A Novel Methodology for Mapping Interstitial Fluid Dynamics in Murine Brain Tumors Using DCE-MRI

Abstract

We present a comprehensive methodology for measuring heterogeneous interstitial fluid flow in murine brain tumors using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) coupled with the computational tool, Lymph4D. This four-part protocol encompasses glioma cell preparation, tumor inoculation, MRI imaging protocol, and histological verification using Evans Blue. While conventional DCE-MRI analysis primarily focuses on vascular perfusion, our methods reveal untapped potential to extract crucial information about interstitial fluid dynamics, including directions, velocities, and diffusion coefficients. This methodology extends beyond glioma research, with applicability to conditions routinely imaged with DCE-MRI, thereby offering a versatile tool for investigating interstitial fluid dynamics across a wide range of diseases and conditions. Our methodology holds promise for accelerating discoveries and advancements in biomedical research, ultimately enhancing diagnostic and therapeutic strategies for a wide range of diseases and conditions.

1. Introduction

Glioblastoma is the most common and deadly form of primary brain tumor. Characterized as highly vascularized with diffuse tumor margins, there are approximately 3.23 in 100,000 cases per year with an average survival of 15 months after diagnosis even after rigorous standard of care and adjuvant therapies [1]. In order to study this disease, rodent models of glioblastoma are often used, which have been indicated to resemble human glioblastoma morphologies and molecular phenotypes [2]. By establishing in vivo tumor microenvironments, murine models enable study of specific tumor-stroma interactions and cell behaviors. Murine models of glioma have been fundamental in understanding tumor-genesis, examine drivers of progression, and testing novel therapeutics [3].

Dysfunctional, leaky vasculature within the tumor contributes to elevated interstitial fluid pressure, which drives interstitial fluid from the tumor into the healthy surrounding parenchyma [4]. Interstitial fluid flow is the movement of fluid traveling from the vasculature to the spaces between cells in the extracellular matrix (ECM). Elevated fluid flow across the invading edges of the tumor bulk has been demonstrated in vitro and in vivo to increase glioma invasion in a CXCR4-CXCL12 dependent manner [5, 6]. Thus, methods to measure transport of interstitial fluid in glioma may be used to identify regions of elevated invasion in vivo, ultimately informing clinicians to optimize resection and treatment margins. Initial approaches to measure interstitial fluid velocities utilized invasive techniques, such as fluorescence recovery after photobleaching (FRAP) [7] or micropore diffusion chambers [8]. These methods are either limited to superficial locations or do not elucidate specific velocity magnitudes throughout the tumor and surrounding brain.

Alternatively, non-invasive methods exist to measure interstitial fluid velocities in vivo utilizing dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), a clinically relevant imaging modality used for initial diagnosis [9], treatment planning [10], and tracking therapeutic response [11]. Contrast enhancement has been readily correlated to survival [12], radiation necrosis [13], inflammatory cascades [14], and serves as a marker for interstitial fluid transport within and around tumors. Experimental studies have calculated interstitial fluid velocities through the rate of change of rim contrast enhancement over time [15] or by fitting signal intensity changes to linear equations, such as Darcy’s law, which assumes a linear relationship between velocity and pressure [16]. However, follow up studies have demonstrated that fluid flow is not uniform due to the heterogeneity of vascular leakage [17]. Here we present, in detail, a methodology for measuring this heterogeneous interstitial fluid flow in vivo using DCE-MRI and a previously developed computational tool, Lymph4D. Lymph4D is unique in that it finds the velocity magnitude, direction, and diffusion coefficient that best describe the signal intensity differences over time of DCE-MRI images using biological transport principles, namely diffusion-advection, as a foundation [18]. This methodology is a four-part protocol including glioma cell preparation, tumor inoculation, MRI imaging protocol, and histological verification using Evans Blue [18]. For those conducting in vivo glioma work, using this methodology allows the creation of visualizations and quantitative measures of physiologic flow conditions and disease-associated changes of this flow. This additional in vivo data will enable a better understanding of how interstitial flow plays a role in disease dynamics and treatment.

2. Materials and methods

Measurement of interstitial fluid flow in the brain has been performed on murine GL261 and xenograft human glioma stem cells (GSCs). We have optimized the interstitial fluid flow imaging protocol on a 7T Clinscan system (Bruker, Ettlingen, Germany) and a 9.4T BioSpec 94/20 (Bruker, Ettlingen, Germany) MRI machines. Protocol differences between cell lines and MRI machines are explicitly stated. A complete list of reagents, materials, and suppliers is found in Appendix A.

2.1. Cell preparation for glioma implants (Figure 1A)

Figure 1:

Overview of mouse methods for interstitial fluid measurements in murine glioma. A) Cells are stereotactically injected at concentrations dependent on the cell line. B) Tumor sizes are tracked and confirmed using T2-weighted MR imaging. Typically, DCE is performed on Day 9, thus tumor tracking days are adjusted as needed. C) Interstitial fluid flow measurements require localizer images to orient brain, followed by a T2-weighted image taken on the day of DCE-MRI to visualize nearby cerebral structures. A pre-contrast, T1-weighted image is acquired for three minutes, followed by injection of gadolinium-based (Gd-based) contrast agent. Post-contrast images are acquired for 12 minutes post injection. D) Following imaging, Evans Blue is injected as a surrogate marker for interstitial fluid paths. The following day, brains are harvest and prepared for cyrosectioning.

2.1.1. Cell Culture

GL261-GFP cells were generated as previously described [19]. Cells were maintained for at least three passages before injection with Dulbecco’s Modified Eagle Medium (DMEM) + 10% Fetal bovine serum (ThermoFisher, Gibco). Glioma stem cells (GSCs) G34 cells were derived following the previously described protocol [20]. GSCs were cultured in Neurobasal media (ThermoFisher) with N2 and B27 without vitamin A supplements (ThermoFisher), human recombinant bFGF and EGF (50 ng mL−1, ThermoFisher), Glutamax (ThermoFisher) and Penicillin–Streptomycin (ThermoFisher) in low-adhesion tissue culture flasks (Grenier).

Anticipated total time: 10 days.

2.1.2. Preparing cell concentration for injection

At low volumes and high cellular concentrations, cell volume must be accounted for in final volumetric measurements.

1. Passage and count cells following standard protocol

   1. Example: 5.3E6 total cells

2. Calculate the maximum number of animals that can be injected based on the counted cell number

   1. Example: 100,000 cells/mouse. 5.3E6 cells/100,000cells/mouse = 53 total mice

3. Calculate the volume required to resuspend total number of mice in correct concentration

   1. Example: For GL261 implants, we inject a total of 100,000/5uL (final concentration 20,000 cell/uL). Thus, each mouse requires 5uL.

   2. 53 mice x 5uL = 265uL total volume

   3. Confirm total cells in total volume equates to correct final concentration

      1. 5.3E6/265uL = 20,000 cells/uL

4. Spin down cells for 5 min at 1.1rpm

5. Remove all of supernatant

6. Aliquot 500uL of serum free media into a separate 1.5mL tube

7. Resuspend cells in approximately 1/3 of the total volume using serum free media from 1.5mL tube

   1. Example: 265uL total volume/3 = 88uL

   2. Resuspend cells in 88uL of serum free media

8. Set a 1000uL pipet to the final volume needed (265uL)

9. Carefully pipette cell solution only so that there are no bubbles or empty space in the pipette tip. This step is accounting for volume that cells occupy at low volumes

10. Place pipette tip in 1.5mL tube of serum free media and pipette remaining volume to reach a final volume of 265uL

11. Thoroughly mix cell suspension

Anticipated total time: 1 hour.

2.1.3. Needle check

1. With a UV-sterilized, 10uL Hamilton syringe (Hamilton), pipette 4uL of cell suspension onto a piece of parafilm

2. Add 6uL of serum free media to cells for a final volume of 10uL

3. Add 10uL of AOPI (Revvity) to obtain a final volume of 20uL and dilution ratio of 1:4

4. Mix solution and add to automatic cell counter (Revvity) setting dilution factor to 4

5. Verify cell concentration read out is within 10% of target concentration, which can also be performed using trypan blue and a hemocytometer

   1. Example: Cytometer reads 19.2E6 cells/mL of living cells, which equates to 19,200 cells/uL

   2. The target concentration is 20,000 cells/uL, thus cells are within target range

6. Place cells on ice and clean syringe with by rinse with ethanol, water, and 1X PBS

Anticipated total time: 10 minutes.

2.2. Tumor inoculation (Figure 1A)

All animal experiments are approved under the University of Virginia’s Animal Care and Use Committee (Protocol 4021) and Virginia Tech’s Institutional Animal Care and Use Committee (Protocol 20–196). 8–10 week old male Nonobese diabetic sever combined immunodeficient (NOD SCID) mice were injected with GSCs (G34s). A complete list of equipment, tools, and reagents used for surgical procedures are provided in Appendix A.

Many crucial, life-preserving steps are required during glioma implantation. Thus, the author strongly encourages the use of a checklist both prior to vivarium entrance as well as during the procedure. Regardless of expertise level or qualifications, checklists are a vital aspect of tasks involving multiple steps (25).

2.2.1. At least one day before surgery

1. Autoclave all surgical tools

2. UV-sterilize Hamilton syringe

3. Prepare cells following steps described in section 2.1

2.2.2. Preparing the surgical space

1. Weigh isoflurane scavengers and do not use if weight exceeds limit

2. Clean all surfaces with Rescue or 70% Ethanol

3. Place a heating pad on the bed of the stereotax to maintain body mouse body temperature during the procedure

4. Turn on the bead sterilizer

5. Prepare recovery cage by placing the cage atop a heating pad. Place moistened food in a tray and a hydrogel for easy access.

6. Arrange surgical tools, alcohol wipes, disposable blades, ear punch, Nair, betadine, cotton tipped swabs, ketoprofen, insulin syringes, eye lube and sutures

2.2.3. Preparing the mouse

1. Weigh mouse and calculate appropriate pain and recovery medications. Inject ketoprofen, buprenorphine and Ringers solution as recommended by IACUC

2. Place mouse in incubation chamber with oxygen flow of 1L/min and isoflurane concentration at 2.5–3 for initial anesthesia

3. Place mouse in ear bars of stereotax making sure head of mouse is flat adjusting stereotax as necessary. Lower isoflurane to 1.5.

4. Perform a toe pinch to assure mouse is under anesthesia. Continue to monitor mouse respiration lowering isoflurane levels as needed

5. Remove all metal ear tags, if applicable, using either plastic ear tags or ear punches for inner-cage mouse identification

6. Use Nair to remove hair on top of the skull

7. Sterilize injection site with three iterative betadine and ethanol washes

2.2.4. Glioma injection

1. Perform a toe pinch to confirm the mouse is under anesthesia

2. Make an incision with the scalpel approximately 2cm in length with minimal pressure

3. Use the blade to scrape away the periosteum and use sterile cotton swabs to soak excess blood

4. Locate bregma, which is where the coronal suture meets the midline

5. Connect the stereotactic arm with the drill and sterilized drill bit. Sterilize the drill bit beforehand using the bead sterilizer

6. Move stereotactic arm so that the drill bit is directly above lambda. With this location as the origin point, move to coordinates of interest.

   1. Example: To target the hippocampus, move the drill bit 2mm lateral and 2mm posterior to bregma

7. Slowly drill downwards to drill a dent in the skull. The hole does not need to expose the brain. Test that the surface feels soft, not hard, with a sterile syringe tip

8. Remove the drill from stereotactic arm and replace with the syringe pump attachment

9. Prepare the Hamilton syringe by performing an iterative wash with 70% ethanol, sterile water, and sterile 1X PBS

10. Pipette cells to resuspend loose cell pellet that forms after prolonged sitting

11. Pipette 7uL of cells using the Hamilton syringe. Pipette cells once and eject to verify syringe is appropriately pulling volume. Make sure there are no bubbles within the syringe.

12. Attach syringe to stereotactic injection pump and set injection volume to 5uL and injection rate to 1ul/min

13. Lower the needle to the bottom of the burr hole. When using beveled needles, submerge the bevel within the skull before transitioning to the stereotactic coordinate

14. Lower the syringe 2.5mm and retract 0.5mm. This creates a small pocket for tumor formation

15. Start the injection and wait 3 minutes following injection completion to prevent reflux

16. Dry the surface with a cotton swab and apply a small amount of bone wax to cover the hole

17. Suture incision closed with 2–3 stitches. To perform a stitch that allows proper healing, hold the base of a curved suture needle with forceps and pull suturing thread through the skin on both sides of the incision, leaving a few inches of slack not pulled through. Loop thread twice around a pair of open bent forceps. Grab the few inches of thread from the other side, left as slack, with the forceps and pull the two loops through the thread and tighten. Repeat this process three times to complete one stich.

18. Place mouse into a recovery cage. Mice should take no more than 10 minutes to recover from surgery

Anticipated total time: 45 minutes per mouse.

2.3. Magnetic Resonance Imaging (MRI)

MRI imaging generates many files of data, thus proper management and labeling of files is imperative. Appendix B is a suggested table to track key details surrounding multi-animal MRI experiments. Specifics of the MRI and corresponding attachments can be found under section 2.3 MRI within Appendix A.

2.3.1. T2-weighted tumor tracking (Figure 1B)

Suggested days for GL261 tumor tracking: Post inoculation Day 4, Day 7, Day 9 (and DCE)

1. Place the mouse under anesthesia in induction chamber with oxygen flow at 0.7L/min and isoflurane at a concentration of 3%

2. Once the mouse is unresponsive to toe pinch, turn on MRI anesthesia machine at an oxygen rate of 0.7L/min at isoflurane concentration of 2%

3. Migrate the mouse to the mice cradle in the MRI scanner and secure the head by the tooth bar and ear bars

4. Continue to monitor mouse respiration, adjusting isoflurane levels to acquire a breath rate between 60–120 per minAdjust the slice positioning and the location of the field of view for MRI using the two-dimensional gradient-echo localizer images. Perform a T2-weighted scan with MRI parameters outlined in Table 1

5. Place the Bruker 20 mm receiver-only surface coil above skull and secure with tape

6. Maintain the respiration rate between 60 and 120 breaths per minute during imaging by adjusting the isoflurane concentration. Push the mouse into the scanner using the manual animal transport system.

7. Perform three localizer images to orient the brain in the axial, coronal, and sagittal planes with matrix size 256 x 256, FOV 40 mm x 40mm, in plane resolution 156 x 156 um. Slice thickness 1mm.

Table 1:

Imaging parameters for T2-weighted images

	7T MRI	9.4T MRI
Sequence		RARE
TE/TR	650ms/5500ms	40ms/2600ms
Number of slices	30	16
Slice Thickness	500mm	400mm
Rare Factor		8
Flip angle		90, 180
FOV	20mmx20mm	19.2x19.2mm
Matrix Size	192x192	192x192
Repetitions	1	1
Averages	2	9
Time of Acquisition	5min	9min 21sec
SNR	8.35-12.7	16.4-23.1

Anticipated total time: 15 minutes per mouse

2.3.2. Dynamic-contrast enhanced MRI (DCE-MRI) (Figure 1C)

DCE-MRI leverages the efflux of Gd-based contrast agent from leaky, dysfunctional vasculature within tumors to measure interstitial fluid transport. A balance between temporal sampling, to capture transport kinetics, while maintaining high signal-to-noise must be considered. We obtain an in-plane spatial resolution of 100–104um/pixel, with a temporal resolution of approximately 184–194sec/slice.

2.3.2.1. Tail vein catheterizations

Catheterization is required so that contrast can be injected without the movement of the mouse between pre-contrast and post-contrast weighted images.

2.3.2.1.1. Creating in-house tail vein catheters

Although tail vein catheterization is a standard protocol for murine DCE-MRI, we describe methods to create in-house catheters that are easy to make, characterize, cost-effective, and are easy to use (Fig.2)

Figure 2:

Tail vein catheterization using in-house catheters. The plastic adapter of the needle is cut and exposed to connect tubing (A-B). The other end of the tubing is attached to a needle and syringe for injection (C-D). The mouse is placed on a heating pad with a nose cone (E). The lateral tail vein is identified (yellow arrow) and catheterized (F-G).

1. Use a blade to cut 1mm below a GAUGE needle tip (30Gx1/2, BD) so that the needle is fully exposed (Figure 2A)

2. Scrape excess glue if needed

3. Connect tubing (Intramedic I.D. 0.28mm; O.D 0.61mm) to exposed needle ending (Figure 2B)

4. Measure distance of ear bars of MRI to platform outside of the MRI to estimate the length of tubing required

   1. The approximate length of tubing used is 1 meter, which occupies an approximate dead space volume of 20uL.

5. Place a second needle connected to a syringe in ending of tubing (Figure 2C)

6. Attach a syringe and flush line with sterile water, examining for leakage (Figure 2D)

7. Immediately before placing the tail vein catheter, flush the line with Heparinized sterile saline (20units/mL)

Anticipated total time: 5 minutes.

2.3.2.1.2. Placing tail vein catheter

1. Weigh and record mouse weight

2. Place mouse under anesthesia at an oxygen rate of 0.7L/min and concentration of 3% isoflurane in an induction chamber

3. Once the mouse is anesthetized, move to a nose cone placed on a heating pad (Figure 2E)

4. Confirm the mouse is not responsive by performing a toe pinch.

   1. Continue to monitor mouse respiration, adjusting isoflurane levels to acquire a breath rate between 60–120 per mins

5. Examine both lateral tail veins of the mouse to identify the larger vessel (Figure 2F)

6. Optional: Vessel dilation. Dilate the lateral vein by dipping a cloth (paper towel or similar) into warm water. Never submerge the tail in hot water. Note that the use of hot water is beneficial as the vein becomes larger, however, as the hot water cools, the tail will get colder and constrict the vessel. The author recommends using hot water only if needed.

7. Confirm no air is in the tip of the needle by flushing with heparinized saline

8. The following is written as right-hand dominate: Constrict the vessel at the base of the tail with the middle finger of the left hand, and use the thumb of the left hand to hold the base of the tail static.

9. The vein is easiest to see towards the base of the tail, especially in C57Bl/6 mice. Begin insertion attempts at approximately 1” from the base of the tail. Move up the tail as error occurs. Never begin attempts close to the base of the tail, as Gd-based contrast agent will leak through damaged vessel.

10. Insert the needle at a 30-degree angle to the table, bevel up, parallel to the lateral vein approximately 1” from the base of the tail (Figure 2G)

11. Two methods are used to confirm correct placement. First, gently press on the lateral vein above the needle close to the base of the tail. Blood should enter the tubing.

12. Once blood enters the tubing, quickly flush the line of blood. No resistance should occur upon injection. Resistance indicates poor placement.

13. Repeat step 10 until steps 11 and 12 are accomplished

14. Secure the needle in place using Transpore tape (Amazon). Two pieces are used: One to secure the needle to the tail, the other to secure the tubing to the tail. Place a piece of tape approximately 3” long below the needle and tail. Fold the sides of the tape together, applying pressure to the tape and never pressing down on the needle

15. With a second, 2” piece of thin tape, secure the tubing and the tail together

16. Exchange the heparinized saline syringe used for catheter placement with Gd-based contrast agent 0.2 mL/kg (0.1 mmol/kg, MultiHance, Bracco Diagnostics, Princeton, NJ)

    1. See Appendix B for detailed calculation of injection volume of Gd-based contrast agent

17. Following imaging and injections, flush the tubing with sterile water to avoid accumulation of PBS salt deposits

Anticipated total time: 3–30 minutes per mouse. Expect initial experiments to be delayed due to tail vein catheter placement.

2.3.2.2. Acquisition of DCE-MRI

1. Turn on MRI anesthesia machine at an oxygen rate of 0.7L/min at isoflurane concentration of 2%

2. Carefully migrate mouse from heating pad where tail vein catheter was placed to the mice cradle in the MRI scanner

3. Generously apply eye lube (Neosporin)

4. Secure tail vein catheter in place by taping tubing to MRI scanner. Length of tubing should allow the syringe to be placed at the entrance of the small animal bore when the mouse in pushed fully into the scanner.

5. Place the Bruker 20 mm receiver-only surface coil above skull and secure with tape

6. Maintain mouse temperature during imaging using a water-based heating pad set to 51 °C. Pad is placed below mouse during image acquisition.

7. Maintain the respiration rate between 0 and 120 breaths per minute during imaging by adjusting the isoflurane concentration. Push the mouse into the scanner using the manual animal transport system.

8. Perform three localizer images to orient the brain in the axial, coronal, and sagittal planes with matrix size 256 x 256, FOV 40 mm x 40mm, in plane resolution 156 x 156 um. Slice thickness 1mm.

9. Perform a T2-weighted scan with the same parameters outlined in Table 1

10. Perform a pre-contrast, T1-weighted scan parameters outlined in Table 2

11. Following the pre-contrast weighted image, enter into the MRI room and inject Gd-based contrast agent (~100µL) over approximately 5 seconds through the syringe placed on the outside of scanner

12. Perform four, post-contrast T1-weighted images using the parameters outlined in Table 2

    1. To note, an average percent signal enhancement between baseline and the initial post contrast image of the tumor region should be around 157%

13. Following imaging, remove catheterized mouse from the MRI scanner and place back on original heating pad and isoflurane machine used to place tail vein catheter to recover

14. Replace Gd-based contrast agent syringe with sterile filtered Evans Blue (1.6mL/kg, Sigma) and allow to circulate overnight (~12 hours)

    1. See Appendix B for detailed calculation of injection volume of Evans Blue

Table 2:

Imaging parameters for T1- weighted images

	7T MRI	9.4T MRI
Sequence	FLASH	FLASH
TE/TR	11ms/500ms	3ms/180ms
Number of slices	22	16
Slice Thickness	700mm	400mm
Flip angle	15	70
FOV	20mmx20mm	19.2x19.2mm
Matrix Size	192x192	192x192
Repetitions	1	1
Averages	2	7
Time of Acquisition	3 min 14 sec	3 min 1 sec
SNR	22.2-30.7	24.2-32.2

Anticipated total time: 30 minutes per mouse

2.4. Tissue harvesting, cryosectioning, and microscopy (Figure 1D)

1. Euthanize mice via CO2 asphyxiation followed by cardiac perfusion with 5mL of 1XPBS and 4% formalin (NewComerSupply)

2. Dissect brains and place in 4% formalin overnight for further fixation.

3. Rinse brains with 1X PBS and place in 30% sucrose (Fisher) until complete submersion

4. Place brains in O.C.T compound (Fisher) and section at 12um on a cryostat (Leica)

5. Image for Evans Blue in Cy5 and DAPI (ThermoFisher) at 20X using an Olympus Slide Scanner (Olympus)

Anticipated total time: 30 minutes per mouse

2.5. Interstitial fluid flow analysis (Figure 3)

Figure 3:

Analysis methods to measure interstitial fluid transport using Lymph4D. A) Sample MRI file organization highlighting experiment numbers associated with sequence. Organization emphasizes 2dseq files to maintaining correct scaling between images B) Tumor boundaries and contrast-enhancing parenchyma regions are delineated on a T1-weighted MRI slice (scale bar =1mm) C) Lymph4D user interface D) Interstitial fluid velocity magnitude vector field of tumor (black line) and contrast-enhancing parenchyma (scale bar =1mm) E) Inset of velocity magnitude vector field (scale bar =1mm) Heatmaps generated from lymph4D within the tumor (black line) of flow direction (F), velocity magnitude (G), and diffusion coefficient (H). Velocity magnitudes range from 0-2µm/s while diffusion coefficients range from 0-20µm²/s (scale bars =1mm unless otherwise noted).

Lymph4D is the computational tool that takes the DCE-MRI image sequence acquired in Section 2.3 as input, solves the inverse problem, and provides as output the advection velocity magnitude and direction, and diffusion coefficient at every pixel in the MRI images analyzed. Once DCE-MRI is performed, files are organized and run through Lymph4D to calculate interstitial fluid transport parameters. Each parameter is based on the transport of gadolinium-based contrast agent.

1. Organize all raw data collected during the MRI session into individual mouse folders. Each folder should contain the acquired scans (T2, pre-contrast, post contrast 1–4) (Figure 3A)

   1. MRI machines export images differently. It is important to note whether individual images have been scaled. If so, obtaining scaling factors from raw 2dseq files is imperative to convert back to original pixel brightnesses before automatic scaling

2. Identify the slice of interest to be analyzed using either the T1- or T2-weighted MRI

   1. Criteria may include: largest tumor, proximity to key structures, or minimal needle track damage

3. Stack all temporal slices of desired slice of interest into a three-dimensional matrix

4. To account for movement during imaging session, register all slices within the temporal stack to the T2-weighted image. This way, all images will be registered to each other. If no T2-weighted image is available, register the temporal stack to the pre-contrast image

   1. In either case, MATLAB’s imregister built-in function was used with a rigid transform type to allow only translation and rotation

5. Solve the diffusion-advection equation using Lymph4D software (Figure 3B). We include here a step-by-step demonstration of this analysis. Sample data can be found under the supplemental material folder “Demo Data“

   1. Download Lymph4D through https://github.com/avaccari/Lymph4D, version 1.7.0

   2. Open “Lymph4D-main” folder In MATLAB

   3. Open and run the “viewer” MATLAB script

   4. Select “File under the “Load” window

   5. Select registered temporal stack from Step 4

      1. In “Demo data“ folder, this file is “An13_1_Slice13_TemporalStacks”

   6. Under the drop down menu under “directionality” select “Difs-Adv.”

   7. Check the “Use local nhood” box, with nhood set to 3.

   8. Set the “Temporal slices range” from 2 to 5, as the pre-contrast image is not used for calculation

   9. Do NOT select the “Use sliding time win” or “Smooth before model fit”

   10. Under “Analysis” select “Polygon”

   11. To set the region of analysis, click once on MRI image. A text box will appear that states, “Click on the image to add new vertices. To close the polygon, click on the first vertex. The temporal evolution will be shown in real time as the vertices are moved. To remove the polygon, double click on it.” Click OK.

   12. When crosshairs appear, select points to define boundary. Continue until polygon is closed

       1. Optional: Save boundary for future use by clicking “Save” under “Templates/Poly”

   13. Set (dx, dy): [um/pxl] to the spatial resolution

       1. For the demo data, the spatial resolution was 104.17 um/pxl

   14. Set dt: [s/slice] to the temporal resolution between slices

       1. For the demo data, the temporal resolution was 195 secs

   15. Click “map” within the “Directionality” box

   16. On the heatmap that opens, click “Ovrl ->“ which will save all variables to a three-dimensional MATLAB matrix which includes velocity magnitude and diffusion coefficient

       1. This matrix includes more information than velocity magnitude and diffusion coefficient. The pop-up window of averages highlights velocity magnitude in x is saved in the 11^th dimension, velocity magnitude in y is saved in the 12^th dimension while diffusion coefficient is saved in the 6^th dimension. This window can be used as a reference to extract further information from the ovrl matrix such as directionality.

6. Define the tumor boundary using T1-weighted contrast enhancement and identify pixels of signal enhancement within DCE-MRI imaging period. (Figure 3C). Use these boundaries to export data from the generated ovrl file in Step 5.

   1. Identification of contrast-enhancing pixels is important as interstitial fluid transport measurements are only accurate where Gd-based contrast agent has traveled within the imaging time.

7. Relevant outputs of Lymph4D include interstitial fluid velocity magnitude vector fields (Figure 3D–E), flow directions (Figure 3F), velocity magnitude heatmaps (Figure 3G), and diffusion coefficient heatmaps (Figure 3H)

   1. As noted previously, all metrics are based on the transport of gadolinium-based contrast agent through tissue. As the reported diffusion coefficient is of gadolinium, it is to be expected that Lymph4D calculated rates are slower than reported rates for water, due to the difference in size between water and gadolinium.

2.5.1. Lymph4D software and hardware requirements

Lymph4D was developed in MathWorks MATLAB [21]. The following toolboxes are used by the main package: Image Processing Toolbox (ver. 23.2 or higher), to smooth the image if required by the user; Deep Learning Toolbox (ver. 23.2 or higher), to implement the minmax() function (this can be replaced by two separate calls to the min() and max() functions eliminating the requirement for the toolbox); Optimization Toolbox (ver. 23.2 or higher), to solve the inverse problem (this is required); Parallel Computing Toolbox (ver. 23.2 or higher), to accelerate the solution of the inverse problem (this is not required and, if it is not installed, Lymph4D will use a single thread instead of multiple threads); Mapping Toolbox (ver. 23.2 or higher), to implement the extractfield() function (this can be replaced by code that does not require this toolbox).

Lymph4D will run on any system that can run MATLAB with the above toolboxes installed or after the suggested modifications to remove the dependencies.

2.5.2. Lymph4D computational complexity

The following computational times were evaluated based on the analysis of a full slice from a temporal DCE-MRI stack with the following dimensions: (x, y, z, t) = (192, 192, 22, 5).

The reported times are calculated as averages of 10 analysis runs of 10 different slices from one stack.

MATLAB configuration	Average slice analysis time (s)
Parallel Computing Toolbox enabled (8 threads)	1.87
Parallel Computing Toolbox disables (1 thread)	11.39

The times listed above include the visualization of the results and were obtained on an Apple MacBook Air with an M1 chipset and 16GB of memory).

2.5.3. Lymph4D limitations

One of the main constraints to the use of Lymph4D is the signal-to-noise ratio (SNR) of the contrast agent. Since Lymph4D assumes the presence of advective and/or diffusive processes and solves the inverse problem using the signal produced by the time-varying contrast agent, there are a few situations where this approach might not lead to optimal results. One of the main requirements to obtain meaningful results is that the amplitude of the MRI signal is larger than the MRI measurement noise. In case the two have the same order of magnitude, the results will be driven by the MRI noise. If the analyzed area contains region where this is the case, it would be possible to remove such regions by setting the accepted SNR threshold or, alternatively, look at the behavior over the time of the DCE acquisition of the variance within voxels neighborhood and remove those for which the variance is constant.

2.5.4. Lymph4D availability

Lymph4D is available under GPLv3 through https://github.com/avaccari/Lymph4D.

These methods describe the measurement of interstitial fluid within the tumor and contrast-enhancing parenchyma of implanted murine glioma using Lymph4D.

2.4. Statistics

For multiplanar data reported, six mice were included per group based on power analysis. Graphs are reported as mean ± STD. Paired one-way ANOVAs were used to compare transport metrics across planes. Spearman r correlation analysis was run to test correlation between planes. Statistical analyses were run using GraphPad Prism software where p<0.05 was considered statistically significant.

3. Theory

The DCE-MRI image sequence provides a series of images showing the passage of contrast agent through the tissue imaged, in this case the brain. In these DCE-MRI images, the brightness of each pixel in the image corresponds to the concentration of Gd-based contrast agent within the tissue. By analyzing how this brightness changes over the course of the imaging sequence, properties about the movement of fluid within the tissue can be identified. Here we use a physics-based method where we assume that the movement of Gd-based contrast agent through the tissue is governed by the diffusion-advection equation.

The diffusion-advection equation is a fundamental partial differential equation used to model the transport of a substance through a medium, accounting for both the effects of diffusion and advection. Diffusion refers to the gradual spreading of a substance due to random molecular motion, while advection describes the bulk motion of the substance carried by the flow of a surrounding fluid. Generally, the diffusion-advection equation in solved for the concentration of the particles over time given initial conditions and the known advection and diffusion parameters. Here we must solve the inverse diffusion-advection equation, as we have the concentration of particles over time and are attempting to identify the advection and diffusion parameters.

While Lymph4D solves this equation in two dimensions, as is the dimensionality of the DCE-MRI images provided, here we first consider the direct 1D case to highlight the process of solving the inverse problem. In 1D, the direct process can be modelled by the following differential equation:

$$\frac{\partial c\left(x,t\right)}{\partial t}=\frac{\partial }{\partial x}\left[D\left(x,t\right)\frac{\partial }{\partial x}c\left(x,t\right)\right]-\frac{\partial }{\partial x}\left[v\left(x,t\right)c\left(x,t\right)\right]+S\left(x,t\right)$$ (1)

where, at location $x$ and time $t$:

$c\left(x,t\right)$ is the concentration of gadolinium,

$D\left(x,t\right)$ is the diffusion coefficient,

$v\left(x,t\right)$ is the advection velocity,

$S\left(x,t\right)$ is the source.

Evaluating the derivative in the right side of (1), and using a more compact differentiation notation, we can write:

$$c_t\left(x,t\right)=D\left(x,t\right)c_{xx}\left(x,t\right)-v\left(x,t\right)c_x\left(x,t\right)+c_x\left(x,t\right)D_x\left(x,t\right)-c\left(x,t\right)v_x\left(x,t\right)+S\left(x,t\right)$$ (2)

Given the duration and set-up of the experimental protocol, we can apply the following approximations: $v\left(x,t\right)=v\left(x\right)$ (no dependence on time for the advection velocity), $v_x\left(x,t\right)=0$ (incompressible flow), $D\left(x,t\right)=D\left(x\right)$ (no dependence on time for the diffusion coefficient), $D_x\left(x,t\right)=0$ (locally constant diffusion coefficient), and $S\left(x,t\right)=S\left(x\right)$ (no dependence on time for the source). Under these constraints (2) reduces to:

$$c_t\left(x,t\right)=D\left(x\right)c_{xx}\left(x,t\right)-v\left(x\right)c_x\left(x,t\right)+S\left(x\right)$$ (3)

Under the assumption that the MRI signal is linearly proportional to the concentration of Gd-based contrast agent, we can replace the concentration $c\left(x,t\right)$ with the intensity of the MRI signal. To obtain a numerical solution, we discretize (3). With $i$ representing the discrete location and $n$ the discrete time, we can write the intensity of the MRI signal at location $i$ and time $n$ as $I_i^n$. As eventually we are interested in the inverse problem, and we do not have the stability issues typical of the forward problem, we used the forward-time, central-space (FTCS) finite difference method [22]. In this model, and with the assumption above, we can rewrite the derivative operators as follows:

$$\begin{array}{c}{c}_t\left(x,t\right)\to \frac{I_i^{n+1}-I_i^n}{\text{Δ}t}\\ c_x\left(x,t\right)\to \frac{I_{i+1}^n-I_{i-1}^n}{2\text{Δ}s}\\ c_{xx}\left(x,t\right)\to \frac{I_{i+1}^n-2I_i^n+I_{i-1}^n}{\text{Δ}{s}^2}\end{array}$$ (4)

Where $\text{Δt}$ is the time interval between consecutive acquisitions of the same region of interest, in this method 196 seconds, and $\text{Δ}s$ is the physical spacing between neighboring MRI pixels (in-plane resolution, identical in the $x$ and $y$ directions), in this method 104.17µm.

The discretization results in the following 1D discrete-domain iterative direct model:

$$I_i^{n+1}=I_i^n+\frac{\text{Δ}t}{\text{Δ}{s}^2}{D}_i\left(I_{i+1}^n-2I_i^n+I_{i-1}^n\right)-\frac{\text{Δ}t}{2\text{Δ}s}{v}_i\left(I_{i+1}^n-I_{i-1}^n\right)+\text{Δ}t{S}_i$$ (5)

Where $D_i$, $v_i$, and $S_i$ are the discretized versions of $D\left(x\right)$, $v\left(x\right)$, and $S\left(x\right)$ respectively.

An example of the application of (5), for a total simulation time of $2.5s$ over a length of $1m$, with $D_i=0.01m^2\text{/}s$, $v_i=0.15m\text{/}s$, $\text{Δ}t=0.0004s$, $\text{Δ}s=0.02m$, and $S_i=0$, to a Gaussian initial condition (thicker curve) is illustrated in Figure 4.

Figure 4 -.

Diffusion-advection of a Gaussian initial condition (thicker curve) and a subset of curves of the intensity defined by $D_i=0.01m^2\text{/}s$, $v_i=0.15m\text{/}s$, $\text{Δ}t=0.0004s$, $\text{Δ}s=0.02m$, and $S_i=0$.

Again, while (5) describes the expected temporal evolution of the intensity ${\text{I}}_{\text{i}}^{\text{n}}$ at each discrete location $i$ given the initial condition, and the parameters $D_i$, $v_i$, $S_i$, $\text{Δ}t$, and $\text{Δ}s$, what we are interested in is the inverse problem. In the most general case we would seek to estimate the parameters $D_i$, $v_i$, $S_i$ at each discrete location $i$ from the temporal changes of the MRI signal under the assumption of the convective transport model in (5). For our particular application, we will limit ourselves to an equation representing advection-diffusion without the source term. These solutions have been previously validated through in vitro phantoms which have been previously published using Lymph4D [18].

Given the typical number of temporal acquisitions, this results in an overdetermined system that we solve employing an optimization approach designed to identify the solution that minimizes the $L^2$ norm between the observed and model-predicted changes in the MRI signal intensity between all the pairs of consecutive time points at each discrete location. Under the above assumptions on $D_i$ and $v_i$ the application of (5) to $N$ consecutive MRI images (observation time points) results in a system of $N-1$ equations, and the optimization problems becomes:

$${\mathit{b}}_{i_{opt}}=argmi{n}_{{\mathit{b}}_i}\frac{1}{2}\Vert {\mathit{A}}_i^T\cdot {\mathit{b}}_i-{\mathit{y}}_i{\Vert }_2^2$$ (6)

For the 1D problem, ${\mathit{y}}_i={\left[\left(I_i^2-I_i^1\right),\left(I_i^3-I_i^2\right),\cdots ,\left(I_i^N-I_i^{N-1}\right)\right]}^T$ is the vector given by the differences in MRI signal intensity values between two consecutive temporal frames, the matrix ${\mathit{A}}_i^T={\left[\frac{\text{Δ}t}{\text{Δ}{s}^2}\left(I_{i+1}^n-2I_i^n+I_{i-1}^n\right),-\frac{\text{Δ}t}{2\text{Δ}s}\left(I_{i+1}^n-I_{i-1}^n\right)\right]}_{n=1,2,\dots ,N-1}$ contains discrete derivatives evaluated for each temporal frame, and ${\mathit{b}}_i={\left[D_i,v_i\right]}^T$ represents a vector of the unknown parameters. All these parameters are evaluated independently at every discrete location $i$.

Figure 5 shows an example of the orbits generated by the parameters ${\mathit{A}}_i^T$ (as $\text{x}$ and $\text{y}$ coordinates) and ${\mathit{y}}_i$ (as $\text{z}$ coordinate) for a subset of discrete locations $i$, (different colors). The orbits are generated by evaluating ${\mathit{A}}_i^T$ and ${\mathit{y}}_i$ for consecutive values of $n$ as described above, for the same experiment illustrated in Figure 4. As it can be seen, each orbit is contained in a plane whose coefficient $\left(D,v\right)$ are determined by optimizing (6).

Figure 5 -.

Orbits of parameters for the inverse problem sampled at different discrete locations (left). Same orbits view from a different angle to illustrate the alignment in plane (right).

The solution of (6) is computed separately for each location $i$ after imposing the additional $D\ge 0$ constraint on the diffusion coefficient. This yields the optimal values for each parameter of the transport model at each discrete location $i$ as illustrated in Figure 4.

This optimal control approach is designed to estimate $D_i$, $v_i$, through the observed changes in intensity over time. In this way, its applicability is only valid in regions where intensity changes are discernible. In Figure 4, the thin black line represents the total intensity detected over all time at that discrete location. We observed minimal to no signal intensity below the discrete location 0.2 or above 0.8, leading to unsurprisingly inaccurate estimates for both diffusion and velocity. This highlights the importance of exclusively examining these computed coefficients for pixels where signal enhancement was observed during the DCE-MRI imaging period.

To use this method on DCE-MRI imaging sequences, this problem was naturally extended to higher dimensionality by replacing the discrete differentiation operator with the corresponding higher dimensionality ones. In particular, for the problem describe in this paper, instead of a 1D problem, we looked at coplanar slices within MRI images and their temporal evolution. In this case, with similar assumption for $D_{i,j}$ and ${\mathit{v}}_{i,j}$ (now a 2D vector with components $v_{x_{i,j}}$ and $v_{{\mathit{y}}_{i,j}}$) (5) can be rewritten as:

$$I_{i,j}^{n+1}=I_{i,j}^n+\frac{\text{Δ}t}{\text{Δ}{s}^2}{D}_{i,j}{\nabla }^2{I}_{i,j}^n-\frac{\text{Δ}t}{2\text{Δ}s}{\mathit{v}}_{i,j}\cdot \nabla {\text{I}}_{i,j}^{\text{n}}$$ (7)

Where:

${\nabla }^2$ is the 2D discrete approximation of the Laplace operator using the five-point kernel

$${\nabla }^2\to \left[\begin{array}{ccc}0& 1& 0\\ 1& -4& 1\\ 0& 1& 0\end{array}\right]$$

$\nabla$ is the 1D discrete approximation of the continuous gradient operator obtained using three-point kernels ${\nabla }_x\to \frac{1}{2}\left[\begin{array}{ccc}-1& 0& 1\end{array}\right]$ and ${\nabla }_{\mathit{y}}\to \frac{1}{2}\left[\begin{array}{c}-1\\ 0\\ 1\end{array}\right]$

In this case, the ${\mathit{A}}_{i,j}^T$ and ${\mathit{b}}_{i,j}$ in (6) are modified as follows:

$${\mathit{A}}_{i,j}^T={\left[\frac{\text{Δ}t}{\text{Δ}{s}^2}{({\nabla }^2{I}^n)}_{i,j},-\frac{\text{Δ}t}{2\text{Δ}s}{\left({\nabla }_x{I}^n\right)}_{i,j},-\frac{\text{Δ}t}{2\text{Δ}s}{\left({\nabla }_{\mathit{y}}{I}^n\right)}_{i,j}\right]}_{n=1,2,\dots ,N-1}$$

$${\mathit{b}}_{i,j}={\left[D_{i,j},v_{x_{i,j}},v_{{\mathit{y}}_{i,j}}\right]}^T$$

Where the differential operators are first applied to the entire image at time $n\left(I^n\right)$, and the result is indexed at location $i$, $j$.

The optimization problem (6) was originally solved for location $i$, $j$ independently from the behavior of its neighbors occasionally resulting in very sharp transition within the derived parameters maps. To provide a tighter coupling between the solutions evaluated at neighboring pixels, the optimization process was modified to extend $\mathit{y}$ and $\mathit{A}$ to include values from within a square region around the original voxel under analysis effectively utilizing all temporal values for all voxels within the region as part of the optimization process.

The output of this optimization problem is now the 2D map representing the diffusion coefficient $D_{i,j}$, and the magnitude and direction of the advection velocity $v_{i,j}$, for each pixel in the MRI image sequence.

In summary, Lymph4D serves as a practical computational tool for analyzing DCE-MRI images, providing insights into tissue properties and fluid dynamics. Through its physics-based approach rooted in the diffusion-advection equation, Lymph4D accurately characterizes the movement of Gd-based contrast agent within tissue. Its availability on GitHub makes it easily accessible for research and clinical use. As computational analysis and imaging techniques like DCE-MRI continue to evolve, tools like Lymph4D contribute to our understanding of biological systems, potentially enhancing diagnostic and treatment approaches in any disease where dynamic imaging is available.

4. Results

Measurement of transport metrics across multiple axial slices using Lymph4D

As transport within and around murine gliomas is often assumed to be homogeneous due to spherical tumor growth modeling, we can test this hypothesis using the methodology presented here by investigating transport across all tumor-bearing slices in the axial plane using Lymph4D (Figure 7A). Velocity magnitudes and diffusion coefficients are calculated within identified tumor boundaries and contrast enhancing parenchymal regions (Figure 7 B–J). By examining all slices of the tumor, we see tumor volumes follow standard growth patterns, with the largest slice falling predominately in the middle slice of the tumor volume (Figure 7K). Slice-by-slice analysis reveals velocity magnitudes across mice fall within a similar range across slices, while diffusion coefficients have a larger range across mice, but are more homogeneous within each mouse (Figure 7L–M). Interestingly, mice that have high slice-to-slice velocity magnitude heterogeneity do not have corresponding variability in their diffusion coefficient, as seen in Ms5.

Figure 7: Measurement of transport metrics across multiple axial slices.

A) Schematic of selected axial slices (MRI Slice 16, 13, 11) traversing from superior to inferior. B, E, H) Tumor boundary (cyan) and contrast-enhancing parenchyma (yellow) regions overlaid on a T1-weighted MRI across three distinct axial slices. C, F, I) Heat map of velocity magnitude within the tumor (black line) and contrast-enhancing parenchyma. Velocity magnitudes range from 0-2µm/s. D, G, J) Heat map of diffusion coefficient within the tumor (black line) and contrast enhancing parenchyma. Diffusion coefficients range from 0-20µm²/s (N=6, scale bars =1mm). Superior to inferior tumor volume measurements (K), tumoral velocity magnitudes (L), and tumoral diffusion coefficients (M) across all slices in all mice (enlarged black points highlight representative slices 16, 13, and 11).

Measurement of transport metrics across anatomical planes

Transport metrics can be measured across each plane to capture differences in transport metrics in relation to surrounding anatomical structures (Figure 8A). Velocity magnitudes and diffusion coefficients are calculated within identified tumor boundaries and contrast enhancing parenchymal regions for axial (Figure 8B–D), coronal (Figure 8F–H), and sagittal (Figure 8J–L) planes. By examining the distribution of all tumor-associated pixels in a single mouse (Ms1), we found velocity magnitudes across planes to be similar, with the most variability existing in the coronal plane (Figure 8M). In contrast, diffusion coefficients within a single mouse had much more variability in the axial plane (Figure 8N). Across all mice, mean velocity magnitudes were similar in the axial, coronal, and sagittal planes, with mean velocities of 0.77, 0.85, and 0.88µm/s, respectively. Diffusion coefficients were also similar across axial, coronal, and sagittal planes, with mean diffusion coefficients 11.7, 10.4, and 14.3µm²/s, respectively.

Figure 8: Measurement of transport metrics across anatomical planes.

A, E, I) Schematic representing each analyzed anatomical plane. B, F, J) Tumor boundary (cyan) and contrast-enhancing parenchyma (yellow) regions overlaid on a T1-weighted MRI across the three anatomical planes. C, G, K) Heat map of velocity magnitude within the tumor (black line) and contrast-enhancing parenchyma. Velocity magnitudes range from 0-2µm/s. D, H, L) Heat map of diffusion coefficient within the tumor (black line) and contrast enhancing parenchyma (all scale bars = 1mm). Diffusion coefficients range from 0-20µm²/s (scale bars =1mm). Frequency distribution of velocity magnitude (M) and diffusion coefficient (N) across three planes of Ms1. Scatter plot of average velocity magnitudes (O) and diffusion coefficients (P) across all planes and mice (N=6).

Correlation of interstitial fluid transport between anatomical planes

The data provided by the methodology was used to test whether trends in transport are conserved across all planes of imaging. We performed correlative analysis across velocity magnitude and diffusion coefficients between sagittal and coronal (Figure 9A–B), coronal and axial (Figure 9C–D) and sagittal and axial (Figure 9E–F) planes. Only velocity magnitudes across the sagittal and axial planes were significantly correlated. However, all correlations were of moderate to strong effect size and in the positive direction indicating that generally, there is a consistency in the average values of metrics within the same mouse, regardless of plane of analysis.

Figure 9:

Correlation of interstitial fluid transport between anatomical planes. Correlation of velocity magnitude and diffusion coefficient between sagittal and coronal (A-B), coronal and axial (B-C), and sagittal and axial (C-D) planes.

Evans Blue drainage follows DCE-MRI identified fluid flow within anatomical planes

Previous studies report Evans Blue to be elevated in regions of outward interstitial fluid flow (17). Here we examine Evans Blue paths in the axial (A), coronal (B), and sagittal (C) planes. Histologically, we found tumors have distinct growth patterns within each plane. In the axial plane, tumors congregate close to the hippocampus (Figure 10D). In the coronal plane, tumors show close proximity to the ventricles (Figure 10E), and in the sagittal plane, tumors show ventricular proximity, as it appears both the hippocampus and ventricles restrict tumor growth (Figure 10F).

Figure 10:

Evans Blue as a histological marker of interstitial fluid paths. Schematic of axial (A), coronal (B), and sagittal (C) anatomical planes. Histological slices stained for cell nuclei (DAPI, white) and human glioma stem cells (vimentin, green) across axial (D), coronal (E), and sagittal (F) planes. Histological slices stained for cell nuclei (DAPI, white) and Evans Blue (magenta) across axial (G), coronal (H), and sagittal (I) planes. Velocity magnitude streamlines where dark blue represents the originating point and yellow represents where the streamline terminates within the axial (J), coronal (K), and sagittal (L) planes.

Due to these distinct anatomical features of the tumor in each plane, the Evans blue drainage patterns are quite distinct, and are identified in the fluid flow data provided by the methodology described here. In the axial plane, we see Evans Blue bulk drainage travels posteriorly (Figure 10G). This pattern is recapitulated in the DCE-MRI obtained flow data as there is minimal flow in the anterior direction (Figure 10J). Upon examination of a separate tumor in the coronal plane, we see significant efflux of Evans Blue (Figure 10H). The fluid flow from DCE-MRI of this tumor also shows significant and ubiquitous outward flow from the tumor (Figure 10K). This is in stark contrast to the tumor examined in the sagittal plane, where there is minimal efflux of Evans Blue (Figure 10I). This is reflected in DCE-MRI obtained fluid flow where most transport is directed inward (Figure 10L).

5. Discussion

In the methodology described here, we extend the use of DCE-MRI to measure and characterize interstitial fluid transport in murine brain tumors. As DCE-MRI is already an established method within these models, this imaging modality can be implemented to measure interstitial fluid transport in addition to currently existing outcomes. Currently, the primary purpose of DCE-MRI is to examine vascular perfusion. Our methods highlight that by evaluating flow metrics on the basis of biological transport principles, we are able to quantify interstitial fluid directions, velocities, and diffusion coefficients.

DCE-MRI is a widely used imaging modality currently used to study glioma in mice [23], rats [24], and pigs [25]. Additionally, perturbations of interstitial fluid have been associated with a variety of non-cancerous disease states [26], including Alzheimer’s disease [27], hydrocephalus [28], and traumatic brain injury [29]. Thus, there is a crucial need to be able to accurately measure this fluid flow in vivo not only in the context of glioblastoma. Outside of brain research, DCE-MRI is used in a variety of preclinical cancers, such as cervical [30], pancreatic [31], breast [32], and colon [33] all of which have the capacity to extend existing outcomes to interstitial fluid transport metrics.

Mapping physiologic flow conditions and disease-associated changes will enable a better understanding of how interstitial flow plays a role in underlying biology such as cellular activation, motility, and matrix remodeling. Clinically, the mapping of interstitial fluid transport in healthy and disease-associated conditions will provide further insight into how lesions, whether cancerous or non-cancerous, have impacted the normal flows of the organ. Currently, healthy flow is not well understood, thus alterations to flow in diseased states have no underlying context. It is possible that disease-associated transport simply extenuates healthy baseline flows. By mapping interstitial flow paths in healthy and disease-associated conditions, we may be able to better assess the degree of malignancy and perturbation to normal flow patterns, which may be informative for treatment strategies.

Wide use of the methodology presented here to create reference guides for interstitial fluid flow could be immensely beneficial to the scientific community. Such guides could not only enhance our understanding of the physiological dynamics of interstitial fluid but also play a crucial role in reducing reliance on animal models in research [34]. By providing detailed maps and data on the movement of interstitial fluid within various tissues and organs, these guides could offer essential insights into previously identified underlying various biological processes, such as nutrient exchange, waste removal, and immune cell trafficking.

In conclusion, the addition of interstitial fluid flow mapping can enable investigations capable of targeting hypotheses about transport in various models and in various diseases. We highlight that DCE-MRI in conjunction with Lymph4D can be used to extract critical, yet currently unused information about interstitial fluid flow in these numerous applications. This could facilitate discoveries and advancements in biomedical research, ultimately leading to improved diagnostic and therapeutic strategies for a wide range of diseases and conditions.

Figure 6 -.

Estimated diffusion coefficient (left) and velocity (right) for the problem illustrated in Figure 4. Blue line represents the calculated diffusion and velocity at that location while red represents the true value input into the simulation $D_i=0.01m^2\text{/}s$, $v_i=0.15m\text{/}s$. The thin black line represents total intensity detected over all time at that discrete location i.

Appendix

Appendix A:

Cell Preparation for glioma implants materials and suppliers
Dulbecco’s Modified Eagle Medium	ThermoFisher Catalog No 11965118
Fetal bovine serum	Gibco Lot# 2631850RP
Tissue culture flasks	Genesee 25-207
Neurobasal media	Gibco Catalog No 21103049
N2 supplement	ThermoFisher 17502001
B27 without vitamin A supplement	ThermoFisher Catalog No 12587001
Human recombinant bFGF and EGF	ThermoFisher Catalog No PHG0023
Penicillin- Streptomycin	Millipore Sigma P0781-100mL
Low-adhesion culture flasks	Genesee 25-214
Cell counter	Nexcelom
Cellometer cell counting slides	Revvity CHT4-SD100-014
ViaStain AOPI Staining Solution	Revvity CS2-0106-25mL
Tumor Inoculation
Small scissors	Fine Science Tools Item No. 14058-11
Curved medium point general purpose forceps (2)	Fisher Scientific Catalog No. 16-100-110
Straight hemostats	Fine science tools Item No. 13010-12
Curved hemostats	Fine science tools Item No. 13011-12
Excel Sterile Disposable Scalpels-#10-10/Box	FisherScientific Catalog No. 14-840-00
Isoflurane	Covetrus
Isoflurane scavengers	Vet Equip
Ketoprofen	MWI
Buprenorphine	Ethiqa XR
Lactated Ringers Solution	Henry Schein
Heating pads	Amazon
70% Ethanol	FisherScientific
Bead Sterilizer	FisherScientific
Paralube Vet Ointment	Med-vet animal health
Cotton tipped swabs	Covetrus
Nair	Amazon
Betadine	Fisher Scientific
Alcohol prep pads	Fisher Scientific
Insulin syringes	Fisher
Bone wax	Harvard Apparatus
Ethicon 5-0 monofilament sutures	Fisher Scientific
10ul Hamilton Syringe Model 701 Cemented Needle Special (SN) Syringe. Point Style: 4 (beveled). Gauge: 26s. Needle length, 1in. Angle 12	Hamilton, Part No 80308
Stereotax	Kopf Model 900
Drill holder for sterotax	Kopf
Drill and speed controller (foot pedal)	Fordom K1070
Dremel drill bit (0.5mm diameter)	Fine science tools (19007-05)
Injection pump	Harvard Apparatus
Magnetic Resonance Imaging
9.4T MRI	Bruker
112/86 mm volume coil for RF transmit	Bruker
20mm receive-only surface coil	Bruker
BD Precision Glide Needle 30G x ½ (0.3mmx13mm)	Fisher Scientific
0.9% Sodium Chloride	Fisher Scientific
Heparin Sodium Injection	Covetrus
3M Transpore surgical tape	Amazon
Gd-based contrast agent (MultiHance)	Bracco Diagnostics
Water bath	ThermoFisher
Respiration monitor	Bruker
Isoflurane Induction chamber	Harvard Apparatus
Heating pads	Bruker, K&H Pet Products
Neosporin	Amazon
Evans Blue	Sigma
Tissue Harvesting, cryosectioning, and microscopy
Cryostat	Leica
Formalin	New Comer Supply
Sucrose	Fisher
O.C.T Compound	Fisher
DAPI	ThermoFisher
Slide Scanner	Olympus

Appendix B: Key details to track and injection calculations during MRI experiments

Animal No.	Cage/Ear Punch	Sex	DOB	Group	Date of MRI	Weight (g)	Gd Injection (uL)	Evans Blue injection (uL)	Pre	Post (1)	Post (2)	Post (3)	Post (4)	T2

Sample calculation for Gd-based contrast agent injection:

Gd-based contrast agent dosage: 0.2 mL/kg

First, create working stock of Gd-based contrast by performing a 10-fold dilution of Gd-based contrast with sterile 1X PBS and calculate dead space of tubing.

Injection volume [mL] = mouse weight [kg] * Gd dosage [mL/kg] * dilution factor (10) + dead space volume [mL]

Sample calculation for Evans blue injection:

Evans Blue (EB) dosage: 1.6 mL/kg

First, dissolve 0.01g Evans Blue in 2mL of 1X PBS to create a 0.5% solution and filter sterilize using 0.22um pore filter.

Injection volume [mL] = mouse weight [kg] * EB dosage [mL/kg] * + dead space volume [mL]