Cerebral microbleeds have been associated with a variety of neurological and neurodegenerative disorders and are indicative of vascular pathology [1]. Cerebral microbleeds are common in the elderly and patients with Alzheimer’s disease (AD) [2]. Cerebral microbleeds are hemosiderin deposits in the brain [3], and hemosiderin is made up of iron components that are made up of metallic materials [4]. These metallic materials are more susceptible than tissue, resulting in inhomogenities in the local field. As a result, microbleeds can alter the microvascular structure in the elderly and AD brains.

Pathological examinations after biopsy or by extracted samples, which demonstrate the characteristics of alterations of microvascular structures, such as microvessel density or size, are standard in clinics to obtain information about microvessel structures [5]. Furthermore, magnetic resonance imaging (MRI) has been developed to image the cerebral microvascular structure using differences in relaxation rates before and after contrast agent injection, which are referred to as ΔR2 or ΔR2* if acquired with a multi-echo spin-echo (SE) sequence or a multi-echo gradient-echo (GE) sequence, respectively [6]. The contrast agent alters the susceptibility value in the microvascular system and the relaxation time. As a result, it is possible to change the R2 and R2* before and after contrast agent injection. The ΔR2 or ΔR2* modulates signals in the microvascular system [7]. Several microvascular indices have been developed [7] and applied in brain tumors [8], subcortical vascular dementia [9], and the AD model mouse [10] to provide useful quantitative metrics of vascular morphology in vivo. However, no research has been conducted to evaluate the microstructure alteration in the presence of cerebral microbleeds, which cause a local field perturbation in an imaging voxel. We believe that it is important to evaluate relaxation rate differences and microvascular indices in the presence of microbleeds in an imaging voxel. This study aims to examine the microvascular signal in the presence of microbleeds in an imaging voxel using a clinical 3T MRI system with gadolinium (Gd)-chelated contrast agent to other field strengths, such as 1.5T and 7.0T MRI systems. Using the finite perturbation method and Monte Carlo simulations, we simulated alterations in ΔR2* and ΔR2 and calculated microvascular imaging indices against microvessel size and microbleed loads [11].

1. Modeling of vascular structures with and without microbleeds

To model vascular structures, finite cylinders imitating vessels were randomly generated to match the blood volume fraction (BVf) of 2% in a three-dimensional (3D) binary voxel of 256×256×256 µm³ (cell size=1 µm³) without overlapping with each other. The radius of the cylinder was created as 1 to 30 µm while maintaining a volume of 2%.

We modeled the microbleeds as spheres with a 3D binary voxel for modeling vascular structures with microbleeds. We generated the sphere that mimics microbleeds at random so that spheres account for 0.25%–4.63% of the total voxel. The radius of the sphere was determined at random to be 1–100 µm [12]. We combined simulations of microbleeds and vascular structures. A previous study found that microbleed concentrations in the brains of normal elderly control and AD patients were 1.83% and 3.81%, respectively [13-15].

2. Calculation of the microvascular indices

First, we calculated the transverse relaxation rate differences before and after contrast agent injection, ΔR2* and ΔR2 values, which were ΔR2*=R*_2(after)−R*_2(before) and ΔR2=R_2(after)−R_2(before), where ΔR2* was acquired with a multi-echo GE sequence and ΔR2 was acquired with a multi-echo SE sequence.

Second, the following microvascular indices were calculated using ΔR2* and ΔR2 values: mean vessel diameter (mVD) [6], BVf [16], vessel size index (VSI) [7], mean vessel density (Q) [17], and microvessel-weighted imaging (MvWI) [18]. The details were previously published in our paper [13].

3. Simulation conditions with varying microvascular sizes and microbleed loads

First, the simulation was performed with three different types of main magnetic field strengths (B₀) of 1.5T, 3T, and 7T. Second, three different echo times were used for the SE and GR sequences. The SE imaging is 100, 80, and 20 ms. The GE imaging is 60, 40, and 15 ms. Third, the simulation was performed with two types of contrast agents: Gd-chelated contrast agent and superparamagnetic iron oxide nanoparticle (SPION)-based contrast agent. The intravascular and extravascular magnetic susceptibility differences (∆χ_intra-extra) were 1×10^–7 for Gd at about 3.6 mM concentration [19] and 2×10^–7 for SPION [20]. We assumed that the signal from blood was ignored because paramagnetic materials, such as contrast agents or microbleeds, contributed significantly to the signal in a voxel.

We calculated ΔR2* and ΔR2 for various radii in the microvascular system structures-only model and used them to calculate microvascular indices. We used the microbleed model to simulate microvascular structures with a magnetic susceptibility difference between microbleed and tissue (χ_{diff(microbleed-tissue)}) of 2.0×10^–7 [21]. We calculated the microvascular system indices for various vessel radii and two different concentrations of microbleed by simulating ΔR2* and ΔR2. This simulation was performed on an AMD Ryzen 1700 CPU with 32-GB memory and a Matlab program (R2020a; The MathWorks, Inc., Natick, MA, USA).

1. Effect against the microvessel radius

Fig. 1 shows ΔR2* values at TE=40 ms (blue line) and ΔR2 values at TE=80 ms (red line) as the vessel radius increases. With Gd and SPION contrast agents at 1.5T, 3.0T, and 7.0T magnetic field strengths, microbleed concentrations were assumed to be 1.83% and 3.81%, respectively. ΔR2* and ΔR2 increased as B₀ increased from 1.5T to 7.0T for Gd and SPION, but there was no significant difference between the two contrast agents. ΔR2* increased significantly as vessel radius increased at 1.5T and 3T for Gd and SPION contrast agents. However, ΔR2 did not increase significantly as vessel radius increased for all three magnetic field strengths, except at very small radii at 7T, where it decreased with SPION. ΔR2 did not differ significantly between the two microbleed concentrations of 1.83% and 3.81%, but ΔR2* was greater with the 3.81% microbleed concentration than with the 1.83% microbleed concentration. The main magnetic field difference ∆B between the inside and outside of the vessel is proportional to the radius r² of the vessel [11]. Thus, ∆R2/∆R2* varies depending on the radius.

Figure 1. Variations of ΔR2* at the echo time of 40 ms (blue line) and ΔR2 at the echo time of 80 ms (red line) with increasing vessel radius. Microbleed concentrations were assumed to be 1.83% (straight line with ○) and 3.81% (dot line with ◁). We also simulated with gadolinium (Gd) and superparamagnetic iron oxide nanoparticle (SPION) contrast agents with the 1.5T, 3.0T, and 7.0T magnetic field strengths. GE, gradient-echo.

Fig. 2 shows ΔR2* values at the TE=15 ms (blue line) and ΔR2 values at TE=20 ms (red line) as the vessel radius increases. The other simulation conditions were identical to those shown in Fig. 1. The result was also similar to Fig. 1. ΔR2* increased with increasing vessel radius at 1.5T and 3T for Gd and SPION contrast agents. However, ΔR2 did not increase significantly as vessel radius increased for all three magnetic field strengths, except at very small radii at 7T, where it decreased with SPION. ΔR2 did not differ significantly between the two microbleed concentrations of 1.83% and 3.81%, but ΔR2* was greater with the 3.81% microbleed concentration than with the 1.83% microbleed concentration.

Figure 2. Variations of ΔR2* at the echo time of 15 ms (blue line) and ΔR2 at the echo time of 20 ms (red line) with increasing vessel radius. Microbleed concentrations were assumed to be 1.83% (straight line with ○) and 3.81% (dot line with ◁). We also simulated with gadolinium (Gd) and superparamagnetic iron oxide nanoparticle (SPION) contrast agents with the 1.5T, 3.0T, and 7.0T magnetic field strengths. GE, gradient-echo.

Fig. 3 shows ΔR2* values at TE=60 ms (blue line) and ΔR2 values at TE=100 ms (red line) as vessel radius increases. The result is similar to Fig. 1 and 2. ΔR2* increased gradually as the vessel radius increased, but ΔR2 did not. ΔR2 did not differ significantly between the two microbleed concentrations of 1.83% and 3.81%, but ΔR2* was greater with the 3.81% microbleed concentration than with the 1.83% microbleed concentration.

Figure 3. Variations of ΔR2* at the echo time of 60 ms (blue line) and ΔR2 at the echo time of 100 ms (red line) with increasing vessel radius. Microbleed concentrations were assumed to be 1.83% (straight line with ○) and 3.81% (dot line with ◁). We also simulated with gadolinium (Gd) and superparamagnetic iron oxide nanoparticle (SPION) contrast agents with the 1.5T, 3.0T, and 7.0T magnetic field strengths. GE, gradient-echo.

Fig. 4 shows variations of microvascular indices with increasing vessel radius. In the 1.83% and 3.81% microbleed concentrations, mVD increased dramatically as the vessel radius increased at TE=15 ms for GE and TE=20 ms for SE. This increase was more pronounced with short echo times (15 ms for GE and 20 ms for SE) than with long echo times (60 ms for GE and 100 ms for SE). At 3T and 7T magnetic fields, mVD increment with increasing vessel radius did not differ between Gd and SPION contrast agents and was greater at 3T than 7T for Gd and SPION.

Figure 4. Variations of microvascular indices with increasing vessel radius. These simulations were performed with the echo times of 15 and 20 ms for gradient-echo (GE) and spin-echo (SE), respectively (black line), and 60 and 100 ms for GE and SE, respectively (red line). Microbleed concentrations were assumed to be 1.83% (straight line with ○) and 3.81% (dot line with ◁). mVD, mean vessel diameter; BVF, blood volume fraction; VSI, vessel size index; Q, mean vessel density; MvWI, microvessel-weighted imaging.

In the 1.83% and 3.81% microbleed concentrations, BVf increased slightly as the vessel radius increased at TE= 15 ms for GE and TE=20 ms for SE. This marginal increase was more pronounced with short echo times (15 ms for GE and 20 ms for SE) than with long echo times (60 ms for GE and 100 ms for SE). At 3T and 7T magnetic fields, BVf increment with increasing vessel radius was greater with Gd than SPION contrast agents and was greater at 3T than 7T for Gd and SPION.

In the 1.83% and 3.81% microbleed concentrations, VSI increased significantly as the vessel radius increased at TE= 15 ms for GE and TE=20 ms for SE. This increase was also dominant when short echo times (15 ms for GE and 20 ms for SE) were compared with long echo times (60 ms for GE and 100 ms for SE). At 3T and 7T magnetic fields, VSI increment with increasing vessel radius was greater with the Gd contrast agent than the SPION contrast agent and was greater at 3T than 7T for Gd and SPION.

Q decreased as the vessel radius increased, both with short echo times (15 ms for GE and 20 ms for SE) and long echo times (60 ms for GE and 100 ms for SE). Q did not differ significantly between 1.83% and 3.81% microbleed concentrations. Q did not differ between SPION and GD contrast agents, nor did it differ between 3T and 7T magnetic fields. Q decreased dramatically as the vessel radius increased in a 7T magnetic field strength with the SPION contrast agent.

MvWI did not change as the vessel radius increased at 3T magnetic field strength with Gd or SPION contrast agent but decreased as the vessel radius increased at 7T magnetic field strength, regardless of contrast agents. MvWI differed slightly between 1.83% and 3.81% microbleed concentrations and between Gd and SPION contrast agents.

2. Effect against the microbleed loads

Fig. 5 shows variations in ΔR2* and ΔR2 with increasing microbleed loads for 5-, 15-, and 25-µm microvessel sizes with TE=40 ms for GE (blue line) and TE= 80 ms for SE (red line). ΔR2* increased almost linearly as the microbleed load increased for Gd and SPION contrast agents for 3T and 7T magnetic field strengths, with a greater increment with 7T magnetic field strength with SPION contrast agent for all three microvessel sizes. At 3T magnetic field strength, the increase in Gd and SPION was nearly identical. ΔR2* varied slightly between the three microvessel radius sizes of 5, 15, and 25 µm. However, ΔR2 was almost flat for Gd and SPION contrast agents at 3T for all three microvessel sizes. ΔR2 appeared to be comparable among the three microvessel radius sizes of 5, 15, and 25 µm.

Figure 5. Variations of ΔR2* and ΔR2 with increasing microbleed loads for 5-, 15-, and 25-μm microvessel sizes with the echo times of 40 ms for gradient-echo (GE, blue line) and 80 ms for spin-echo (SE, red line). We also simulated with gadolinium (Gd) and superparamagnetic iron oxide nanoparticle (SPION) contrast agents with 3.0T and 7.0T magnetic field strengths.

Fig. 6 shows variations in ΔR2* and ΔR2 as microbleed loads increase for 5-, 15-, and 25-µm microvessel sizes with TE=15 and 60 ms for GE (blue line) and with TE=20 and 100 ms for SE (red line). The result was similar to Fig. 5. ΔR2* increased almost linearly as the microbleed load increased for Gd and SPION contrast agents for 3T and 7T magnetic field strengths, with a greater increment with 7T magnetic field strength with SPION contrast agent for all three microvessel sizes. The increase in Gd and SPION was nearly identical at 3T magnetic field strength. ΔR2* varied slightly between the three microvessel radius sizes of 5, 15, and 25 µm. However, for all three microvessel sizes, ΔR2 was flat for Gd and SPION contrast agents at 3T and 7T. ΔR2 appeared to be comparable among the three microvessel radius sizes of 5, 15, and 25 µm.

Figure 6. Variations of ΔR2* and ΔR2 with increasing microbleed loads for 5-, 15-, and 25-μm microvessel sizes with the echo times of 15 and 60 ms for gradient-echo (GE, blue line) and 20 and 100 ms for spin-echo (SE, red line). We also simulated with gadolinium (Gd) and superparamagnetic iron oxide nanoparticle (SPION) contrast agents with 3.0T and 7.0T magnetic field strengths.

Fig. 7 shows variations of microvascular indices as microbleed loads increase with a microvessel radius size of 5 µm and TE=40 ms for GE and TE=80 ms for SE. mVD increased dramatically as the microbleed load increased at 3T and 7T with the Gd contrast agent but not significantly with the SPION contrast agent at either magnetic field strength. BVf increased linearly as the microbleed load increased at 3T and 7T with the Gd contrast agent but only slightly with the SPION contrast agent for both magnetic field strengths. VSI displayed a similar pattern to mVD. Q did not change significantly as the microbleed load increased at 3T and 7T nor with either contrast agent. MvWI increased slightly with increasing microbleed load at 3T and 7T with Gd contrast agent but dramatically with increasing microbleed load at 3T and 7T with SPION contrast agent.

Figure 7. Variations of microvascular indices with increasing microbleed loads. These simulations were performed with a microvessel size of 5 μm and echo times of 40 and 80 ms for gradient-echo (GE) and spin-echo (SE), respectively. We also simulated with gadolinium (Gd) and superparamagnetic iron oxide nanoparticle (SPION) contrast agents with 3.0T and 7.0T magnetic field strengths. mVD, mean vessel diameter; BVF, blood volume fraction; VSI, vessel size index; Q, mean vessel density; MvWI, microvessel-weighted imaging.

In this study, we conducted a simulation of changes in ΔR2 and ΔR2* and calculated microvascular system indices against changes in microvessel radius or changes in microbleed loads in a brain voxel, representing a brain with a pathological condition, such as AD. We found that ΔR2* increased as vessel radius increased but ΔR2 did not. As the concentration of microbleeds increased, ΔR2* and ΔR2 also increased. mVD and VSI increased as the vessel radius increased. Furthermore, we discovered that ΔR2* increased with increasing microbleed loads but ΔR2 did not. mVD, BVf, VSI, and MvWI increased as microbleed loads increased, but Q did not. In this section, we will discuss our findings.

1. Effect against the microvessel radius

A GE sequence is sensitive to mapping a relatively large microvessel structure as shown in Fig. 1 to 3. High magnetic field strength is usually required to map ΔR2* accurately. Furthermore, mapping alterations in the microvessel structure are highly sensitive to high concentrations of microbleeds, which should increase the susceptibility effect on the GE sequence. We can map the microvessel structure using a Gd-based contrast agent, which is useful for ΔR2* clinical applications. As shown in Fig. 1 to 3 at 3T, the selection of GE TEs is unimportant in mapping the microvessel structure, whereas the selection of SE TEs is important, which is better for long echo time as TEs=80 ms and 100 ms than a short echo time as TE=20 ms.

As shown in Fig. 4, the mVD and VSI indices were sensitive to explaining microvessel size variation. Because mVD and VSI increased as the vessel radius increased with short TEs for GE and SE, the Gd contrast agent at 3T can be used to map mVD and VSI, indicating that the commercially available contrast agent can sensitively map the microstructure changes. Therefore, the mVD and VSI indices can be used to map microvascular structure changes in patients with brain microbleeds. Mapping of Q and MvWI is better at 7T than at 3T magnetic field strengths and with SPION contrast agents rather than Gd contrast agents. Furthermore, it is difficult to map for BVf in any microvascular size under any conditions. The ∆χ_{(intra-extra)} areas for Gd are approximately twice as small as χ_microbleed. Microbleeds have metallic properties due to the presence of Fe and are highly susceptible. When the vessel radius was changed, the microvascular indices changed, suggesting that microvascular maps may be sensitive to mapping different microvascular sizes in a patient.

2. Effect against the microbleed loads

A GE sequence is sensitive to mapping the effect of microbleed loads as shown in Fig. 5 and 6. ΔR2* increased as the microbleed concentration increased. Although a 7T MRI may be better than a 3T MRI, a 3T MRI system with a Gd contrast agent is useful for evaluating the effect of microbleed loads using ΔR2*. The GE echo time is not an important parameter. This result explains why a multi-echo GE sequence before and after Gd contrast agent injection is a good candidate for evaluating microbleed loads in clinical patients because we can calculate ΔR2* change, which is sensitive to mapping the microbleed load, indicating that the ΔR2* change can be used as an imaging marker to diagnose microbleed-related diseases and to evaluate cognitive decline in patients with AD or stroke due to accumulations of microbleeds. The susceptibility difference between amyloid-beta plaque and microbleeds is approximately 100 times greater. If both amyloid-beta plaque and microbleed are present, the plaque’s signal contribution will be greater, and the microbleed’s signal contribution will not be minimal.

As shown in Fig. 7, candidate indices for evaluating the effect of microbleed loads are mVD, BVf, and VSI. Those index values were increased as the microbleed concentration increased. Transverse rate changes were used to calculate mVD, which was calculated as $mVD=\Delta R_2^{*}/\Delta R_2$ [6]. So, mVD increased as ΔR2* increased with increasing microbleed concentration, but ΔR2 did not change significantly. Furthermore, VSI increased because VSI was calculated using VSI=constant1∙(mVD)^3/2 [7]. Furthermore, because BVf was calculated as $\text{BVf}=\text{constant2}\cdot \Delta {\text{R}}_2^{*}$, BVf increased [16]. However, MvWI increased only slightly because MvWI was calculated as $\text{MvWI=}\Delta R_2\times \Delta R_2^{*}$ [18]. Finally, Q can be reduced or nearly unchanged because Q was calculated as $Q=\Delta R_2/{\left(\Delta R_2^{*}\right)}^{2/3}$ [17]. Clinics, as illustrated in Fig. 7, because BVf is proportional to microbleed loads, it can be used to diagnose microbleed loads in patients with AD or stroke. BVf is only dependent on ΔR2*, not ΔR2, implying that we do not spend extra time scanning the SE image before and after contrast agent administration. This is beneficial to patients. In summary, some microvascular indices can sensitively map microbleed loads. A 3T MRI with Gd contrast agent that is commercially available can be used.

3. Limitations

In this study, we did not conduct any experiments with phantoms or animals to support our simulation results. Therefore, some experimental studies should be performed to validate our findings. Furthermore, we assumed that the model of the microvessel structure was a finite cylinder, which does not respond to the realistic brain. The microvessel structure model will have a more realistic vessel capillary network in a future study [22].

The microvascualr indices mVD, BVf, and VSI were sensitive enough to map changes in microvessel sizes and microbleed loads. Because patients with neurodegenerative diseases often have microbleeds in their brains and VSI and mVD were found to increase with increasing microbleeds, microbleeds can alter signals in a voxel in neurodegenerative disease in the human brain at 3T MRI.

This study was supported by the Basic Science Research Program through the National Research Foundation (NRF) of Korea funded by the Ministry of Education (2016R1D1A1B03930720) (G.H.J.) and by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT (No. 2020R1A2C1004749, G.H.J.), Republic of Korea.

The authors have nothing to disclose.

All data generated or analyzed in this study are included in this published article. The data will be available from the corresponding author upon reasonable request.

Conceptualization: Geon-Ho Jahng. Data curation: Geon-Ho Jahng and Chang hyun Yoo. Formal analysis: Geon-Ho Jahng and Chang hyun Yoo. Funding acquisition: Geon-Ho Jahng. Investigation: Geon-Ho Jahng and Chang hyun Yoo. Methodology: Geon-Ho Jahng and Chang hyun Yoo. Project administration: Geon-Ho Jahng and Junghwan Goh. Resources: Geon-Ho Jahng. Software: Geon-Ho Jahng and Chang hyun Yoo. Supervision: Geon-Ho Jahng and Junghwan Goh. Validation: Geon-Ho Jahng, Chang hyun Yoo, and Junghwan Goh. Visualization: Geon-Ho Jahng, Chang hyun Yoo, and Junghwan Goh. Writing–original draft: Geon-Ho Jahng, Chang hyun Yoo, and Junghwan Goh. Writing – review & editing: Geon-Ho Jahng, Chang hyun Yoo, and Junghwan Goh.