contrast medium in the extravascular space in the tumor is cleared as the contrast medium reenters the vascular system, and this eventually results in a return to baseline attenuation in the tumor.

A correlation between contrast enhancement measures and microvessel density has been reported in renal and lung cancers (1820). High tumoral microvessel density has been demonstrated to be associated with high blood flow by means of uptake of the radiotracer technetium Tc 99m sestamibi in breast carcinoma (21). In addition, newly developed tumor vessels demonstrated increased fenestrations of basement membrane that resulted in increased permeability to large molecules. Thus, the use of functional imaging techniques to assess tissue perfusion and permeability may offer a means to study the angiogenic process in tumors.

Axel (22) first described a method of assessing tissue perfusion by using dynamic contrast-enhanced CT. Because of the technical limitations of early CT scanners, this method was not widely available. With the advent of spiral CT and multi–detector row CT scanners, the technique became more popular and new indications emerged (22,23). The CT perfusion software used in this study models the distribution of contrast medium in tumor by using a distributed model (in which contrast medium concentration is nonuniform) for the intravascular space and a compartmental model (in which contrast medium concentration is uniform) for the extravascular space (1115). This hybrid model allows the simultaneous determination of blood flow, blood volume, vascular mean transit time, and capillary permeability–surface area product, which is its main advantage over the compartmental model. The compartmental model can determine only blood volume and F · E, the product of blood flow (F) and extraction efficiency (E) (1214).

Perfusion CT in Rectal Cancer
There are no published reports about the utility of perfusion CT in rectal cancer. However, many articles have been published about studies of perfusion CT and perfusion MR imaging in tumors of the cervix (24), liver (7), lung (8), heart (25), pancreas (9), spleen, lymph nodes (26), musculoskeletal system (27), and head and neck (10). In most of these studies, researchers focused on the detection of metastases, differentiation of benign from malignant lesions, and assessment of therapeutic response.

Comparison of Perfusion Parameters between Normal Rectum and Rectal Cancer
Compared with normal rectum, rectal cancer consistently showed high blood flow and shorter mean transit time. There was no significant difference in blood volume and permeability in rectal cancer compared with those in normal rectum. These results suggest that angiogenesis in the rectal tumors studied stimulated the opening of a significant number of arteriovenous shunts rather than the acquisition of a new vascular supply. The arteriovenous shunts have very low resistance to flow, which results in markedly increased blood flow and shorter mean transit time. These vessels facilitate the direct passage of blood from the arterial to the venous outlets without passage through the exchange vessels (capillaries) and, thus, result in no change in permeability–surface area product (28). We found that the duration of data collection for the arterial input concentration curve Ca(t) and the tissue curve Q(t) affected the accuracy and precision with which the permeability–surface area product was determined. If only first-pass data are acquired, then blood flow, blood volume, and mean transit time can be accurately determined with precision of about 15% (13).

Perfusion Changes after Chemotherapy and Radiation Therapy
Previous studies demonstrated increase in fractional vascular volume and contrast medium clearance per unit of volume (a measure of permeability) after radiation therapy, which may represent a hyperemic response to radiation therapy (29). Similarly, Mayr et al (24) studied cervical cancer with perfusion MR imaging and found that high tumor perfusion before radiation therapy and increasing or persistent high perfusion early in the course of therapy were favorable signs. In our study, however, there was a consistent decrease in blood flow and a consistent increase in mean transit time after chemotherapy and radiation therapy. These results may be attributable to the addition of chemotherapeutic agents in our treatment regimen and to the interval between therapy and subsequent perfusion imaging. Many of the present chemotherapeutic agents are cytotoxins that are capable of damaging the vascular endothelium, an effect that would have prevented the hyperemic response generally observed after radiation therapy. The timing of perfusion imaging after radiation therapy has a substantial effect on perfusion values, as early changes after radiation therapy result in leaky capillaries and late changes result in fibrosis with few vessels. This fact also explains the consistent increase in mean transit time in all of our patients. In our study, perfusion CT was performed 1–2 weeks after chemotherapy and radiation therapy. In addition, seven of nine patients showed a significant decrease in blood flow after chemotherapy and radiation therapy. Two patients showed a mild increase in blood flow; these two patients, however, also showed an increase in mean transit time.

Prediction of Response on the Basis of Baseline Perfusion Study
In numerous prior studies, measures of tumor perfusion have been correlated with response to therapy. Results of these studies have not always been in agreement. It is logical to think that high perfusion values, which indirectly suggest a high rate of angiogenesis and microvessel density within the tumor, may indicate a high grade of tumor and, therefore, may indicate a poor response to therapy and/or a worse prognosis. There are many publications that indicate a relationship between tumor angiogenesis, as determined by microvessel density, and prognosis (24,3032). In our study, tumors with high blood flow and low mean transit time at baseline perfusion imaging showed a poor response. DeVries et al (33) reported similar findings in their study, in which pretherapeutic perfusion MR imaging indexes of rectal cancer were compared with therapeutic response after chemotherapy and radiation therapy. A high blood perfusion index (mL/min/100 g tissue) in tumors was associated with a poor response. Sokmen et al (34) observed similar findings in their analysis and showed that increased tumor vascularity was associated with decreased survival among patients with rectal cancer. High perfusion values in association with a poor response to chemotherapy and radiation therapy can be explained by large numbers of intratumoral arteriovenous shunts with a high perfusion rate and low exchange of oxygen (35). Our results also suggest high intratumoral arteriovenous shunts without the development of new blood vessels. High perfusion could also be a result of intrinsic high angiogenic activity of tumor or a secondary response to tissue hypoxia (36,37). Comparison of the results from different CT and/or MR perfusion studies, however, has to be made cautiously, as the values measured are dependent on the mathematic model and the pharmacokinetics of the contrast medium used. Thus, the application of different models to the same data may well yield different perfusion values.

A low vascularity, however, was related to a high local recurrence rate in cervical cancer after radiation therapy (38). In liver, high arterial perfusion peripheral to metastases was associated with better survival (39). Similarly, poor perfusion of the portal venous system was associated with a poor prognosis (40). These findings suggest that an assessment of response on the basis of perfusion values should be individualized to the type of tumor, the treatment modality, and the mathematic model used to evaluate perfusion parameters.

Limitations in Our Study
There were several limitations in our study. First, we did not study tumor permeability, which might have served as an independent predictor of tumor grade or response. Second, the size of the study population in this pilot study was too small to permit a power analysis. Third, the tumoral response was based on a comparison between initial radiologic findings and final pathologic findings, a method that could have caused an inadvertent bias, as the stage of some tumors would have been under- or overestimated because of the limitations inherent in imaging modalities. An alternative method based on imaging would involve measurement of tumor volume before and after therapy. This approach was avoided because of the irregular shape of some tumors and the limited view of tumors afforded by four-section repeated imaging. In addition, peristalsis in the rectum can introduce motion artifacts, which may interfere with calculation of perfusion values.

In conclusion, perfusion CT of rectal cancer can be useful for assessing tumor vascularity and changes in perfusion after chemotherapy and radiation therapy. In our small patient sample, tumors with initial high blood flow and short mean transit time tended to respond poorly to chemotherapy and radiation therapy. To obtain more conclusive results, however, a larger patient population must be studied. It should be emphasized that the results of our study are specific to the analytic methods and software employed.


    APPENDIX
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
The Johnson and Wilson model (Fig A1) is based on the assumption that the distribution volume of CT contrast medium in tissue consists of capillaries and interstitial space, since the contrast medium is extracellular (1115). All the capillaries are represented together as a single cylinder of length L, which contains blood volume Vb. The interstitial tissue is assumed to be a cylindrical annulus around the capillary, with volume Ve. As the bloodborne contrast medium enters the capillary at a flow rate of F, it starts to diffuse across the capillary endothelium; thus, the blood concentration of contrast medium, or Cb(x,t), will be a function of both the axial position x along the capillary and time t. The interstitial tissue concentration of contrast agent, Ce(t), depends only on time; in other words, the interstitial tissue is treated as a "well-stirred" compartment. This assumption is justified because capillaries in tissue tend to be randomly oriented so that their arterial and venous ends are juxtaposed with respect to each other, and this configuration leads to a uniform concentration of contrast medium in the interstitial tissue when a large ensemble of capillaries is studied, as is the case at perfusion CT (15).



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Figure A1. Diagram of Johnson and Wilson model for the distribution of bloodborne contrast medium in tissue. Contrast medium concentration in the intravascular space, Cb(x,t), is dependent on position along the capillary and decreases from the arterial end of the capillary, Ca(t), to the venous end, Cv(t). Interstitial tissue is assumed to be a compartment with no internal concentration gradient. Ce(t) = contrast medium concentration in interstitial tissue, F = flow rate, PS = permeability-surface area product, Vb = blood volume, Ve = volume of interstitial tissue.

 
The governing equations of the Johnson and Wilson model may be expressed as follows:

{r05mr12e01}
and as

{r05mr12e02}
where PS is the capillary permeability–surface area product (14,41,42). Equation (A1) describes the convective and diffusive transport of the contrast medium in the capillaries, while Equation (A2) gives the rate of change in contrast medium concentration in the interstitial compartment. St Lawrence and Lee (43) used an adiabatic approximation to derive a closed-form solution of the model in the time domain. The mass of contrast medium per unit mass of tissue, Q(t), can be expressed as

{r05mr12e03}
where * is a convolution operator and where R(t), the impulse residue function, is expressed as follows (43):

{r05mr12e04}
where E is the extraction efficiency. This is the fraction of contrast medium present in arterial inlets that diffuses from the intravascular space to interstitial tissue during a single passage of blood from the arterial end to the venous end of the capillaries of a tissue (41,42). PS and E are related as demonstrated in the following equation (41,42):

{r05mr12e05}

Figure A2 is a plot of F · R(t) or the blood flow–scaled impulse residue function. It lends itself to the following interpretation: If a bolus of contrast medium is injected directly into the arterial inlet of the tissue so that the arterial concentration curve, Ca(t), is held at unity for a very short period (approaching 0 seconds), the total mass of contrast medium delivered to the tissue is numerically equal to F. The blood flow–scaled impulse residue function, F · R(t), which reflects the mass of contrast medium remaining in the tissue, therefore, would reach a height of F immediately and maintain this height for a duration equal to the vascular mean transit time of the tissue, Vb/F. The shaded area in Figure A2 is, therefore, the blood volume Vb, according to the central volume principle (44,45). After a time equal to Vb/F, unextracted contrast medium starts to leave the tissue, F · R(t) drops to a height of F · E, and thereafter contrast medium in the interstitial tissue diffuses back into the intravascular space (capillary) and is washed out by blood flow. This portion of F · R(t) is described by a decreasing monoexponential function with a rate constant equal to FE/Ve. With Ca(t) and Q(t) measured with CT, F · R(t) can be determined by model deconvolution (46) according to Equations (A3) and (A4), and the parameters F, Vb, MTT, and E(PS) can be determined as discussed previously.



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Figure A2. Curve of blood flow-scaled impulse residue function (IRF) according to adiabatic solution of the Johnson and Wilson model. F = flow rate, Vb = blood volume.

 
The duration of data collection for the arterial input curve Ca(t) and the tissue curve Q(t) affects the accuracy and precision with which the functional parameters are determined. If only first-pass data are acquired, then blood flow, blood volume, and mean transit time can be accurately determined with a precision of 15% (13,16).


    FOOTNOTES
 
Abbreviation: ROI = region of interest

T.Y.L. is a consultant with GE Healthcare (formerly GE Medical Systems) on their CT Perfusion software product. He is also supported in his research by grants from GE Healthcare.

Author contributions: Guarantor of integrity of entire study, D.V.S.; study concepts, D.V.S.; study design, D.V.S., C.G.W., S.S.; literature research, S.P.K., D.V.S.; clinical studies, C.G.W., D.V.S.; data acquisition, D.V.S., S.P.K.; data analysis/interpretation, S.P.K., L.M.H., D.V.S.; statistical analysis, S.P.K., L.M.H.; manuscript preparation, S.P.K., D.V.S., T.Y.L., L.M.H.; manuscript definition of intellectual content, D.V.S., S.P.K.; manuscript editing, D.V.S., P.F.H., S.P.K., L.M.H., T.Y.L.; manuscript revision/review, all authors; manuscript final version approval, D.V.S.


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 

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