Quantitative analysis of tissue perfusion and blood volume was performed using established tracer kinetic models, which have been extensively reviewed in the literature (Ostergaard et al., 1996; Wu et al., 2003). In brief, the mathematical approach to this process starts from the linear relation between the T2^* relaxation time variation [transverse relaxation rate change (R2*(t))], signal intensity change, and the concentration of the contrast agent. These relations go as follows:

C_m(t) is the concentration of contrast agent measured in the tissue, TE is the echo time, S(t) is the signal intensity at a given time, S₀ is the signal intensity before the contrast agent injection, and k is a proportionality constant which, to a first approximation, does not depend on the size and geometry of the vessel, or in the density of the capillary bed.

The tissue response to the arrival of the contrast agent is very sensitive to many factors such as the bolus arrival time and the vascular system, causing the delay and dispersion of the bolus injected. In order to obtain an accurate quantification taking into account these effects, an arterial input function (AIF) is used, measuring the concentration of contrast agent arriving at the vessel. The use of arteries as reference vessels is widely documented in the literature, but it is also possible to use veins [venous output function (VOF)]. The AIF is semi-manually obtained from the DSC-MRI images by delineating and masking the desired region.

In terms of system analysis, the measured concentration curve, C_m(t), the output (response of the tissue to the injection of contrast agent), is related to the ideal concentration curve with no delay or dispersion, k(t), the input, through the convolution of the former with the AIF, the impulse response function, as shown in the following equation:

The ^* represents the convolution and it can be interpreted as the C_AIF(t) modifying the shape of the ideal concentration curve k(t), to give the measured concentration curve C_m(t). Through the inverse operation, known as deconvolution, it is possible to obtain k(t), needed for the following analysis, given that both C_m(t) and C_AIF(t) are known. This ideal concentration curve, k(t), it can be also referred as flow-scaled residue function (Fieselmann et al., 2011).

An optional step before the deconvolution process can be taken by fitting the curve C_AIF(t) to a gamma variate function (Calamante et al., 2000):

where t₀ is the bolus arrival time (BAT) and determines the arrival of the bolus to any given region. This step helps to reduce noise and avoid other effects such as the recirculation of the contrast agent.

The deconvolution step can be computed using different methods. Truncated single value decomposition (TSVD) and Tikhonov regularization are two of these methods, both being appropriate for the resolution of ill-posed problems like this one (Calamante et al., 2000; Fieselmann et al., 2011). In our program, we have implemented both methods of resolution. Then, the quantitative perfusion parameters, CBF, CBV, and MTT, can be obtained from the concentration curves resulting.

CBF and CBV are computed using deconvolution (Fieselmann et al., 2011):

k_H being a constant that groups together all the parameters needed to obtain absolute measurements of the perfusion parameters. (KTKA)(=0.136) is the tissue-to-artery concentration scale factor ratio, H_A(= 0.45) is the assumed hematocrit in large arterial vessels, H_T(= 0.25) is the assumed hematocrit in the capillary bed in the tissue, and ρ_Voi(= 1.04 g/ml) is the apparent brain density. It should be noted that, CBV can be obtained via an alternative non-deconvolution method, relating the contrast agent in the tissue, C_m(t), with the contrast agent in the AIF, C_AIF(t) (Calamante et al., 1999, 2000; Konstas et al., 2009; Fieselmann et al., 2011),

Finally, the MTT values are related to the CBF and CBV through the central volume theorem,

This equation holds true for the volume of interest, and it can be applied independently of the method used to calculate the CBV.

Due to being supported by a reliable mathematical model, CBF, CBV, and MTT are considered the three main perfusion parameters. However, there are other parameters that also provide important information outside those three main quantities. SR and PSR are two of those and they play important roles in the clinical diagnosis of GBM. These variables provide insightful information even when no underpinning mathematical model is present. Contrary to previous hemodynamic parameters, whose calculation requires time-consuming post-processing of the DSC-MRI images, obtaining SR and PSR is much faster and more straightforward. Following (Huhndorf et al., 2016) they can be calculated as,

These two parameters only depend on the signal intensities at different times of the bolus passage through the tissue. S_post is the signal intensity at a time after the bolus arrival, usually 60 s after, S_pre is the signal intensity at baseline, before the bolus arrival to the tissue, and S_min is the minimum in signal, corresponding to the peak of the bolus. Restoring baseline signal intensity corresponds to a value of 100% on the PSR and SR maps.

This study presents an open DSC quantification tool for preclinical studies (Perfusion-Nobel). The implementation was carried out with Python (V 3.8.1), and the following libraries were used: NumPy (V 1.24.1) (Harris et al., 2020), SciPy (V 1.10.0) (Virtanen et al., 2020), Re (V Python 3.9) (Van Rossum, 2020), Matplotlib (V 3.6.2) (Hunter, 2007), Pillow (V 9.4) (Murray et al., 2023), OpenCV (V 4.7.0.68) (Bradski, 2000), Pydicom (V 2.3.1) (Mason, 2011), and IPython (V 8.8.0) (Perez, 2007).

Modular construction has been used to implement the DSC quantification method. As a result, it is possible to easily replace existing stages or add new ones to the quantification workflow (for instance, new pre-processing algorithms or additional fitting models). The following is the processing workflow from the images acquired in the MR system (Figure 1):

All experimental animal procedures were conducted under procedure numbers: 15011/2021/002, 15011/2021/003, 15011/2023/002, and 15011/2021/001 approved by the Animal Care Committee, according to European Union Rules and the Spanish regulation (2010/63/EU and RD53/2013). Animals were kept in a controlled environment at 22 ± 1°C and 60 ± 5% humidity, with 12:12 h light: darkness cycles, and were fed ad libitum with standard diet pellets and tap water. All surgical procedures and MRI studies were conducted under sevoflurane (Abbott Laboratories, IL, USA) anesthesia (3–4%) using a carrier 70:30 gas mixture of N₂O:O₂.

Thirty Sprague-Dawley rats with a weight between 250 and 350 g were used to test the developed program in animal models of different pathologies. Five groups of experiments are shown in Figure 2.

We used healthy Sprague-Dawley (SD) rats with no surgery or treatment as the control healthy group (n = 6).

Healthy rats (n = 4) were anesthetized, and X gr/Kg of mannitol [25% mannitol dissolved in isotonic 0.9% sodium chloride solution (B. Braun Medical SA, Barcelona, Spain)] was then intravenously injected (i.v.) in the lateral tail vein. MRI-DSC measurements were made starting 10 min after the mannitol injection (Duong et al., 2000).

A group of rats (n = 4) were induced cerebral chronic hypoperfusion (CCH) by two-vessel occlusion (2VO), also known as permanent bilateral common carotid artery occlusion, as previously described by Cao et al., 2018. The animals were anesthetized, and the right common carotid artery was isolated and ligated with a 4-0, not absorbent suture through a ventral median incision in the cervical area. After 1 week, the left common carotid artery was ligated following the same protocol. MRI-DSC measurements were made 3 weeks after the surgery.

GBM was induced in a group of rats (n = 7) by the implementation of the F98 cell line (Bulin et al., 2022). After anesthesia, animals were then mounted onto a stereotaxic frame. A midline incision was performed, and a burr hole was punctured using a 16-gauge needle. The burr hole coordinates were, using the bregma as a reference point, 1 mm anterior and 3 mm lateral to the right. Then 1 × 10⁵ cells suspended in a volume of 5 μl of non-supplemented DMEM were injected into the brain with a 26-gauge needle at a depth of 6 mm from the surface of the skull (injection rate of 0.2 ul/min). MRI-DSC measurements were evaluated 10 and 20 days after the surgery.

Regarding the stroke group (n = 9), transient focal ischemia was induced in rats by transient middle cerebral artery occlusion (MCAo) following surgical procedures previously described in Vieites-Prado et al. (2016). In brief, using 6-0 silk sutures, the right external carotid artery as well as the pterygopalatine artery of the internal carotid was ligated. A silicon rubber-coated size 4–0 monofilament (diameter 0.19 mm, length 23 mm; diameter with coating 0.37 ± 0.02 mm; coating length 3–4 mm) (Doccol Corporation, Sharon, MA) was inserted into the stump of the right common carotid artery and advanced into the internal carotid artery to 20 mm from the bifurcation to occlude the origin of the MCA. A laser Doppler flow probe (tip diameter 1 mm) attached to a PeriFlux 5000 Laser Doppler Flowmeter (Perimed AB, Stockholm, Sweden) was placed over the thinned skull in the MCA territory (4 mm lateral to bregma) to obtain a continuous measure of relative cerebral blood flow during the experiment Diffusion-weighted imaging (DWI), magnetic resonance angiography (MRA), and MRI-DSC measurements were made starting 20–30 min after the onset of MCA occlusion. The suture was removed 75 min after the occlusion.

All studies were conducted on a Bruker BioSpec 9.4 T MR scanner (horizontal bore magnet with 12 cm wide Bruker BioSpin) equipped with actively shielded gradients (440 mT m⁻¹). Animals were imaged with a combination of a linear birdcage resonator (7 cm in diameter) for signal transmission and a 2 × 2 surface coil array for signal detection, positioned over the head of the animal, which was fixed with a teeth bar, earplugs, and adhesive tape. Animals were physiologically monitored throughout the MR imaging experiments. Transmission and reception coils were actively decoupled from each other.

DSC-MR images were acquired using ultra-fast gradient-echo methods (EPI-T2^*) with the following parameters: 6.2 ms of echo time (ET), 1 s of repetition time (RT), number of repetitions (NRs) = 180, 1 average, 50 kHz spectral bandwidth (SW), flip angle (FA) of 90°, and 5 slices of 1.5 mm. Field of view (FOV) of 2.2 × 2.2 cm², and a matrix size of 128 × 128, giving an in-plane resolution of 172 μm/pixel, implemented without fat suppression. The contrast agent was quickly administrated as a bolus 20 s after starting acquisition [intravenous (i.v.) bolus injection of gadolinium contrast agent (0.3 mmol/kg)]. The total DSC scan acquisition time was 3 min.

Brain volumetry study was also evaluated from T2-wi using a rapid acquisition with relaxation enhancement (RARE) sequence (axial and coronal orientations): with an ET = 11 ms, RT = 2.5 s, Rare Factor (RF) = 8, FA = 180°, NA = 3, SW = 37 KHz, 14 slices of 1 mm, 25.6 × 25.6 mm² FOV, and a matrix size of 256 × 256 (isotropic in-plane resolution of 100 μm²/pixel).

To evaluate the status of MCAo in a non-invasive manner during occlusion in the stroke animal model, time-of-flight magnetic resonance angiography (TOF-MRA) was performed. The TOF-MRA scan was performed with a 3D FLASH sequence with TE = 2.5 ms, TR = 15 ms, FA = 20°, NA = 2, SW = 98 KHz, 1 slice of 14 mm, FOV = 30.72 × 30.72 × 14 mm³, and a matrix size of 256 × 256 × 58 (resolution of 120 × 120 × 241 μm³/pixel). Moreover, apparent diffusion coefficient (ADC) maps were obtained from diffusion-weighted image (DWI) using a spin echo-planar imaging sequence (DTI-EPI): ET = 26.91 ms; RT = 4 s; SW = 200 KHz; seven b-values of 0, 300, 600, 900, 1,200, 1,600, and 2,000 s/mm²; FA = 90°; NA = 4; 14 consecutive slices of 1 mm; FOV = 24 × 16 mm², and a matrix size of 96 × 64 (isotropic in-plane resolution of 250 μm²/pixel).

We used region of interest (ROI) analysis to quantify the absolute maps CBV, CBF, MTT, and SR, PSR obtained in our new program. Next, through ImageJ software (Rasband W, NIH, Bethesda, MD, USA), we placed a circular ROI over each hemisphere cortex at the plane and a whole-brain ROI. For the ischemic stroke animal model, ROIs were situated in the core, penumbra region of the ipsilateral (IL) hemisphere, and cortex of the contralateral (CL) hemisphere. In the last group, the peripheral tumor area (tumor rim) and core ROIs were placed. Adjacent slices were measured to permit discrimination between intra- and inter-subject variance. To test whether the two slices can be considered samples of the same mean, a paired t-test was performed with the values from the two slices (p < 0.05). We generated Bland–Altman (BA) plots to compare our results (CBV, CBF, and MTT) with the literature data, where the horizontal axis represents the mean value [(our data + literature data)/2], and the vertical axis represents the difference; this method was used to compare two different measurement techniques (Giavarina, 2015). Data are presented as the mean ± 1.96^*SD.

Changes in hemodynamic parameters were compared using left, right, and whole-brain ROIs between healthy animals and animals subjected to chronic hypoperfusion or temporal BBB dysfunction (Figure 4A). For all regions, CBF decreases by ~49–35.6% in both models compared to healthy animals. The same is for the CBV, although the reduction is only 32–13.7%, respectively. Mean MTT increased in all ROIs by ~40.7%, and SR or PSR shows a lower capacity to discriminate changes in these models.

Figure 4B illustrates the hemodynamic parameter evolution in a stroke animal model during MCAo. As can be seen, we found a CBF reduction of 36.4% and 77.2% in the penumbra and core regions in accordance with previous studies (Robertson et al., 2011; Reid et al., 2012; Cipolla et al., 2017), respectively [75.1 ± 21.1 vs. 47.8 ± 13.4 vs. 17.16 ± 9.0 ml/(100g^*min)]. Moreover, CBF decreases by ~22.5 and 47.5% in both regions (12.0 ± 5.6 vs. 9.3 ± 4.2 vs. 6.3 ± 3.2 ml/100 g). Due to the absence of vascularization in these regions, the MTT values show an increase of 26.1 and 111.5% in the penumbra and core (9.6 ± 2.7 vs. 12.1 ± 3.9 vs. 20.3 ± 6.9 s). We found that SR and PSR have also the capacity to accurately differentiate the core from the other brain regions: CL (−3.3 ± 1.1%, 64.3 ± 11.1%), penumbra region (−2.3 ± 2.6%, 81.7 ± 18.1%), and lesion core (1.1 ± 3.8%, 113.5 ± 46.1%).

Parameters of tumor perfusion were validated in a preclinical GBM model at 10 and 20 days after the surgery known to produce different levels of vascularization (Figure 4C). We can appreciate that it is possible to accurately identify core and peripheral tumor regions at both time points. The CBF values in the tumor core were reduced at 10 and 20 days to 74.5 and 48.8%, respectively. At 10 days, animals showed increased CBV and MTT values in the core compared to the tumor rim (3.4 ± 2.1 vs. 1.3 ± 1.2 ml/100 g, and 16.3 ± 8.5 vs. 2.2 ± 0.9 s). However, at 20 days of CBV and MTT, a change in behavior is detected (1.2 ± 0.4 vs. 4.1 ± 3 ml/100 g, and 0.67 ± 0.1 vs. 1 ± 0.43 s). These results may reflect the heterogeneous structure of the tumor regions, and the time evolution probably also contributes to this heterogeneity. As previously described, SR and PSR maps provided a GBM spatial distribution and add valuable diagnostic information. At 20 days, we found SR core 59.1 ± 6.7% vs. tumor rim 20.4 ± 3.4%, and PSR core −249.4 ± 181.1% vs. tumor rim 253.5 ± 27.3%.

Figure 5 shows the BA plots for our data and healthy SD rats, corresponding to the left and right cortex. We observed low mean differences for CBV (2.5 ml/100 g) and MTT (2.7 s) variables and large differences for CBF [49.9 ml/(100 g^*min)]. Regarding the ischemic stroke model, we compared the lesion core and CL cortex, for our results and literature data (Figure 6). The BA plot highlighted low mean values of bias for CBF [2.6 ml/(100 g^*min)], CBV (1.17 ml/100 g), and MTT (9.7 s) for the core lesion. We found the same for CBV (2.8 ml/100 g) and MTT (3 s) in the CL cortex, but not for CBF [65.2 ml/(100 g^*min)]. Regional BA analysis of the tumor core and CL cortex is illustrated in Figure 7. We observed low mean discrepancies for CBV (−3.45 and 6.63 ml/100 g) and MTT (−4.71 and 0.73 s) variables, and large discrepancies for CBF [30.9 and 32.2 ml/(100 g^*min)] both in the tumor core and in the CL cortex.