- Magnetisation of the mouse colon and in vivo mechanical deformation
The essential prerequisite of the experiments was to develop a methodology for introducing magnetic particles into the mesenchymal tissue of the colon at the intracellular level and at concentrations sufficiently high to allow subsequent magnetic manipulation. Furthermore, the mode of delivery of the magnetic material must preserve the tissue from any other stress, which would become competitive with the mechanic constraint generated magnetically. Thus the delivery must be realized through an indirect route of administration. Systemic delivery via intravenous injection performed outside the region of the colon ranks among the best ways provided that the pharmacokinetics of the magnetic particles is optimized to reduce first-pass hepatic clearance and permit observable distribution in the colon tissue. In this respect, we use submicron liposomes sterically stabilized by poly(ethylene glycol) (PEG) coating as bioavailibity-enhancing carrier of the magnetic particles. Indeed, PEGylated magnetic-fluid-loaded liposomes not exceeding 200nm in diameter have reliably been proved to be long-circulating systems as intact vesicle structures without leakage of their inner content, therefore aptly averting dilution of the magnetic material[22-24]. Moreover they have shown to diffuse from the vasculature into the interstitial tissues without loss of structure integrity and at the intracellular level as well[25, 26]. Said otherwise, the containment of the magnetic particles required for magnetic manipulation and beforehand adjusted within the liposomes is totally conserved during their passage through the vascular endothelium towards the surrounding tissues and upon cellular uptake.
The only rare side-effect of injection is a small hematoma that disappeares in two to three days later. Magnet implantation causes only local skin inflammation that is treated with antiseptics and disappeares in three to four days. No effect on intestinal transit is detected nor dysfunction of the colon, which is largely isolated from skin.
- Ultrasound analysis
The SSI technique is based on the ultrafast ultrasound imaging of a shear wave induced by the radiation force of an initial focused ultrasonic beam acting as a remote palpation in tissues (Extended data Fig. 2e). Under the assumption of a i) a local constant density d, ii) a locally incompressible and iii) isotropic elastic medium, the propagation speed vs of the tracked shear wave is directly linked to the Young's modulus E (in kPa) characterizing the local stiffness via the relationship: E = 3 d.vs2.
i) The assumption of constant density of in vivo soft biological tissues is here valid. Indeed, in biological soft tissues, the density is almost constant d~1000 kg/m3 due to the very high water content of soft tissues. However, small density variations exist as shown in extensive past studies[27, 28]. From these studies, the mean density (among connective tissues, muscle, fat, blood cells, plasma, cornea, spinal cord, spleen, testis) is 1052 kg/m3 +/- 47 kg/m3. Thus, the normalized standard deviation in soft tissues is 4.7 %.
ii) Also, due to their high fluid content, many soft biological tissues and gels exhibit nearly incompressible behavior under physiological loading: they are constrained to undergo essentially volume-preserving deformations and motions. Thus, it is commonly accepted in the field of tissue elasticity measurements that the Poisson’s ratio of tissue has a value between 0.49 and 0.4999, meaning that tissue is nearly incompressible[29, 30]. Of course, this incompressible behavior is only ensured provided that the conditions of interest do not allow the water to diffuse into or out of the tissue during the period of interest. This is the case in the Shear Wave Elastography approach, due to the very small (micrometric) displacements induced by the shear wave used to probe local elasticity. Such tiny displacements do not induce water diffusion outside of the organ.
iii) Although the assumption of local isotropy has to be done to derive the Young's modulus from the shear wave speed measurements, it is not possible today to prove in vivo its validity. In particular tissue such as muscles, an elastic anisotropy was even already proved in vivo[31, 32]. However, the in vivo assessment of such anisotropic elasticity was only made possible in particular configurations such as the human biceps because the structural organization and orientation of the muscular fiber bundles in the human biceps muscle is highly identical over a large region of interest.
Other tissues like breast, arteries, liver are today assumed as isotropic in the field of Elastography. Even if a local anisotropy could potentially exist in these tissues, it is postulated here that it should remain quite small. Indeed, it was recently shown that the anisotropy of shear modulus in the in vivo kidney was quite small with a fractional anisotropy of cortex and medulla < 20 % (see figure 3. of ref ) despite a more important tissue organization in the kidney (due to the alignment of the pyramids) than in the other tissues.
Extensive calibration experiments were performed in the past to demonstrate the ability of Shear Wave Elastography to quantify the Young's modulus of tissues. The standard deviation of Young’s modulus quantification was demonstrated to be lower than 5% on calibrated phantoms mimicking biological tissue properties[34, 35]. A small magnet (3 mm in diameter) was axially approached towards the colon by steps of 0.5 mm until completing 3 mm of absolute axial displacement. For each position of the magnet, strain images were calculated by comparing raw frequency ultrasound images acquired at two consecutive steps . Cumulative one-dimensional strain along y-direction was obtained by summing all strain images (Extended data Fig. 2f). Although the magnet could induce some stress in the full volume in the three directions of space, it is here considered that the strain in the lateral (x) and elevational (z) directions remain small compared to the measured axial (y) strain. Under this assumption of a force that is in majority in the axial z-direction, the quantitative stress σ applied by the magnetic field acting on ferrofluids trapped in colon tissues was retrieved by calculating the one-dimensional Hooke’s law . Using Hooke's law, the standard deviation of σ was experimentally estimated and found to be equal to 0.61 kPa. It is in good agreement with a 0.74 kPa standard deviation of σ derived from equation (1) that describes the influence of E and ε uncertainties (respectively 35.0 kPa +/- 3.0 kPa and 4.3 % +/- 2.1 %) on the uncertainty of σ.
During the experiments, data collection was performed no more than 4 seconds after the compression induced by the magnet motion. Such a small delay ensures that one can avoid any creep behaviour. Indeed, the relaxation time for typical human tissues under compression is of the order of several tens to hundreds of seconds .