Estimation of tumor microvessel density by MRI using a blood pool contrast agent

Abstract

Recognition of importance of angiogenesis to tumor growth, metastasis, and treatment outcome has led to efforts to develop non-invasive methods for longitudinal monitoring of tumor microvasculature. We describe a steady-state MRI technique to determine absolute blood volume (BV) as a marker of microvascular density with improved spatial and temporal resolution using an ultra small super paramagnetic iron oxide (USPIO). A noise reduction scheme for BV imaging was also proposed based on weighting factors derived by pre-contrast signal level as an adjustable additive constant. Gradient echo sequence was used for BV imaging with MRI at 7T. Optimal imaging conditions (USPIO dose and echo time) were determined by USPIO dose-dependent studies ex vivo and in vivo. Improved analysis strategies were at first applied for cerebral BV estimation in mice, which were found in good agreement with the literature values. These methods were then used to determine tumor BV in mice. The optimal concentration of USPIO for BV estimates was found to range from 3.6 to 4.48 mM (estimated as Fe concentration) in ex vivo experiments corresponding to an in vivo dosage of 215–287 μmol/kg body weight, whereas a USPIO dose of 287 μmol/kg leads to higher cerebral BV estimate in vivo than the reported values. Application of the BV imaging method to evaluation of anti-angiogenic effect of Sunitinib in squamous cell carcinoma (SCC) tumor bearing mice revealed ~46% reduction in tumor BV 4 days after start of Sunitinib treatment. The results show that the MRI approach using USPIO yields high-resolution absolute BV images and the method can be conveniently applied to monitor longitudinal tumor microvessel density changes as a function of growth or in response to treatment.

Introduction

Solid tumors are characterized by promoted angiogenesis and resultant structural and functional abnormality of neovasculature (1,2). The lack of adequate pericyte and endothelial coverage results in large vascular pores causing a marked regional heterogeneity in tumor blood perfusion and limited supply of oxygen, glucose, and other nutrients (2–4). In addition, recent treatment strategies using anti-angiogenic drugs have shown that tumor vessels are transiently normalized by pruning immature vessels to make the remaining vessels functionally more efficient (5). Functional improvement of the remaining blood vessels has been attributed to microvascular maturation via improved perivascular cell coverage and decreased vascular permeability. Consequently the increase in blood perfusion and decrease in hypoxic faction improved treatment response to radiotherapy and also enhanced chemotherapeutic drug delivery to an actively dividing cell population (6,7).

Current advances in blood perfusion imaging have made it possible to quantify the number and spacing of blood vessels, measure blood flow and vascular permeability, and analyze cellular and molecular abnormalities in blood vessel walls. Microscopic imaging tools are used for dissecting the cellular and molecular features of microvasculature. MRI, PET, CT and other non-invasive imaging methods can localize sites of tumor angiogenesis in animals and patients. Tumor blood volume (BV), which is directly related to microvessel density, is non-invasively available indicator of angiogenesis. Assessment of BV by MRI using various contrast agents has been described in several studies (8–16).

Ultra small super paramagnetic iron oxide (USPIO) is a steady state blood pool agent that creates contrast through magnetic susceptibility variations proximal to the vascular network (8,10,14,15), which results in changes in inherent and induced transverse relaxation times defined as, respectively, T₂ and T₂*. Accurate evaluation of R₂* (1/T₂*) or R₂ (1/T₂) necessitate defining two or more points on the natural or induced transverse relaxation decay curve. Addition of contrast agent increases R₂* (1/T₂*) thus causing limits on sampling as the T₂* is shortened. It can be shown that:

$$\Delta {\mathrm{R}}_2{}^{\text{*}}\text{or}\Delta {\mathrm{R}}_2\propto \log \left[\frac{{\text{S}}^{\text{post}}}{{\text{S}}^{\text{pre}}}\right]$$ [1]

where, S^pre and S^post are pre- and post-contrast MRI signal intensity. The changes in transverse relaxation rate ΔR₂ (1/ΔT₂) and changes in effective transverse relaxation rate ΔR₂* (1/ΔT₂*) caused by the contrast agent are proportional to BV fraction (9,17–19). Therefore, the capability of USPIO to modulate the effective transverse relaxation rate, R₂*, is exploited where the difference image of R₂* before and after administration of USPIO will be useful in determining microvessel density.

A gradient echo (GE) MRI sequence allows BV assessments in relatively shorter data acquisition times and has the advantage of minimizing artifacts associated with flow effects. A recent report with brain tumor model also shows that the R₂* is more sensitive to the USPIO induced susceptibility change (20) and can be used to estimate tumor BV. Although BV is linearly proportional to ΔR₂ and ΔR₂*, the proportionality constant was shown to be contrast agent dose-dependent (13,16). The apparent BV values of tissues with different composition of arteries, capillaries and veins were shown to be different (13) since ΔR₂ and ΔR₂* are affected by the vessel size (12,18).

The design of the present study was to: a) optimize the choices of the MRI imaging parameters to evaluate the application of GE sequence; b) optimize USPIO dosage and TE based on T₂* changes with blood USPIO concentration after intravenous injection; and c) improve the calculations for the assessment of BV using the difference of pre- and post-contrast signals. Hypo-intense regions with very low proton density (e.g., bone and necrotic areas) in the pre-contrast image contribute to background noise leading to unreliable estimates of BV. A weighting scheme is proposed to BV values to suppress noise arising from such hypo-intense regions. The improved BV imaging technique was applied to evaluate tumor BV change response to anti-angiogenesis treatment in mice.

Materials and methods

Animals.

Six to eight weeks old female C3H mice weighing 20–30 g supplied by the Frederick Cancer Research Center, Animal Production (Frederick, MD) were used for in vivo and ex vivo studies. The animals were housed in climate controlled and circadian rhythm-adjusted rooms and were fed ad libitum. Squamous cell carcinoma (SCCVII) cells were injected subcutaneously as a single suspension of 5×10⁵ cells in the right hind leg. The tumors grew to 1.5 cm diameter (1800 mm³) in 10 days. All in vivo experiments were carried out in compliance with National Institutes of Health approved guidelines for animals [the Guide for the Care and Use of Laboratory Animal Resources (1996), National Research Council, and approved by the National Cancer Institute Animal Care and Use Committee].

Animal preparation for MRI.

In SCC tumor study, mice were anesthetized by isoflurane (1.5%) inhalation and mounted prone on a home built 25 mm (inner diameter) transmit receive resonator coil and holder ensemble where the coil axis (y-direction) was perpendicular to the main magnetic field. This specially designed holder enabled us, not only to mount the animal comfortably with its hip positioned downwards in the resonator while the upper body lay along the z-axis, but also to place phantoms (fiducials). For brain imaging, a 35-mm birdcage coil was used for transmission and reception. A pressure transducer (SA Instruments, Inc., NY, USA) was placed on the mouse to monitor its breathing rate at 60±10 per min under anesthesia. A non-magnetic rectal temperature probe (FISO, Quebec, Canada) was used to monitor the core body temperature of the mouse which was maintained at 36±1°C by a steady flow of warm air. A 30 gauge needle was cannulated into the tail vein and extended using optimum length of polythene tubing (PE-10) for administering USPIO (Molday ION™, 10 g Fe/l, which can be converted to 179 mM as concentration of Fe ion, colloidal size of 30 nm, BioPAL Inc., Worcester, MA, USA). MRI studies were performed in a 7 T horizontal scanner operating on a Paravision platform (Bruker Biospin, Billerica, MA, USA). In anti-angiogenesis study, treatment with Sunitinib (50 mg/kg/day, LC Laboratories, Woburn, MA, USA) or methylcellulose/Tween-80 as control by oral gavage was initiated 10 days after tumor implantation, and MRI measurements were carried out before, 2 days, and 4 days after start of treatment.

Phantoms.

The MRI signal intensity dependence with USPIO concentration was assessed using capillary tubes (1.5 mm diameter x 50 mm length) filled with USPIO at Fe concentrations of 0.36, 0.9, 1.8, 2.39, 4.48 and 8.95 mM (dilutions in phosphate-buffered saline: 1/500, 1/200, 1/100, 1/75, 1/40 and 1/20). Each capillary was subsequently placed inside 5 mm i.d. glass tubes filled with 1% agarose gel. The signal from the surrounding gel in GE image [TE/TR = 5.4/250 msec, Flip angle (FA) = 45°, FOV = 32×32 mm and in plane resolution = 125 μm] provided a distinct background for clear demarcation of capillary walls and the detection of hypointensity regions outside the capillaries due to susceptibility artifacts at high USPIO concentrations. The signal intensity vs. TE traces were used to determine R₂* values at each of these concentrations and R₂* of PBS was subtracted to obtain ΔR₂* values.

Ex vivo experiment.

Dose-dependent changes in T₂* were assessed by intravenous administration of USPIO into mice (n=4) at dosage of 143, 215, 287, and 358 μmol per kg. Ten min after the injection, ~500 μl of blood was drawn from each animal into sample tubes containing heparin (10 μl of 100 U/ml) to prevent blood from clotting. Blood drawn from a fifth mouse that did not receive USPIO was assumed to correspond to the T₂* value prior to USPIO administration. Glass tubes filled with these blood samples were placed vertically in the RF coil and GE-MR images were acquired at six different TE values ranging from 3.4 to 50 msec (TR = 250 msec, FA = 45°, in plane resolution = 125 μm, slice thickness = 2 mm, 3 slices). T₂* maps were calculated by ImageJ software package (http://rsb.info.nih.gov/ij/) using MRI analysis calculator plug-in (Karl Schmidt, HypX Laboratory, Brigham and Women’s Hospital).

In vivo MRI experiments.

A set of orthogonally placed scout images through the tumor and normal leg were acquired using a fast spin echo (FSE) sequence (TE/TR = 47/2500 msec, inplane resolution = 250 μm, slice thickness = 2 mm, 8 slices, 8 echoes). Using these pilot images, 16 contiguous slices encompassing the entire tumor was acquired using a flow compensated GE sequence (TE/TR = 5.4/250 msec, FA = 45°, in plane resolution = 125 μm, slice thickness = 2 mm, FOV = 32×32 mm, number of acquisitions = 4, total imaging time ~4.5 min). USPIO was infused in four increments from 143 to 358 μmol/kg in steps of 72 μmol/kg with ~50 μl of PBS flush following each infusion. Five min after each USPIO infusion and saline flush, which allowed USPIO to reach a steady state in vivo, post-USPIO acquisition was performed under identical scan parameters. Stereotaxically fixed tumor leg remained in alignment during pre- and post-USPIO scans. A capillary tube filled with water was used as a standard to correct for any signal variations between pre- and post-USPIO images. It was assumed that the blood USPIO level increased linearly by incremental infusions considering the long half-life of USPIO relative to the experiment time (~30 min).

Improved blood volume calculation.

In order to improve the BV calculation an expression was derived (Appendix for details derivation). In essence, this formulation is an extension of equation [1], but in contrast, takes into account possible experimental and theoretical limitations.

$$\begin{gathered} \text{BV}(\%)=100\left(1+{\text{D}}_{\text{f}}\right)\left({\text{S}}^{\text{pre}}-{\text{S}}^{\text{poss}}\right)/[{\text{S}}^{\text{pre}}+{\text{S}}^{\text{post}}\left({\text{W}}_{\text{b}}/{\text{W}}_{\text{t}}-1\right)+{\text{D}}_{\text{f}} \\ {\text{S}}_{\max }^{\mathrm{pre}}] \end{gathered}$$ [2]

where S^pre and S^post are the image intensities before and after USPIO infusion, D_f is a numerical value chosen intuitively to account for image noise within an image. W_b (~0.9) and W_t (~0.8) are volume fractions of intra- and extravascular water contents and is maximum signal intensity of S^pre image.

Results

Phantom studies.

Basic relationship between USPIO concentration, image intensity, and detrimental susceptibility artifact was investigated in vitro using MRI image of capillaries filled with different concentrations of USPIO in the range of 0–8.95 mM Fe (Fig. 1A). Mean pixel intensity from regions of interests (ROI) chosen inside the capillary area vs. USPIO concentration is shown in Fig. 1B. A linear correlation was observed between ΔR₂* values and USPIO concentrations up to 4.48 mM (Fig. 1C). Proportionality constant between R₂ and USPIO concentration was reported earlier as 105.9±1.9 mM⁻¹sec⁻¹ in saline solutions (11). Results from our studies using GE sequence agree with this estimate for ΔR₂* vs. Molday ION concentration dependence (106±5 mM⁻¹sec⁻¹) as shown in the slope of the plot in Fig. 1C. Image intensity reduction can be observed outside the capillaries filled with more than 4.48 mM USPIO with TE values longer than 5 msec (Fig. 1A), which may cause overestimation of BV in vivo.

Figure 1.

In vitro measurements using capillary tubes filled with PBS and USPIO at concentrations of 0.36, 0.9, 1.8, 2.39, 4.48 and 8.95 mM Fe (dilutions of Molday ION™ in PBS: 1/500, 1/200, 1/100, 1/75, 1/40 and 1/20). (A), GE image showing the appearance of signal loss at 1.8 mM and susceptibility artifact originating at 4.48 mM. (B), Relative intensities from each tube as a function of Fe concentration of USPIO. (C), (ΔR₂*) vs. Fe concentration of USPIO. Slope = 106×10³ (±5×10³) s⁻¹M⁻¹. The point marked by asterisk is inaccurate estimate resulting from signals approaching noise at USPIO concentration of 4.48 and above.

Ex vivo study.

MRI images of tubes containing blood samples drawn from the animals that were administered different doses of USPIO shows signal intensity variation in a dose-dependent manner (Fig. 2A). At TE = 3.4 msec, the intensity reduction was over 98% at 287 μmol/kg (tube iii) and approached 100% at the higher dose (tube iv). At longer TE values (5 msec), 98% intensity reduction was achieved at lower USPIO concentration (215 μmol/kg). Therefore, at lower doses (143 and 215 μmol/kg), the signal decay profile is sufficiently well characterized so that T₂* values from signal intensity vs. TE plots (Fig. 2B) can be reliably estimated. However, at higher doses (287 and 358 μmol/kg), where the signal approached noise levels, in order to estimate T₂* it was necessary to extrapolate signal value at TE = 0 to define sufficient points on the decay curve. The T₂* values calculated are, respectively, 49, 4.9, 1.5, 0.89, 0.72 msec for 0, 143, 215, 287, 358 μmol/kg USPIO doses (Fig. 2). The relationship between ΔR₂* and USPIO dose was found to be non-linear in contrast to linear relationship observed in saline solutions (data not shown). The slope of this curve increases with the dose of USPIO which is attributed to clearance of USPIO from the blood pool in the animal. Simulated relative intensity differences (S^pre - S^post) vs. TE using above T₂* values are shown in Fig. 2D. The vertical line at TE = 5 msec indicates optimal value for the doses in the range of 215–287 μmol/kg where S^post approaches noise level and (S^pre - S^post) approaches maximum.

Figure 2.

MR signal intensity variation with USPIO concentration in mouse blood (A) tubes filled with blood samples (inside dashed circles) with USPIO doses of (i) 143, (ii) 215, (iii) 287 and (iv) 358 μmol/kg. The center image is from a tube containing normal blood drawn from a mouse that did not receive USPIO (normal). (B), Relative intensity variations by USPIO dose and TE. S^pre is signal from normal mouse blood. Signals below background level were not shown. (C), Simulated intensity vs. TE curves at the doses (i)-(iv) using T₂* values (i) 4.9, (ii) 0.15, (iii) 0.89, (iv) 0.72 msec respectively. S^pre values were calculated using T₂* = 49 msec obtained from center tube. (D), Relative (S^pre-S^post) differences as a function of TE calculated for (i)-(iv). The vertical line drawn at 5 msec indicates the optimal TE value for 215–287 μmol/kg doses of USPIO where S^post approaches noise level and the relative intensity difference (S^pre-S^post) is close to maximum.

In vivo studies.

Based on the data from saline solutions and blood samples, the optimum USPIO dosage was estimated to be between 215–287 μmol/kg and in vivo GE-MR images were acquired at TE = 5.4 msec. An image (4th of 8 slices) of pre- and post-USPIO images of a mouse brain is shown in Fig. 3A and B.

Figure 3.

Effect of D_f on BV (%) calculation. (A and B), A MRI images of the mouse brain before and after USPIO administration (215 μmol/kg). (C), Weighting scheme for BV (%) based on pre-USPIO signal (S^pre) at different values of D_f. At D_f = 0, BV = 100% remains unaffected by S^pre. When D_f > 0, BV (%) value is reduced depending on S^pre value. (D-F), BV (%) images calculated at D_f = 0, 0.02 and 0.04 from equation [2]. The background is masked to accentuate the brain region but the inset at the bottom left show the original noise which is reduced as a function of D_f. High BV (%) values in the background noise and the hypo-intense regions of S^pre are attenuated at D_f = 0.04. (G-I), Histograms of BV (%) images at D_f = 0, 0.02 and 0.04 using BV (%) > 0 within the mouse region. The histograms of BV (%) at D_f = 0.02 and 0.04 show gradual increase in frequencies of low BV (%). The contrast between the mouse region and background increases at high D_f values.

As mentioned in Materials and methods, BV estimation using equation [1], is affected by regional variation of S^pre, the pre-contrast MR intensity, in vivo. In contrast, for the proposed equation [2] and appendix the weighting of BV (%) as a function of S^pre (%) at different damping (D_f) values are shown in Fig. 3C. The effect of D_f on calculated BV image using equation [2], is shown in Fig. 3D–I. BV images were calculated from pre- and post-USPIO images (Fig. 3A and B) according to equation [2] using D_f = 0, 0.02, and 0.04 (Fig. 3D–F). The histograms of these images in the BV (%) range of 0–100% are shown in Fig. 3G–I. The results shown in these figures indicate that unreliable estimation of BV resulting from the noise in background. Such hypo-intense regions of S^pre can be suppressed by the introduction of weighting factor D_f into the basic BV calculation formula.

In vivo effect of the dose of USPIO was investigated in a normal mouse brain and a tumor implanted in the mouse leg. Average cerebral blood volume (CBV) in cortex region and tumor blood volume (TBV) were calculated at four different USPIO doses from 143 to 358 μmol/kg at TE = 5.4 msec using D_f = 0.02 (Fig. 4). The calculated CBV for the four USPIO doses were between 1.5–17.3%, while BVs calculated in the tumor region were between 16.7–44.3% at doses of 143, 215, 287, and 358 μmol/kg, respectively (Table I). Interestingly, the CBV values gradually increased with dose and reached a plateau at 287 μmol/kg dose while there was a continuous increase in TBV for the four USPIO doses used. In addition, BV (%) from muscle area of normal leg was assessed at each of these doses (Table I). These results suggest that the use of optimum USPIO dose and TE value are imperative to estimate the accurate BV.

Figure 4.

(A-D), BV (%) images (slice 4) of mouse brain at USPIO doses 143, 215, 287 and 358 μmol/kg calculated using equation [2] from GE-MR images. The ROI used for average brain BV (%) calculation is enclosed by blue trace. (E), Enlarged view of ROI in (B). (F-I), Slice 4 of BV (%) image of tumor bearing and normal legs of mouse at the same doses as in brain. The traces in cyan encompass both the mouse legs and ROI of the tumor in enclosed by blue trace. (J), Enlarged view of tumor bearing leg in g. TE/TR = 5.4/250 msec FOV = 20×20 mm for brain and 32×32 mm for legs. Matrix size = 256×256, number of slices = 8, slice thickness = 2 mm, and averages = 2. BV (%) images were calculated using D_f = 0.02.

Table I.

Average BV values of ROI in brain, tumor, and muscle as a function of USPIO dose calculated using equation [2].

Dose (μmol/kg)	Brain (%)	Tumor (%)	Muscle (%)
143	1.5	16.7	5.1
215	5.9	26.4	6.1
287	17.3	34.7	6.3
358	15.4	44.3	7.8

Anti-angiogenic drug studies.

Anti-angiogenic treatment is an emerging strategy not only to suppress the tumor growth by shutting off the nutrients and oxygen supply to tumors but also to improve the efficiency of cytotoxic drug and radiotherapy via transit vascular normalization. Feasibility study of monitoring anti-angiogenic effect of Sunitinib, a multi-targeted tyrosine kinase inhibitor under phase III clinical trial, was conducted and results are shown in Fig. 5. BV imaging was implemented with USPIO dose of 215 μmol/kg and TE = 5.4 msec. The SCC tumor region shows high BV values (24.3±12.5%, n=4) before anti-angiogenic treatment suggesting promoted angiogenesis in this tumor. It is noteworthy that in spite of such high BV values, this SCC tumor shows significant hypoxic fractions at this tumor size (4). Substantial decrease in the tumor BV was recognized in the BV images 2 and 4 days after start of daily Sunitinib administration (15.0±3.3% and 13.1±8.8% at days 2 and 4, respectively).

Figure 5.

Effect of anti-angiogenic treatment on tumor blood volume. BV images of SCC tumor-bearing mice were obtained before, 2, and 4 days after start of daily Sunitinib treatment (50 mg/kg/day) with USPIO dose of 215 μmol/kg and TE = 5.4 msec.

Discussion

USPIO has been used as a blood pool contrast agent to estimate tumor BV using MRI (4,20) and the characteristics of USPIO are well documented in several reports (21–24). Steady state BV (%) estimations using USPIO are affected by both external (its concentration, stability, and imaging parameters) and in vivo factors (time to equilibrate in the blood pool, half-life). Therefore, it is necessary to optimize parameters such as the dose, the time between the injection and the start of data acquisition to establish steady state, and the speed of data acquisition.

The USPIO used in this study is an iron oxide-based super paramagnetic contrast agent having a size of 30 nm. It is a blood pool agent with a long intravascular half-life (21) causing susceptibility variations proximal to blood vessels making it suitable for R₂ and R₂* measurements at steady state concentrations. A preliminary pharmacokinetic study (data not shown) indicated that USPIO reaches equilibrium levels in the blood of mice within 5 min after injection. USPIO has dominant T₂* effects over T₁ unlike gadolinium agents which affect both T₁ and T₂ (21).

The results of MRI studies in saline solutions containing USPIO, using GE sequence (Fig. 1B and C) on R₂* vs. USPIO concentration dependence agree with literature data (11). Deviation to the linear relationship of ΔR₂* vs. dose was suggested by results from ex vivo studies. It is widely known that both ΔR₂* and ΔR₂ are dependent on blood vessel size (9,12,18), and the proportionality constant between ΔR₂* and BV (%) is found to be dose and tissue dependent (13,16). Therefore, ΔR₂* and ΔR₂ for BV (%) assessment using equations [1] or [2] (in this study) required scaling factors to obtain BV (%) values which were found to correlate very well (R>0.995).

Optimum TE value.

The difference (S^pre - S^post) in equation [2] depends on both the T₂* and TE values since the signal intensity of GE sequence is proportional to e^-(TE/T₂). The simulated relative intensity vs. TE curves using T₂* values derived from blood samples is shown in Fig. 2C. (S^pre - S^post) vs. TE curves calculated for all four USPIO doses showed gradual increase of (S^pre - S^post) to a peak value and then a slow decrease (Fig. 2D). The signal intensity vs. TE curves (Fig. 2C) and (S^pre - S^post) vs. TE curves (Fig. 2D) suggest that an optimal TE value lies at TE > 2 TE_max. In practice, the attainable TE is also limited by the hardware imposing constraints on minimum TE value.

Choice of D_f value.

D_f is an adjustable parameter whose value depends on how much noise suppression is desired. As D_f increases, from D_f = 0 (no attenuation), the BV (%) calculated using signals greater than 50% are marginally attenuated. However, signals below 10% are attenuated to a relatively larger extent. Since high D_f value underestimates overall BV (%), a small and constant D_f value is desirable for valid comparisons among different BV images. The BV images calculated at D_f = 0, 0.02, and 0.04 (Fig. 3D–F) demonstrate noise reduction in the background areas and contrast enhancement at higher D_f values. This is reflected in the histograms of the BV images as an increase in the frequencies of low BV (%).

Optimum USPIO dose.

Since BV in brain has been relatively well established (14,25,26), dose dependency of USPIO was first investigated in the mouse brain using identical scan parameters and dosages as in tumor studies. The non-linear relationship of the signal intensity to USPIO dose (ex vivo studies on blood samples) indicate a more complex situation in live animals. The doses that were achieved over 98% of signal attenuation (215–287 μmol/kg) corresponded to 3.6–4.8 mM USPIO in saline assuming that the total blood plasma volume of the mouse was 6% of its body weight (27). In phantoms, conspicuous susceptibility variations (Fig. 1A) were observed at 4.8 mM USPIO and higher (TE ≥5 msec). The calculated CBV was 17.3% at this dose whereas the known CBV of mice is only about 5% (14,25,26). As tight junctions in the blood brain barrier are impermeable to USPIO it is unlikely such high values are realistic. Change in R₂* will vary upon vessel size because of its dependency on the local hematocrit in larger vessels vs. smaller capillaries and therefore, GE images are sensitive to micro and macrovasculature (18). A comparison of BV (%) images at low and high doses reveals that the overestimation stems mainly from the effect of USPIO in the extravascular regions through magnetic susceptibility and water exchange between blood and tissue. The lower USPIO dose of 215 μmol/kg was concluded to be preferable for in vivo study.

The tumor data (Table I) indicate that the calculated TBV increase proportionately with USPIO dose in contrast to CBV (%). Since, USPIO is a plasma marker and it is more suited for blood plasma volume (28) estimates, it was assumed that the tumor blood vessels prevent leakage of USPIO. Secondly, as blood consists of plasma and red blood cells where the volume of the latter depends on local hematocrit, the regional variations of hematocrit and the effects of the local hematocrit in the microvasculature (and therefore, on CBV) were assumed to be negligible.

It should be noted that, due to proton exchange, the presence of contrast agent in the vascular bed reduces T₁ in the tissue, resulting in a possible underestimation of ΔR₂. However, due to the use of a long TR in this study (250 msec), the effects of T₁ changes can be assumed to be small and neglected. Therefore, it was also assumed that the T₁ relaxation effects due to USPIO on TBV calculations was minimum because of the TE/TR employed.

This study utilized the same concept of using the steady state susceptibility contrast, exploiting the linear relationship between the change in R₂* and blood concentration of the USPIO (29), but with an improved equation, to calculate the BV (%). Low concentrations of tissue blood USPIO is likely to lead to underestimation of relative BV (%) due competing T₁ effects with T₂* effects. Dose-dependent increase in TBV in contrast to CBV indicates regional variations in BV (%) estimates. Structure and function of tumor neovasculature are architecturally chaotic and blood flow through them is irregular. Therefore, although USPIO is primarily an intravascular agent, vascular anomalies associated with tumor angiogenesis can render the rather large USPIO not confined to the vascular network (27). Nevertheless, 5 min post infusion is the optimum time for attaining equilibrium (data not shown).

In conclusion, blood plasma volume estimates can be quantitative in GE-MRI experiments at optimum concentration of USPIO and TE. In practice, several factors prevent administering optimal USPIO concentration in vivo. Further, the noise and artifacts in images introduce a definite amount of error to absolute BV estimates. Low dose of USPIO (215 μmol/kg) is suitable to identify relatively high blood volume regions while higher doses reveal low BV region at the cost of blurring. The difference between the optimized USPIO doses in vitro and in vivo studies points out the importance of dose optimization to obtain absolute blood volume. The calculated BV (%) values are associated with noise that arises from the noise in pre- and post-USPIO images. The adjustable parameter D_f in equation [2] reduces the noise in BV (%) image improving its contrasts.

Appendix

Blood volume calculation.

BV in a voxel is given by the ratio of volume of blood in the voxel to the tissue mass of the voxel and expressed in milliliters per 100 gram of tissue or microliters per gram (μl/g). Assuming that the total volume of the voxel can be divided by the volumes of intra- and extravascular compartments, V_b and V_t respectively, the BV (%) can be defined as a volume fraction by (29),

$$\mathrm{BV}(\%)=100\left[\text{volume of blood in a voxel/volume of the voxel}\right]\mathrm{or}$$

$$\text{BV}(\%)=100\frac{{\text{V}}_{\text{b}}}{{\text{V}}_{\text{b}}+{\text{V}}_{\text{t}}}$$ [A1]

This model assume, one, that only the intravascular protons become MRI invisible through the magnetic susceptibility gradients caused by USPIO and ignores any susceptibility effects in the extravascular regions through water exchange between blood and tissue, two, the leakage of USPIO from disrupted blood vessels, and, three, T₁ effects caused by USPIO. The signal from a voxel can be divided into two components: a) a component that comes from intravascular protons which is affected by contrast agent and b) a component from extravascular protons that is unaffected by contrast agent. When the signal from intravascular protons is effectively removed, S^post is proportional to extravascular volume. Therefore,

$${\text{S}}^{\text{post}}=k{\text{W}}_{\text{t}}{\text{V}}_{\text{t}}$$ [A2]

and the intravascular volume is,

$$\left({\text{S}}^{\text{pre}}-{\text{S}}^{\text{post}}\right)=k{\text{W}}_{\text{b}}{\text{V}}_{\text{b}}$$ [A3]

where k is a proportionality constant between signal and the number of protons and intra- and extravascular water fractions are W_b (≈0.9) and W_t (≈0.8) respectively (11). Assume that x is a fraction of signal that remains after this effect and $x={\text{e}}^{-\Delta {\mathrm{R}}_2{}^{\text{*}}\text{TE}}$, where $\mathrm{\Delta }{\text{R}}_2{}^{*}=\frac{1}{{\text{T}}_2{}^{*}(\text{USPIO})}-\frac{1}{{\text{T}}_2{}^{*}}$. The signals observed before (S^pre) and after (S^post) USPIO administration in the animal are therefore,

$${\text{S}}^{\text{pre}}={\text{S}}_{\text{b}}+{\text{S}}_{\text{t}}$$ [A4]

$${\text{S}}^{\text{post}}=x{\text{S}}_{\text{b}}+S_{\text{t}}$$ [A5]

and the difference

$${\text{S}}^{\text{pre}}-{\text{S}}^{\text{post}}=(1-x){\text{S}}_{\text{b}}$$ [A6]

Substituting ΔS = (S^pre - S^post), and δ = (1 - x), and rearranging [A7],

$${\text{S}}_{\text{b}}=\mathrm{\Delta }\text{S}/\delta$$ [A7]

Rearranging equations [A2], [A3] and [A4] to extract V_b, V_t and S_t and substitution in [A1], lead to

$$\text{BV}(\%)=100\frac{\mathrm{\Delta }\text{S}/\left(k{\text{W}}_{\text{b}}\delta \right)}{\mathrm{\Delta }\text{S}/\left(k{\text{W}}_{\text{b}}\delta \right)+\left({\text{S}}^{\text{pre}}-\mathrm{\Delta }\text{S}/\delta \right)/\left(k{\text{W}}_{\text{t}}\right)}$$ [A8]

Multiplying the numerator and denominator by kW_bδ, [A8] is simplified to

$$\text{BV}(\%)=100\frac{\mathrm{\Delta }\text{S}}{\mathrm{\Delta }\text{S}+\left({\text{W}}_{\text{b}}/{\text{W}}_{\text{t}}\right)\left(\delta {\text{S}}^{\text{pre}}-\mathrm{\Delta }\text{S}\right)}$$ [A9]

Expansion of ΔS and δ in [A9] and rearrangement gives,

$$\mathrm{BV}(\%)=100\frac{\left({\text{S}}^{\text{pre}}-{\text{S}}^{\text{post}}\right)}{{\text{S}}^{\text{pre}}\left[1-x\left({\text{W}}_{\text{b}}/{\text{W}}_{\text{t}}\right)\right]+{\text{S}}^{\text{post}}\left[\left({\text{W}}_{\text{b}}/{\text{W}}_{\text{t}}\right)-1\right]}$$ [A10]

When x is negligibly small, equation [A10] can be simplified to

$$\text{BV}(\%)=100\frac{\left({\text{S}}^{\text{pre}}-{\text{S}}^{\text{post}}\right)}{{\text{S}}^{\text{pre}}+{\text{S}}^{\text{post}}\left[\left({\text{W}}_{\text{b}}/{\text{W}}_{\text{t}}\right)-1\right]}$$ [A11]

The factor (W_b/W_t - 1) in the denominator accounts for the difference in intra- and extravascular water content. In hypo-intense regions where S^pre = S^post = 0, the denominator in right hand side of equation [A11] would become zero. In this case, BV = 0 since S^pre must be greater than zero if BV > 0. In practice, unreliable and random BV estimates are obtained in these regions due to noise which can be suppressed by adding a small positive quantity σ_b (background noise) to the denominator in right hand side of equation [A11]. Defining a fraction D_f such that ${\text{D}}_{\text{f}}={\sigma }_{\text{b}}/{\text{S}}_{\max }^{\mathrm{pre}}$ where ${\text{S}}_{\max }^{\mathrm{pre}}$ is highest signal intensity of S^pre image and adding this factor to denominator and rescaling by (1 + D_f), equation [11] becomes,

$$\begin{gathered} \text{BV}(\%)=100\left(1+{\text{D}}_{\text{f}}\right)\left({\text{S}}^{\text{pre}}-{\text{S}}^{\text{poss}}\right)/[{\text{S}}^{\text{pre}}+{\text{S}}^{\text{post}}\left({\text{W}}_{\text{b}}/{\text{W}}_{\text{t}}-1\right)+{\text{D}}_{\text{f}} \\ {\text{S}}_{\max }^{\mathrm{pre}}] \end{gathered}$$ [2]

The limits of BV can be set between 0 and 100 for visual representations to eliminate unrealistic negative values arising from noise or increased S^post intensities due to possible T₁ effects. However, average BV (%) estimates of a region of interest (ROI) are calculated without imposing these limits to account for random noise.

Choice of optimum TE and D_f values.

The signal intensity is the same for all USPIO concentrations at TE = 0 but decays differently at different concentrations according to the T₂* values. The term (S^pre - S^post) in equations [1] and [2] can be evaluated at each TE value since the samples with and without USPIO represent post- and pre-USPIO conditions. The peak occurs at a TE value,

$${\text{TE}}_{\max }=\frac{{\text{T}}_2^{*\text{pre}}{\text{T}}_2^{*\text{post}}}{{\text{T}}_2^{*\text{pre}}-{\text{T}}_2^{*\text{post}}}\ln \left(\frac{{\text{T}}_2^{*\text{pre}}}{{\text{T}}_2^{*\text{post}}}\right)$$ [A12]

where T₂^*pre and T₂^*post are the T₂* values before and after USPIO administration. Although the peak (S^pre - S^post) has the advantage of sensitivity, equation [2] also requires negligibly small value of S^post for reliable BV (%) estimation. High S^pre value is desirable for better SNR.

The ratio of ${\sigma }_{\text{b}}/{\text{S}}_{\max }^{\mathrm{pre}}$ where σ_b is noise level that can be estimated by the standard deviation of background pixel intensities. For a ratio of ${\sigma }_{\text{b}}/{\text{S}}_{\max }^{\mathrm{pre}}=0.02$, D_f can be between 0.02 and 0.04. The weights tend to become linearly proportional to S^pre when D_f ≫ 1.