Medical Physics and Informatics
June 2011

Intravoxel Incoherent Motion in Body Diffusion-Weighted MRI: Reality and Challenges


OBJECTIVE. Diffusion-weighted MRI is increasingly applied in the body. It has been recognized for some time, on the basis of scientific experiments and studies in the brain, that the calculation of apparent diffusion coefficient by simple monoexponential relationship between MRI signal and b value does not fully account for tissue behavior. However, appreciation of this fact in body diffusion MRI is relatively new, because technologic advancements have only recently enabled high-quality body diffusion-weighted images to be acquired using multiple b values. There is now increasing interest in the radiologic community to apply more sophisticated analytic approaches, such as those based on the principles of intravoxel incoherent motion, which allows quantitative parameters that reflect tissue microcapillary perfusion and tissue diffusivity to be derived.
CONCLUSION. In this review, we discuss the principles of intravoxel incoherent motion as applied to body diffusion-weighted MRI. The evidence for the technique in measuring tissue perfusion is presented and the emerging clinical utility surveyed. The requisites and challenges of quantitative evaluation beyond simple monoexponential relationships are highlighted.
In the 1980s, the use of clinical diffusion-weighted (DW) MRI was largely confined to the brain for the early detection of cerebral infarction. However, technologic innovations in the last decade, such as improved MRI gradient performance, multichannel surface receiver coils, parallel imaging techniques, and improved fat suppression schemes, have facilitated the translation of such measurements to the body [1]. Applying these technologies enabled high-quality DW-MRI scans to be obtained in free-breathing, which helped to conceptualize the whole-body DW imaging with background signal suppression technique [2].
Because quantitative imaging is likely to grow in scope and importance, the radiologic community has embraced the potential of DW-MRI, such that there is now a steady stream of publications on its use in the body for oncologic and nononcologic applications. The technique enables the calculation of tissue apparent diffusion coefficient (ADC), a quantitative measure of tissue diffusivity. This makes it possible to objectively compare results, such as when evaluating tumor ADC before and after chemotherapy to identify treatment response.
However, it has been recognized for some time that the calculated ADC value is sensitive to capillary perfusion, which represents bulk motion of intravascular water protons within imaging voxels [36]. In 1986, Le Bihan et al. [3] proposed the principles of intravoxel incoherent motion (IVIM) and suggested that using a more sophisticated approach to describe the relationship between signal attenuation in tissues with increasing b value would enable quantitative parameters that separately reflect tissue diffusivity and tissue microcapillary perfusion to be estimated. There is growing interest in applying analytic techniques beyond simple ADC calculations to tease out the effects of microcapillary perfusion from DW-MRI data [7]. This is driven by the realization that the assumption of a simple exponential relationship between signal attenuation and b value for ADC calculation is simplistic and by the perceived value of obtaining perfusion-related data from a relatively simple measurement. However, to do this in a meaningful way demands insight into the approach and a clear understanding of the strengths and limitations of the method.
This article is aimed at radiologists and technologists who are currently engaged in applying DW-MRI in the body for disease evaluation and who are interested in extending the quantitative potential of the technique in their practice or research. In this review, the principles of IVIM are discussed and the published literature surveyed to examine the link between quantitative parameters derived by IVIM-based analysis and vascular perfusion. The emerging extracranial applications of IVIM DW-MRI in clinical studies are examined, focusing on the potential of such analysis to inform about disease states. Finally, we will highlight challenges of implementing such complex data acquisition and analysis. The basic principles of DW-MRI are assumed and will only be briefly discussed. The reader should refer elsewhere for a more comprehensive discussion of the basic principles of DW-MRI [1, 8].

Understanding DW-MRI and IVIM

DW-MRI is sensitive to the thermally driven random motion of water protons, which is modified in tissues by their interactions with cell membranes and macromolecules. Thus, the apparent diffusion of water in tissues reflects tissue cellularity, the tortuosity of the extracellular space, integrity of cell membranes, and viscosity of fluids [1]. Stejskal and Tanner [9] described a spin-echo MRI experiment that can be used to measure water diffusion and remains the basis for many body DW-MRI sequences in use today.

Calculation of ADC From DW-MRI Measurements

By performing DW-MRI with at least two diffusion weightings, or b values, the differential signal attenuation at different b values can be used to calculate the ADC. In its simplest form, the slope of the line that describes the relationship between the logarithm of the signal intensity and the b value is the ADC (Fig. 1). If the calculation is repeated for each voxel of the DW-MRI, then the ADC value for every image voxel can be derived and displayed as a parametric ADC map. Thus, voxels that show a steeper slope of signal attenuation with increasing b values will have higher ADC values (indicating higher water diffusivity) compared with voxels that show a gradual slope of signal attenuation. Cellular tissues (e.g., tumor tissues) in the body often return lower ADC values compared with native tissues, which facilitates their detection and characterization. The ADC is usually expressed in units of 10–3 mm2/s. Although an ADC map may be generated under optimal measurement conditions by using just two b values, using more than two b values at image acquisition generally gives more accurate ADC values, especially where the likely ADC values are not known a priori.
Fig. 1 Apparent diffusion coefficient (ADC) calculation. Simplified scheme shows ADC calculation from b value diffusion-weighted imaging. For each image voxel acquired at same anatomic position at increasing b value, logarithm of relative signal intensity is plotted against b value. Slope of line (monoexponential fit) is ADC of that image voxel. Process is repeated for every voxel on image, and ADC values of all voxels can be displayed as parametric ADC map. In this example, metastasis in left lobe of liver (arrow) returns low ADC, indicating relatively impeded water diffusion, whereas cyst in right kidney (arrowhead) returns high ADC. Note that cyst also shows high signal on b value images due to relatively long T2 relaxation time, phenomenon known as “T2-shine through.”

Microcapillary Perfusion: Implications for DW-MRI Measurements and ADC Calculations

When DW-MRI is performed in well-perfused body tissues within the b value range usually applied for body imaging (i.e., 0–1000 s/mm2), the measured signal attenuation at low b values (e.g., 0–100 s/mm2) arises not only from water diffusion in tissues but also from microcirculation within the normal capillary network. Both these processes result in phase dispersion at DW-MRI, leading to signal attenuation. Le Bihan et al. [3] termed the behavior of protons that display signal attenuation at DW-MRI as showing IVIM.
Microcirculatory perfusion of blood within capillaries has no specific orientation and can therefore be thought of as a type of “pseudodiffusion,” which depends on the velocity of the flowing blood and the vascular architecture. The effect of pseudodiffusion on the signal attenuation in each imaging voxel is also b value dependent. However, the rate of signal attenuation resulting from pseudodiffusion is typically an order of magnitude greater than tissue diffusion because of larger distances of proton displacement during the application of the motion-probing gradients. Therefore, in normal perfused tissue at higher b values, pseudodiffusion accounts for only a small proportion (if any) of the measured signal in each imaging voxel. However, at lower b values, this relative contribution to the DW-MRI signal becomes significant.
A plot of the signal attenuation of a well-perfused tissue (liver parenchyma) with increasing b values from a healthy individual is shown in Figure 2. Not surprisingly, protons associated with flowing blood have relatively large diffusion distances, and the signal is suppressed by small diffusion weightings (e.g., b value ≤ 100 s/mm2). Thus, there is a steeper slope of signal attenuation for b values near zero, which can be attributed to microcapillary perfusion. By contrast, larger b values are less sensitive to contributions from microcapillary perfusion because the signal attenuation of the perfusing protons is essentially complete. At larger b values (e.g., > 100 s/mm2), the slope of signal attenuation is less steep, which is more reflective of tissue diffusivity. Hence, in this example, a line drawn to best fit all the data points has the shape of a hockey stick, which is described by the IVIM model. The IVIM approach uses a biexponential function to describe the DW-MRI data and makes the assumption that the measured signal attenuation at DW-MRI comprises a mixture of tissue perfusion and tissue diffusivity effects. Using IVIM-based analysis, it is possible to derive other quantitative indexes that describe tissue water diffusivity, tissue perfusion (pseudodiffusion coefficient), and the perfusion fraction of tissues, which can also be displayed as parametric maps (Fig. 3). In this review, the IVIM analysis and graphical plots are averaged over entire regions of interest and are computed using a method described by Neil and Bretthorst [10]. However, other mathematic methods can be applied to do this, but a discussion of these methods is beyond the scope of this review.
Fig. 2 Healthy 30-year-old man. Plots show logarithm of relative signal intensity versus b value from normal liver parenchyma. Note that there is initially steeper decrease in plotted signal values (circles) at low b values (within rectangular box A) compared with more gradual attenuation of signal at higher b values (within rectangular box B). By applying intravoxel incoherent motion (IVIM) analysis, biexponential behavior of signal attenuation is characterized (solid line), resulting in typical hockey stick appearance of fitted curve. Using simple monoexponential apparent diffusion coefficient (ADC) line fitted to data (dotted line) in this case provides suboptimal characterization of signal attenuation behavior.
Currently, on most commercial MRI systems, the ADC value is calculated automatically and by default using all available b value images with a monoexponential function (e.g., a straight line fit to the logarithm of signal intensity versus b value) (Fig. 2). Thus, depending on the range and number of b values used at imaging, the calculated ADC by this approach is, to various extents, influenced by microcapillary perfusion.
From the above discussion, it should be clear, therefore, that the ADC value of perfused tissues calculated from only low b value images (e.g., ≤ 100 s/mm2, sometimes referred to as ADClow) would be perfusion sensitive, whereas the ADC value calculated from images of higher b values (e.g., > 100 s/mm2, sometimes referred to as ADChigh) and excluding lower b values would be relatively perfusion insensitive. It can also be reasoned that ADChigh values are likely to be very similar to the diffusion coefficient derived by IVIM-based analysis for any particular tissue (Fig. 3). It is also worth-while remembering that, although ADClow is perfusion sensitive, it is also affected by diffusion effects in tissues.
Fig. 3 Healthy 30-year-old man. Diffusion-weighted MRI of liver was performed in coronal plane. By applying intravoxel incoherent motion (IVIM)–based biexponential analysis of normal liver, different parts of signal attenuation curve (solid line) for each image voxel are closely linked to estimated quantitative parameters of diffusion coefficient (D), which reflects tissue diffusivity; pseudodiffusion coefficient (D*), which reflects microcapillary perfusion; and perfusion fraction (f). Results for all voxels are displayed as parametric maps as shown. Note also that apparent diffusion coefficient value calculated from images using only higher b values (> 100 s/mm2) (ADChigh) will approximate D, because they have similar gradients.
Fig. 4 Diffusion-weighted MRI in rat with two implanted rhabdomyosarcoma tumors (arrow and arrowhead, all panels) performed antemortem and postmortem. Parametric maps of apparent diffusion coefficient (ADC) were generated using all b values (0, 50, 100, 150, 200, 250, 300, 500, 750, and 1000 s/mm2), ADClow using b values of 0, 50, and 100 s/mm2; ADChigh using b values of 500, 750, and 1000 s/mm2; and ADCperf calculated as ADClow –ADChigh. Note that ADClow maps revealed tumor values (arrow and arrowhead) to be higher in antemortem state compared with postmortem state, in keeping with effects of microcapillary perfusion, whereas ADChigh maps, which are perfusion insensitive, appeared similar. Subtraction maps (ADCperf) in antemortem state showed perfusion fraction within tumors but this was not observed postmortem. (Courtesy of Ni Y and De Keyzer F, University of Leuven, Leuven, Belgium)

Evidence for Tissue Perfusion Using DW-MRI Measurements

There are experimental and clinical data to support the biexponential behavior of signal attenuation observed in body tissues at DW-MRI and that indicate the signal attenuation observed at low b values is related to tissue perfusion.
Fig. 5A 54-year-old man with biopsy-proven adenocarcinoma of pancreas.
A, Axial scans were performed using navigator-controlled spin-echo echo-planar diffusion-weighted MRI with eight b values (0, 25, 50, 75, 100, 250, 500, and 900 s/mm2). Mean signal attenuation curves by intravoxel incoherent motion–based analysis of pancreatic tumor and normal pancreatic tissue with increasing b value are shown with offset in vertical axis for data display.
Fig. 5B 54-year-old man with biopsy-proven adenocarcinoma of pancreas.
B and C, Parametric maps of diffusion coefficient (D) (B) and perfusion fraction (f) (C). Positions of tumor (T) and normal pancreas (P) are indicated by regions of interest. There is slight difference in mean diffusion coefficient of tumor compared with normal pancreas (1.30 × 10–3 vs 1.44 × 10–3 mm2/s). However, perfusion fraction is reduced within tumor compared with normal pancreas (0.06 vs 0.10). Note “flattening” of mean signal attenuation curve at low b values in tumor suggesting lower perfusion compared with normal pancreas.
Fig. 5C 54-year-old man with biopsy-proven adenocarcinoma of pancreas.
B and C, Parametric maps of diffusion coefficient (D) (B) and perfusion fraction (f) (C). Positions of tumor (T) and normal pancreas (P) are indicated by regions of interest. There is slight difference in mean diffusion coefficient of tumor compared with normal pancreas (1.30 × 10–3 vs 1.44 × 10–3 mm2/s). However, perfusion fraction is reduced within tumor compared with normal pancreas (0.06 vs 0.10). Note “flattening” of mean signal attenuation curve at low b values in tumor suggesting lower perfusion compared with normal pancreas.

Phantom Studies

Le Bihan et al. [4] used a phantom that could show the effects of perfusion using DW imaging. This included a chromatographic column packed with resin microspheres (Sephadex G100, Sigma-Aldrich) through which water percolates under gravity. Protons within the microspheres showed only diffusion, whereas water in the spaces between microspheres was reasoned to show flow analogous to microcapillary perfusion. DW-MRI was performed on the phantom using six b values, and water flow through the resin column varied. It was shown that reducing water flow through the resin column resulted in a decrease in the measured ADC and perfusion fraction calculated by biexponential fitting of the data [4]. This indicates that DW-MRI measurement is sensitive to flow effects.

Preclinical and Clinical Studies

A number of preclinical studies have compared ADC obtained in living versus postmortem animals to show the influence of tissue perfusion on ADC [11, 12]. Sakuma et al. [11] using implanted human tumors in nude mice showed that the measured ADC in tumors was significantly higher in living mice compared with mice that were sacrificed. In another study, Sun et al. [12] calculated perfusion-sensitive ADCs (using b values of 0–100 s/mm2) and perfusion-insensitive ADCs (using b values of 500–1000 s/mm2) in rat livers implanted with rhabdomyosarcoma in living and postmortem animals. They found the perfusion-sensitive ADC significantly decreased in tumors and normal liver in the postmortem state, but no significant change was observed in the perfusion-insensitive ADC (Fig. 4).
Other studies have modulated vascular flow in living animals to observe changes in diffusion measurements. Neil et al. [13] and Henkelman et al. [14] altered cerebral blood flow in rat brains by increasing the arterial carbon dioxide concentrations, leading to increased cerebral perfusion. They found that the perfusion parameters (pseudodiffusion coefficient and perfusion fraction) by IVIM-based analysis were correlated with the arterial carbon dioxide concentrations. Wang et al. [15] increased blood flow in a mammary adenocarcinoma rat model by administering the vasodilator hydralazine. Injection of IV hydralazine increased tumor blood flow, which was accompanied by a measurable increase in the IVIM-derived pseudodiffusion coefficient. In another study, a dog kidney was excised, isolated, and perfused using a mechanical pump [16]. On DW-MRI, the ADC and perfusion fraction of the kidney increased as flow through the kidney was increased by the mechanical pump, but tissue diffusivity showed no significant change. In a recent clinical study [17], the perfusion fraction in normal pancreatic tissue was reduced by suppression of flow at low b values, but the diffusion coefficient was unchanged. These studies show that DW-MRI measurements are sensitive to tissue perfusion, and the technique could thus be potentially harnessed to provide assessment of the microcirculatory perfusion of tissues, in addition to measuring tissue diffusivity.

Relationship Between Microcapillary Perfusion Measured by DW-MRI and Perfusion Measured by Other Imaging Techniques

In theory, there should be close agreement between perfusion quantified by DW-MRI and perfusion evaluated by other techniques. Henkelman [18] argued that perfusion measured by DW-MRI could be different from perfusion measured using intravascular tracers (e.g., contrast medium) because such perfusion estimates were based on tissue uptake or removal of the injected tracer. However, Le Bihan and Turner [19] reasoned that, even with the use of freely diffusible tracers, the delivery of tracer to tissues is still dependent on intravascular flow and there is thus highly likely to be a relationship between tissue perfusion measured using DW-MRI and tissue perfusion measured using tracer kinetic methods.
In the published literature, DW-MRI–derived perfusion indexes have been reported to correlate with perfusion parameters derived using other techniques. One study [20] in the brains of 28 volunteers compared IVIM-based analysis with relative blood flow and relative blood volume obtained by dynamic susceptibility contrast enhancement imaging. The perfusion fraction was correlated with the relative blood volume, and the pseudodiffusion coefficient was correlated with the relative blood flow. In another study in patients with renal artery stenosis [21], relative blood flow determined by radionuclide tracer technique was found to correlate with the ADC.
However, perhaps not surprisingly, no clear relationship could be found between DW-MRI–derived parameters and perfusion derived using other techniques on other occasions [22]. One of the likely reasons is because the “fast component,” or perfusion fraction measured by DW-MRI, may comprise more than one physiologic process (e.g., glandular secretion and ductal flow). Evidence that this is likely has been shown by increase in ADC of normal salivary glands in response to gustatory stimulation [23, 24]. These bulk flow phenomena will also contribute to the signal attenuation measured at low b values and will be difficult, if not impossible, to isolate from microcapillary perfusion effects. For these reasons, doubt was expressed by Muller et al. [25] as to whether IVIM evaluation could measure true vascular perfusion in kidneys. They argued that the lack of a clear strong biexponential signal decay in the kidney and the relatively small difference between the measured cortical and medullary ADC suggest that the generally high diffusion values encountered in the kidneys (typically about 2 × 10–3 mm2/s) [26] may be more related to other flow-dependent transport mechanisms (e.g., renal tubular flow) rather than renal vascular perfusion. Even if vascular flow does contribute to the signal attenuation measured in the kidneys, it is currently not possible to isolate the signal contribution of vascular flow from renal tubular flow by IVIM analysis. Clearly, more work is needed to verify the physiologic basis for the DW-MRI measurements in functionally complex organs. Nevertheless, most recent studies have shown that the measured ADC of the normal renal cortex is higher than that of the medulla [2629], suggesting that perfusion is still a probable contributor to the observed difference.
TABLE 1: Summary of Diffusion-Weighted (DW) MRI Studies Using Quantitative Indexes Beyond Simple Monoexponential Apparent Diffusion Coefficient (ADC) Evaluation

Clinical Applications of DW-MRI for Extracting Perfusion-Related Information

Despite some uncertainties with regard to the physiologic basis of DW-MRI observations that relate to tissue perfusion, clinical application of these techniques has yielded interesting results. These studies are summarized in Table 1.
It was found that the signal attenuation of the prostate gland with increasing b value conformed to a biexponential behavior [30, 31]. Both the fast (pseudodiffusion) and slow component (tissue diffusivity) of diffusion were reportedly lower in prostate cancer compared with normal peripheral or transitional zones [32].
In the pancreas, the identification of pancreatic carcinoma and distinguishing between tumor and focal pancreatitis still pose significant diagnostic challenges. In a recent study [33], the perfusion fraction of pancreatic carcinoma was shown to be significantly lower than and showed little overlap with normal pancreatic parenchyma (Figs. 5A, 5B, and 5C). These results suggest that the perfusion fraction could be helpful to identify and characterize pancreatic malignancy.
Fig. 6A Signal attenuation behavior of abdominal viscera at diffusion-weighted (DW) MRI in healthy 30-year-old man.
A, Coronal DW-MRI scan (b = 0 s/mm2) shows rectangular regions of interest drawn over liver (L), right kidney (K), pancreas (P), and spleen (S).
Fig. 6B Signal attenuation behavior of abdominal viscera at diffusion-weighted (DW) MRI in healthy 30-year-old man.
B, Mean curves by intravoxel incoherent motion–based analysis displayed with offset in vertical axis showing attenuation of signal intensities within these organs at b values of 0, 25, 50, 75, 100, 150, 250, 500, 650, 800, and 1000 s/mm2. Note that curves from liver and pancreas have hockey stick appearance typical of biexponential behavior, with transition between two components observed at low b values (< 100 s/mm2). However, this is not obvious within spleen or kidney.
In the abdomen, IVIM DW-MRI [34] of intraabdominal organs, such as the liver, spleen, and kidneys (Figs. 6A and 6B), revealed a biexponential pattern of signal attenuation. Using the IVIM model, the calculated ADC values using all b values of these organs were significantly higher than the corresponding tissue diffusion coefficients. In colorectal liver metastases [35], the estimated perfusion fraction of colorectal liver metastases was lower than that in normal liver parenchyma, in keeping with the hypovascular nature of these lesions (Figs. 7A and 7B). More recently, IVIM analysis in patients with liver cirrhosis found that the pseudoperfusion coefficient and the ADC of the liver were both lower in cirrhotic liver than in normal liver.
The diffusion coefficient and the perfusion fraction were reportedly higher in the cortex compared with the medulla in normal kidneys [36]. However, this differentiation was lost in renal transplant allograft [36] (Fig. 8). Interestingly, the perfusion fraction could be correlated with creatinine clearance [36, 37], suggesting that the technique has the potential to noninvasively assess the renal function. Applying a biexponential model was also shown to reduce errors in ADC quantifications across the whole kidney, within the renal cortex or the medulla [38].
These clinical studies show the evolving utility of the perfusion-sensitive component of diffusion to inform on disease states. However, such data are only beginning to emerge. Critically, such analysis cannot yet be performed using standard vendor software that only applies a simple monoexponential fit to all b values data. However, before such an analytic approach can be generalized, it is important to reflect on some of the challenges that need to be addressed.

Challenges to Implementation of Biexponential Fitting of DW-MRI Data

There is recognition that using monoexponential fitting of DW-MRI data in the body can be an important source of variation in reported ADC measurements [38]. However, it is important to remember that, for any quantitative metric to be useful, the process of image acquisition, image processing, model fitting to the acquired data, and analysis of parametric maps will need to be sufficiently robust so that accurate and reproducible measurements can be made to yield biologically relevant and clinically meaningful results. Applied inappropriately, quantitative indexes obtained using IVIM or other more sophisticated mathematic models may be highly uncertain, erroneous, or even misleading [10]. In the following subsections, we discuss some of the challenges and unresolved issues in adopting more complex analyses of DW-MRI data.
Fig. 7A 45-year-old man with colorectal liver metastasis to right lobe of liver.
A, Axial diffusion-weighted MRI scan (b = 0 s/mm2) shows regions of interest drawn over tumor (T) and normal liver (L). Note high signal centrally within metastasis suggesting necrosis.
Fig. 7B 45-year-old man with colorectal liver metastasis to right lobe of liver.
B, Mean signal attenuation curves by intravoxel incoherent motion biexponential analysis shows typical behavior of liver, with significant perfusion fraction. By contrast, signal attenuation curve for metastasis is relatively flat at low b values suggesting low perfusion fraction. This observation is in keeping with known pathology of colorectal liver metastases, which are usually hypovascular compared with normal liver parenchyma.
Fig. 8 65-year-old woman with left transplanted kidney with biopsy-proven type 2 posttransplant rejection. Coronal apparent diffusion coefficient (ADC) map was calculated from diffusion-weighted MRI scans acquired using 10 b values (0–900 s/mm2). Dysfunctional transplanted kidney (arrow) returned lower mean ADC value in renal cortex (1.76 × 10–3 mm2/s) compared with normal kidneys (2.03 × 10–3 ± 0.09 × 10–3 mm2/s, not shown). (Courtesy of Thoeny H, University Bern Inselspital, Bern, Switzerland)

Number and Choice of b Values

To enable perfusion-sensitive information to be gained from DW-MRI, imaging using lower b values (e.g., < 100–200 s/mm2) is critical. However, there is as yet no consensus on the number of b values that should be used for clinical measurements and the magnitude of b values that should be applied.
The number of b values used for extracting perfusion-sensitive information at DW-MRI varies between studies and ranges from four to more than 10. Because there are four fitted parameters, a minimum of four b values are needed to characterize biexponential signal attenuation, though this choice is not recommended. A larger number of b values would provide more data support for the estimates and, in particular, would enable parameter uncertainties to be evaluated, which is not possible with four b values. Hence, studies utilizing 10 or more b values (combined with least-squares data fitting using a biexponential model) are not unusual in the published literature.
More sophisticated methods for analysis of multiexponential DW-MRI data analysis have been developed [39, 40] and are widely used in the scientific community. These methods can potentially provide more informative analysis than the biexponential approach because the number of exponential components is determined from the data rather than assumed. However, such analysis will only be successful with very high quality data obtained using a large number of b values (e.g., > 10) and multiple signal averages. Because this translates to very long measurement times, this is unlikely to be acceptable to patients or be clinically feasible.
Fig. 9 Diffusion-weighted MRI data for liver and right kidney in 45-year-old man, fitted using mathematic models. Plots (circles) of mean logarithm of relative signal intensities versus b values are shown. Same data points for each organ can be described using biexponential intravoxel incoherent motion (IVIM)–based model (black line) but may also be described using other mathematic models that make different assumptions about signal attenuation behavior (e.g., stretched exponential, gray line). In liver, data points are better characterized using IVIM-based analysis. However, in kidney, both IVIM and stretched exponential models provide very close descriptions of data.
A practical solution is therefore to perform DW-MRI using six to eight b values with several signal averages and to describe the tissue signal attenuation by mathematic model fitting. Because measurements at higher b values have been shown to be relatively stable and reproducible [41], it is theoretically possible to use fewer high b value samplings (e.g., two to three) and acquire more lower b values data (e.g., four or more) to concentrate acquisition time on the more challenging perfusion sensitive range. The choice of b values could potentially be further individualized to the tissue under evaluation, by taking into account the anticipated pattern of signal attenuation with increasing b values and the tissue ADC values [42].
Using multiple b values also affects the choice of DW-MRI technique: free-breathing or respiratory-triggered acquisitions are usually necessary to accommodate multiple b values, although repeated breath-hold examinations using different pairs of b values have also been successfully applied [33]. A typical clinical imaging protocol used to acquire DW-MRI data for IVIM analysis is shown in Table 2.

Confidence in Measurements at Lower b Values

One of the most important challenges to obtaining good biexponential fitting of DW-MRI data are the ability to accurately measure and characterize the tissue signal attenuation at lower b values. From a practical point of view, some MRI platforms do not currently have the flexibility to allow users to specify b values and only fixed values or increments can be chosen, which limits the magnitude and number of lower b values that can be accommodated within the DW-MRI measurement. Future effort is thus required to ensure that all MRI scanners can accurately deliver small b values over any specified set of imaging parameters, field of view, matrix size, and readout gradient. The consistency of this could be quality assured using phantom studies.
Even assuming that lower b values can be freely and accurately prescribed, signal measurements at low b values (e.g., ≤ 100 s/mm2) are more prone to measurement errors and are highly sensitive to signal-to-noise variations [5, 43], thus posing significant challenges to model fitting. Not surprisingly, it has been found that the reproducibility of ADC values calculated using low b values is poor [41]. There is also a large SD in the estimation of perfusion fraction [35]. For these reasons, voxel-by-voxel analysis may not be appropriate for current IVIM-based evaluation in body DW-MRI, and results generalized over larger regions of interest or across entire target volumes are likely to be more robust. In addition, sophisticated statistic-based data processing could also be performed to both improve fitted results and provide parameter uncertainty estimates [10].
TABLE 2: Typical Scan Parameters Used to Perform Diffusion-Weighted MRI in the Body to Obtain Data for Biexponential Intravoxel Incoherent Motion–Based Analysis

Mathematic Model for Data Fitting

The reader should be aware that the IVIM model represents only one particular description of water diffusion in tissues, which relates the signal attenuation phenomenon observed at low b values to a pseudodiffusion phenomenon, usually ascribed to tissue perfusion. However, as previously discussed, although imaging at low b value is sensitive to tissue vascular perfusion, other secretory physiologic processes in organs may be difficult or impossible to distinguish from vascular perfusion at DW-MRI.
TABLE 3: Summary of Mathematic Models Used for Describing Diffusion-Weighted MRI Data
There are also other mathematic models that are currently being explored as descriptors of DW-MRI data. These include a stretched exponential model [44], a gaussian model [45], and a model that includes diffusion and kurtosis (skewness of distribution) [46]. These have been applied to evaluate DW-MRI studies in the brain [47], as well as in the head and neck area [48]. Many models do not directly relate the signal change to a specific physiologic explanation, such as vascular perfusion and tissue diffusivity, but recognize the nonmonoexponential behavior of the diffusion signal attenuation in tissues. A summary of the different models that have been used to describe DW-MRI data in the body is presented in Table 3.
Using the stretched exponential model, for example, the distributed diffusion coefficient and alpha parameters are derived (Fig. 9). Although the distributed diffusion coefficient may be viewed as reflecting tissue diffusivity, interpreting alpha (also known as the heterogeneity index) is less straightforward because there is no direct physiologic underpinning for this parameter. Thus, even though alpha has been shown to change with treatment in tumors [47], there is currently no clear link between the parameter and a pathophysiologic explanation, and thus its potential to be a true biomarker has yet to be established. Nevertheless, the current evidence suggests that alpha and other parameters may be useful as statistical markers of disease, but until their biologic relevance is understood, it is essential that this distinction is clear and articulated by practitioners.
From the foregoing discussion, it perhaps comes as no surprise that the IVIM model remains the most popular approach to explore non-monoexponential DW-MRI signal attenuation in tissues. Although IVIM has a biologic interpretation for the observations, it may not always provide the most concise description for acquired data. Consequently, the most appropriate compromise between applying the biologically relevant IVIM model that may be a suboptimal descriptor for the data versus using other models that provide a better mathematic fit but have uncertain biologic significance has yet to be established (Fig. 9). Even allowing a wider application of the IVIM model, the best way to derive the diffusion coefficient, pseudodiffusion coefficient, and perfusion fraction from acquired data is still being explored. Because pseudodiffusion coefficient and perfusion fraction parameters are highly correlated, one approach would be to fix the pseudodiffusion coefficient value using a priori information [33].
Fig. 10A 25-year-old healthy woman who underwent axial diffusion-weighted (DW) MRI using navigator-controlled spin-echo echo-planar imaging with 10 b values (0, 25, 50, 75, 100, 150, 250, 500, 750, and 900 s/mm2).
A, Axial DW-MRI of upper abdomen (b = 0 s/mm2) is shown.
Fig. 10B 25-year-old healthy woman who underwent axial diffusion-weighted (DW) MRI using navigator-controlled spin-echo echo-planar imaging with 10 b values (0, 25, 50, 75, 100, 150, 250, 500, 750, and 900 s/mm2).
B, Colorized map shows, on voxel-by-voxel basis, probability that each model best describes signal attenuation data (strong colors indicate high probability, and mixed colors represent model ambiguity; black = monoexponential, red = stretched exponential, blue = intravoxel incoherent motion biexponential, and green = gaussian). Note considerable heterogeneity of signal attenuation pattern in tissues, indicating challenges in generalizing such behavior to region of interest or to whole organ.
The situation is potentially even more complex because of heterogeneous patterns of signal attenuation on a voxelwise basis in normal tissues and tumors. By way of an illustrative example (Figs. 10A and 10B), a voxel within a tissue may exhibit signal attenuation best described by the IVIM model, but adjacent voxels may show signal loss best described by other models. The difficulty in generalizing such behavior to a region of interest is indeed challenging, because choosing to fit all voxels in a region to one model can result in approximation. Clearly, future studies should aim to improve our understanding of the biologic relevance of a range of mathematic models and developing novel algorithms to describe complex DW-MRI tissue behavior [10].

Software for Data Analysis

Currently, most commercial MRI platforms cannot perform complex analysis of DW-MRI data. However, vendors are interested in introducing more sophisticated analytic techniques onto their imaging platforms. IVIM-based analysis is currently possible with the appropriate technical support or through the use of third-party software. Nevertheless, the repeatability and usefulness of the nonmonoexponential model–derived parameters still need to be established and improved in larger prospective studies, so that these may be meaningfully applied.


DW-MRI performed using a range of low and high b values can allow estimates of tissue perfusion and diffusivity to be made by IVIM-based analysis. Clinical studies have shown the potential value of such parameters for disease assessment, particularly in oncology. However, it should be recognized that, although the fast diffusion component suppressed using low b values is sensitive to microcapillary perfusion, other bulk flow phenomena such as tubular flow or glandular secretion can contribute to the signal attenuation and may be difficult to distinguish from perfusion effects.
Radiologists should be aware that there are still significant challenges in implementing more complex quantitative DW-MRI analysis and there are uncertainties associated with such approaches. Robust DW-MRI data analysis beyond simple monoexponential ADC evaluation is not straightforward, requiring high-quality data acquired using multiple b values and confidence in the measurements at low b values. Even when these conditions are met, the choice and execution of the mathematic models remains a complex issue. Future work should be directed at these challenges to enable more sophisticated diffusion quantitative parameters to be developed as biomarkers.


Supported by the Cancer Research UK and EPSRC Cancer Imaging Centre in association with the MRC and Department of HEalth (England) grant C1060/A10334 and National Health Service funding to the NIHR Biomedical Research Centre.


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Information & Authors


Published In

American Journal of Roentgenology
Pages: 1351 - 1361
PubMed: 21606299


Submitted: August 10, 2010
Accepted: December 15, 2010


  1. diffusion
  2. MRI
  3. oncology
  4. perfusion



Dow-Mu Koh
Department of Radiology, Royal Marsden Hospital, Downs Rd, Sutton SM2 5PT, UK.
David J. Collins
Department of Radiology, Royal Marsden Hospital, Downs Rd, Sutton SM2 5PT, UK.
Cancer Research UK-EPSRC Cancer Imaging Centre, Institute of Cancer Research, Sutton, UK.
Matthew R. Orton
Department of Radiology, Royal Marsden Hospital, Downs Rd, Sutton SM2 5PT, UK.
Cancer Research UK-EPSRC Cancer Imaging Centre, Institute of Cancer Research, Sutton, UK.


Address correspondence to D. M. Koh.

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