4D ultrasound is a dynamic volume that is acquired utilizing a linearly translating motor attached to an ultrasound transducer, allowing the acquisition of sequential cardiac- and respiratory-gated video loops across a region of interest. This method is useful for visualizing complex structures such as the heart, where hypertrophy or infarction causes unique geometries, or aortic aneurysms, where asymmetric vessel expansion and dissection often occur in tortuous vessels. Additionally, 4D data can provide high-resolution spatial and temporal information, which is also important for cardiovascular imaging.

The DDE method applied to 4D ultrasound data is superior to other methods because it uses non-rigid image registration. Deformation gradient tensors are traditionally estimated from displacement fields following digital volume correlation. In contrast, the DDE method intrinsically estimates deformation gradient tensors during volume registration by optimizing a warping function that is carefully chosen to be directly analogous to the deformation tensor. The warping function depends on both spatial position and the warping parameter (p):

(2)

The first three elements of this function represent the deformation gradient tensor, F, allowing the calculation of deformation to be directly incorporated into the warping function. This warping method has been proven to increase the accuracy and precision of strain estimation when compared to similar previous techniques because it allows for large or localized deformations commonly found in soft tissues.

Using the procedure described above, 4D ultrasound of an angiotensin II-induced suprarenal dissecting abdominal aortic aneurysm (AAA) of a mouse was acquired. Multiple short-axis EKV video loops were acquired along the aorta and combined to create 4D data, as shown in Figure 1. This data was then converted into a MAT file using a custom code, which was then analyzed in a 3D strain calculation code using a warping function. After optimizing the parameters of the code for a specific data set, a representative, long-axis view with corresponding strain values was produced as well as a 3D slice visualization plot with an overlaid strain color map (Figure 2). This DDE technique and strain data highlight the heterogeneous spatial variations in strain, particularly when a thrombus is present. These results can then be correlated with vessel structure to determine the relationship between in vivo deformation and aneurysm composition.

Figure 1: ECG-gated kilohertz visualization (EKV) loops of the aorta are acquired from manually inputted starting and ending locations, following a step size of 0.2 mm.

Figure 2: 4D high frequency ultrasound data of a murine dissecting abdominal aortic aneurysm represented at systole (A) with principal strain fields estimated and overlaid (B) (Scalebar = 5 mm). Long- and short-axis views representing both aneurysmal and healthy regions corresponding principal strain over one cardiac cycle (systole: t= 0.4) (C, D). These data show relatively high strain levels in healthy regions and reduced strain values within the dissecting aneurysm.

Localized in vivo mechanical characterization is an important part of understanding the growth and remodeling of biological tissues. Compared to existing approaches, the strain quantification procedure described here uses an improved method of accurately calculating 3D strain through optimally warping the undeformed image before cross-correlation. This method does not use any material assumptions in determining strains within tissue volumes. Unfortunately, the strain estimation is reliable only down to a kernel size of 15x15x15 voxels when using ultrasound data, suggesting that this DDE approach may not detect subtle features within a strain field. Despite this limitation, it remains an important tool for investigating mechanical responses, diagnosing pathology, and improving disease models.

Many areas of research beyond aortic aneurysms can benefit from this strain measurement tool. Cardiac strain can also be easily quantified using this method. Because the myocardium undergoes 3D deformation during the cardiac cycle, quantifying strain in three dimensions is integral to reliably characterizing the dynamics of this tissue. Reliable strain data is especially important when tracking disease progression in animal models.

3D strain analysis can also be applied to intestinal ultrasound imaging. Mechanical characterization of intestinal tissue is most commonly conducted in vitro. However, this is not always a true representation of the actual behavior of the intestines in vivo because of effects from surrounding structures. As an example of clinically translating this approach, calculating the strain from images of intestinal fibrosis due to abnormal luminal pressure could provide early detection of problematic areas that require surgical intervention.

Beyond the larger scale applications, this method can also be applied to the cellular level by using higher resolution imaging techniques, such as confocal microscopy. Characterizing the extracellular matrix is important for understanding how cells communicate. Much research has been conducted on the biochemical characterization, but understanding how communication can be conducted through mechanical responses requires an understanding of deformation and strain. Bulk strain is not beneficial because there is no way to determine the origin of the deformation change. Applying a high-resolution DDE approach could directly reveal how the extracellular matrix responds to mechanical changes.

ACKNOWLEDGEMENTS

We would like to acknowledge John Boyle, Guy Genin, and Stavros Thomopoulos for the contribution of the DDE custom Matlab code capable of directly estimating Lagrange-Green strain.