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However, such waveforms are often variably sensitive to time\u2010dependent diffusion, causing rotational variance and spectral mismatch. We propose double\u2010isotropic matched encoding (DIME), which enforces isotropy in diffusion\u2010 and restriction\u2010weighting tensors ( and ) and STE\/LTE pairs matched in restriction sensitivity.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>DIME uses trapezoidal pulses, optimized to yield isotropic  and  while generating a spectrally matched LTE. The design ensures concomitant gradient balance and constrains peripheral and cardiac nerve stimulation. Rotational invariance and spectral matching were assessed by simulations in ideal and realistic substrates at 80 and 200\u00a0mT\/m via CV across rotations and STE\/LTE mean diffusivity (MD). DIME was compared to numerically optimized waveforms (NOWs).<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>DIME had the lowest rotational variance and best spectral matching. In cylinders, the median (IQR) CV was 2.0% (1.5%\u20133.3%) and 1.7% (1.2%\u20132.7%) at 80 and 200\u00a0mT\/m, versus 2.5% (1.8%\u20134.1%) and 2.0% (1.4%\u20133.5%) for NOW. In spheres, the maximum MD mismatch (MD) was 0.08 versus  for NOW. In realistic substrates, DIME was superior (MD\u00a0=\u00a0) compared to NOW (). DIME increased encoding duration by 13\u201322\u00a0ms.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>By controlling both  and , DIME improves STE rotational invariance and reduces spectral mismatch under time\u2010dependent diffusion, enabling more reliable tensor\u2010valued encoding tailored to hardware and nerve stimulation constraints.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1002\/mrm.70602","type":"journal-article","created":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T06:17:58Z","timestamp":1790317078000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimized Gradient Waveforms for Tensor\u2010Valued Diffusion MRI Under Time\u2010Dependent Diffusion Using Double\u2010Isotropic Matched Encoding (DIME)"],"prefix":"10.1002","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-1585-4415","authenticated-orcid":false,"given":"Felix","family":"Mortensen","sequence":"first","affiliation":[{"name":"Department of Medical Radiation Physics Lund University  Lund Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-7031-305X","authenticated-orcid":false,"given":"Viktor","family":"Olsson","sequence":"additional","affiliation":[{"name":"Department of Medical Radiation Physics Lund University  Lund Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Athanasios","family":"Grigoriou","sequence":"additional","affiliation":[{"name":"Radiomics Group Vall d'Hebron Institute of Oncology, Vall d'Hebron Barcelona Hospital Campus  Barcelona Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Samo","family":"Lasi\u010d","sequence":"additional","affiliation":[{"name":"Department of Diagnostic Radiology Lund University  Lund Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8540-8424","authenticated-orcid":false,"given":"Malwina","family":"Molendowska","sequence":"additional","affiliation":[{"name":"Department of Medical Radiation Physics Lund University  Lund Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ronnie","family":"Wirestam","sequence":"additional","affiliation":[{"name":"Department of Medical Radiation Physics Lund University  Lund Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Filip","family":"Szczepankiewicz","sequence":"additional","affiliation":[{"name":"Department of Medical Radiation Physics Lund University  Lund Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,9,24]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.68.3555"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/jmri.1076"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1212\/WNL.51.3_Suppl_3.S47"},{"issue":"6","key":"e_1_2_11_5_1","first-page":"581","article-title":"Evaluation of Cancer Therapy Using Diffusion Magnetic Resonance Imaging","volume":"2","author":"Ross B. 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