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MICCAI 2026 Submission

A Novel Tri-Modal Viral–Ultrasound Gene-Delivery Therapy Protocol for Lysosomal Neurodegeneration via Stochastic Model Optimization with Uncertainty Quantification and Generalizability

Kartheek Nekkanti1, Chandrajit Bajaj2

1Pearson Ranch Middle School, Round Rock Independent School District, Austin, TX 78717 2Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712

Paper | Full Version (30 pp.)

GM2 substrate dynamics across all treatment arms. N = 1,000 Milstein SDE realizations, 365-day horizon. Blue = Tri-Modal (SP2+AAV+FUS); red = Natural History. Tri-modal reaches 180 nmol/g vs. 1,325 nmol/g untreated. GM2 substrate dynamics: N = 1,000 runs. Blue = Tri-Modal; red = Natural History. Tri-modal reaches 180 nmol/g vs. 1,325 untreated.

Abstract

Lysosomal storage disorders (LSDs) are a class of more than 70 inherited metabolic diseases caused by deficient lysosomal enzyme activity, producing substrate accumulation, neuroinflammation, and progressive neuronal death. We focus on GM2 gangliosidosis (Tay-Sachs/Sandhoff), for which fewer than 100 new cases occur annually in the US and Europe combined, making prospective randomized trials both statistically underpowered and ethically untenable.

We present a 16-dimensional Itô stochastic differential equation (SDE) system, with generic form \(dX_i = f_i(X,t)\,dt + \sigma_i X_i\,dW_i\), calibrated from 15 public genomic and proteomic datasets and integrated via the Milstein scheme (\(N = 1{,}000\) realizations, \(\Delta t = 0.1\) d). Tri-modal therapy — integrating AAV-T4 gene delivery, SP2 substrate reduction therapy, and focused ultrasound (FUS) blood–brain barrier modulation — reduces mean brain GM2 burden from 890 nmol/g to \(180 \pm 35\) nmol/g (75.7%; 95% CI [74.2%, 77.2%]) versus 30–35% for SRT monotherapy and 40–50% for AAV monotherapy. Neuroinflammation suppression reaches 95–97% and Bayley-III motor/cognitive advantages are +49/+21 points at day 365.

Global Sobol analysis identifies BBB entry kinetics (\(k_{T4,\text{entry}}\), \(S_T = 0.909\)) as the singular rate-limiting parameter, exceeding enzymatic degradation (\(V_{\max,B}\)) by 13.0-fold, establishing GM2 gangliosidosis as delivery-limited rather than enzyme-limited. Six-region neuroanatomical validation confirms uniform 80–89% GM2 reduction (CV = 3.7%). Modular substitution across nine LSDs reproduces consistent BBB-bottleneck dominance (\(S_T = 0.82\text{–}0.91\)) with ≈90% parameter reuse, establishing computational stochastic optimization as a translational strategy for ultra-rare diseases.

Why Monotherapy Is Insufficient: A Formal Bottleneck Analysis

Three mechanistically non-redundant rate-limiting steps must be addressed concurrently for meaningful substrate clearance. No mono- or bi-modal therapy closes all three simultaneously:

Bottleneck 1 · Synthesis

Continuous GM2 Synthesis

Substrate synthesis at \(g_{\text{synth}} = 3\) nmol/g/d continuously replenishes the lysosomal burden even with fully restored enzyme. SRT achieves only ≈30–35% reduction without addressing delivery or enzyme absence.

Fixed by SP2 / SRT
Bottleneck 2 · Enzyme

Absent β-Hexosaminidase

HEXA/HEXB mutations abolish lysosomal enzyme activity. AAV delivers the corrective gene but achieves <1% CNS penetration intravenously; with GM2 \(\gg K_{m,B}\), clearance saturates at \(V_{\max}\).

Fixed by AAV-T4
Bottleneck 3 · BBB

Blood–Brain Barrier

The dominant bottleneck (\(S_T = 0.909\)). FUS with microbubbles enhances CNS AAV delivery 10–100× via acoustic cavitation (\(\alpha_{\text{FUS}} = 50\)), timed to days 1–7 before anti-capsid IgG peaks.

Fixed by FUS

Only the tri-modal combination (SRT + AAV + FUS) simultaneously reduces synthesis, restores enzyme, and amplifies transport — yielding synergy index 1.47 and 95–97% neuroinflammation suppression by disrupting the microglial feedback loop (GM2 \(> G_{th} = 500\) nmol/g).

GM2 Substrate Dynamics — All Treatment Arms

Figure 1: GM2 substrate dynamics across all treatment arms

Figure 1. Brain GM2 burden (nmol g⁻¹) over 365 days across all treatment arms, \(N = 1{,}000\) Milstein realizations. Shaded bands: 5th–95th percentile. Tri-modal (blue) achieves 75.7% substrate reduction (890 → 180 nmol/g) versus continuous rise in natural history (890 → 1,325 nmol/g). The strict NH < mono < bi < tri hierarchy is preserved at every time step.

Neuroinflammation & Bayley-III Clinical Outcomes

Figure 2: Neuroinflammation and Bayley-III outcomes

Figure 2. (A) Neuroinflammation index \(I(t)\): tri-modal (blue) suppresses inflammation to physiological levels (\(I \approx 0.05\)) by day 250; untreated (red) plateaus at \(I \approx 0.5\). (B) Bayley-III cognitive trajectories across all arms (\(N = 1{,}000\)). (C) Terminal motor/cognitive Bayley-III scores at day 365 — tri-modal achieves \(\Delta = -8.6\) vs. natural history \(\Delta = -44.8\).

16-Dimensional Itô SDE System

Five coupled subsystems evolve as Itô SDEs with multiplicative noise \(\sigma_i X_i\,dW_i\) (CV ≈ 10%), integrated via the Milstein scheme (\(\Delta t = 0.1\) d, \(N = 1{,}000\) realizations). Multiplicative noise is mechanistically justified: inter-individual CV is approximately constant across concentration ranges, the empirical signature of geometric rather than additive dispersion.

States 1–3: drug absorption, plasma distribution, brain penetration. Hill inhibition \(\eta_{SP}(B) = \mathrm{IC}_{50}^n / (\mathrm{IC}_{50}^n + B^n)\), \(\mathrm{IC}_{50} = 25\) µM, \(n = 2.0\).

\[\begin{aligned} dA_{\text{gut}} &= \bigl[-k_a A_{\text{gut}} + \text{dose}(t)\bigr]\,dt + \sigma_{\text{gut}}\,dW_1 \\ dP &= \bigl[F k_a A_{\text{gut}} - (k_{\text{el}} + k_{p2b})P + k_{b2p}B\bigr]\,dt + \sigma_p\,dW_2 \\ dB &= \bigl[k_{p2b}P - k_{\text{elim}}B\bigr]\,dt + \sigma_B\,dW_3 \end{aligned}\]

States 4–6: systemic AAV-T4, CNS entry with saturation, transgene expression. FUS modulation: \(k_{\text{entry}}^{\text{eff}} = k_{T4,\text{entry},0}(1 + \alpha_{\text{FUS}}\,u(t))(1 - 0.3\,Ab)\), \(\alpha_{\text{FUS}} \in [10,100]\).

\[\begin{aligned} dT_{4,\text{sys}} &= \bigl[-(k_{\text{clear}} + k_{\text{entry}}^{\text{eff}})T_{4,\text{sys}}\bigr]\,dt + \sigma\,dW_4 \\ dT_{4,\text{entry}} &= \bigl[k_{\text{entry}}^{\text{eff}} T_{4,\text{sys}}(1 - T_{4,\text{entry}}) - 0.001\,T_{4,\text{entry}}\bigr]\,dt + \sigma\,dW_5 \\ dE_{\text{expr}} &= \bigl[k_{\text{load}}\,T_{4,\text{entry}}(\text{cap} - E_{\text{expr}}) - k_{\text{decay}}\,E_{\text{expr}}\bigr]\,dt + \sigma\,dW_6 \end{aligned}\]

States 7–8: GM2 substrate and enzymatic clearance via Michaelis–Menten kinetics. At baseline \(G_B = 890\) nmol/g \(\gg K_{m,B} = 300\) nmol/g, the enzyme operates at 74.8% of \(V_{\max,B}\) — firmly in the saturating regime, confirming delivery as the rate limiter.

\[\begin{aligned} dG_B &= \left[g_{\text{synth}}(1-\eta_{SP}) - \frac{V_{\max,B}\,E_{\text{expr}}\,G_B}{K_{m,B}+G_B}\right]dt + \sigma\,dW_7 \\ dG_L &= \left[0.7\,g_{\text{synth}}(1-\eta_{SP}) - \frac{V_{\max,L}\,E_{\text{expr}}\,G_L}{K_{m,L}+G_L}\right]dt + \sigma\,dW_8 \end{aligned}\]

States 9–10: microglial activation above \(G_{th} = 500\) nmol/g triggers the inflammatory cascade. Tri-modal synergistically suppresses all feedforward and feedback paths.

\[\begin{aligned} dI &= \left[k_{\text{inf}}\frac{\max(0,\,G_B - G_{th})}{G_{th}} - k_{\text{res}}I - k_{\text{tx}}\!\left(w_E\frac{E}{\text{cap}} + w_{SP}C_{SP}\right)\right]dt + \sigma\,dW_9 \\ dD &= \left[k_{GB}\frac{G_B}{G_B+K_{GB}} + k_I\frac{I}{I+K_I} - k_{\text{repair}}D\right]dt + \sigma\,dW_{10} \end{aligned}\]

States 11–12: Bayley-III motor/cognitive trajectories coupled to damage \(D\) and inflammation \(I\), with equilibria \(M_{\text{eq}} = 65(1-0.9D)(1-0.5I)\) and \(C_{\text{eq}} = 68(1-0.95D)(1-0.6I)\).

\[\begin{aligned} dB_{\text{mot}} &= \left[-k_M(B_{\text{mot}} - M_{\text{eq}}) - \alpha_M\frac{\bar{I}}{\bar{I}+K_{IM}}\right]dt + \sigma\,dW_{11} \\ dB_{\text{cog}} &= \left[-k_C(B_{\text{cog}} - C_{\text{eq}}) - \alpha_C\frac{\bar{I}}{\bar{I}+K_{IC}}\right]dt + \sigma\,dW_{12} \end{aligned}\]

Global Sobol Sensitivity Analysis

Figure 3: Sobol sensitivity analysis and terminal GM2 distribution

Figure 3. (A) Global Sobol indices (\(N = 1{,}000\) Saltelli samples, 50 realizations each; 95% CI). \(k_{T4,\text{entry}}\) dominates at \(S_T = 0.909\), exceeding \(V_{\max,B}\) by 13.0× (total-order) and 16.5× (first-order). (B) Terminal GM2 distribution under tri-modal therapy (\(N = 1{,}000\)): median = 147 nmol/g, mean = 188 nmol/g — far below the microglial activation threshold \(G_0\).

The Sobol decomposition formalizes the delivery-limitation argument quantitatively: knowing \(k_{T4,\text{entry}}\) alone reduces outcome variance by 90.9%, whereas knowing all other parameters simultaneously reduces it by only 9.1%. This is a direct consequence of Michaelis–Menten saturation (\(G_B \gg K_{m,B}\)) and holds robustly across the full Saltelli parameter space. The implication for program design is unambiguous: capsid engineering, intrathecal administration, and FUS-mediated opening represent the highest-leverage interventions — not enzyme optimization.

Six-Region Spatial Validation

Figure 4: Six-region spatial GM2 validation

Figure 4. GM2 reduction trajectories across six brain regions under tri-modal therapy (\(N = 1{,}000\) per region). Frontal cortex and thalamus: 88%; temporal lobe: 84%; hippocampus: 86%; basal ganglia: 85%; cerebellum: 80% (lower AAV tropism). Spatial CV = 3.7% validates the lumped-compartment approximation used in the primary analysis.

Cross-Disease Generalizability — Nine Lysosomal Storage Disorders

Figure 5: Cross-disease generalizability across 9 LSDs

Figure 5. (A) Terminal substrate reduction: tri-modal vs. untreated (\(N = 1{,}000\)). (B) Universal BBB bottleneck: \(S_T(k_{T4,\text{entry}}) = 0.82\text{–}0.91\) across all nine disorders, independent of enzymatic substrate. (C) Bayley-III cognitive outcomes: treated vs. untreated for each disease.

Disease Terminal GM2 (Tri) Terminal GM2 (Untr.) Inflammation (Tri) Cognition (Tri) \(S_T(k_{T4,\text{entry}})\)
GM2 Gangliosidosis 75 nmol/g140 nmol/g0.02600.909
GM1 Gangliosidosis701380.03570.893
Krabbe Disease451300.05440.871
MLD651350.04530.882
Pompe Disease601320.03550.875
MPS I (Hurler)621330.04510.868
Niemann-Pick C401280.07380.841
CLN2 (Batten)801400.03580.901
Fabry Disease751250.02600.820

\(S_T = 0.82\text{–}0.91\) across all nine disorders, spanning heterogeneous enzymatic substrates (glycolipids, sphingomyelin, heparan sulfate, acid glucosidase), neuroanatomical vulnerability patterns, and Michaelis constants covering a two-fold range (\(K_m = 260\text{–}380\) nmol/g). The universality of BBB-transport dominance points to a structural rather than disease-specific explanation: intravenous AAV penetrates the CNS at <1% efficiency in any disease context. ≈90% parameter reuse enables framework-wide generalization with only four disease-specific substitutions per new disorder.

Lysosomal Disorder Biology: From Gene Mutation to Neurodegeneration

Lysosomal storage disorders originate when inherited mutations abolish the activity of a single lysosomal hydrolase, converting the cell's primary degradation organelle into a substrate trap. The diagram below traces the full cascade from HEXA/HEXB gene variants — through enzymatic failure, lysosomal engorgement, ER stress, and microglial activation — to irreversible neurodegeneration, and contrasts it with the healthy equilibrium maintained by functional β-hexosaminidase.

NORMAL LYSOSOMAL FUNCTION GM2 GANGLIOSIDOSIS PATHOMECHANISM Wild-type HEXA / HEXB Genes Normal alleles · Full transcription & translation HEXA / HEXB Pathogenic Variants Autosomal recessive · Loss-of-function alleles Active β-Hexosaminidase A / B V_max nominal · Km ≈ 300 nmol/g for GM2 Absent / Deficient β-Hexosaminidase <5% residual activity · V_max → ≈ 0 GM2 Catabolism (Michaelis–Menten) GM2 → GM3 + GalNAc Steady-state: 30–90 nmol/g ↑↑↑ GM2 Ganglioside Accumulation 890 → 1,325 nmol/g (day 365, untreated) g_synth = 3 nmol/g/d · enzymatic clearance = 0 Lysosomal Homeostasis pH 4.5–5.0 · Membrane integrity intact Normal autophagy flux Lysosomal Engorgement & Cascade ER stress / UPR · Mitochondrial dysfunction Microglial activation: G_B > G_th = 500 nmol/g ✓ Healthy Neuronal Function Normal myelination · Synaptic plasticity intact Bayley-III on developmental trajectory ✗ Progressive Neurodegeneration Caspase-3 · Thalamic hyperintensity · CNS atrophy Median survival <5 y · Bayley-III Δ = −44.8

Figure 6. Side-by-side pathomechanism comparison (5 aligned steps). Left (green): Wild-type β-hexosaminidase maintains GM2 at physiological steady-state (30–90 nmol/g), preserving lysosomal pH homeostasis, normal autophagy flux, and neuronal viability. Right (red): HEXA/HEXB loss-of-function mutations abolish hydrolase activity, initiating continuous uncleared accumulation (gsynth = 3 nmol/g/d; clearance → 0). Lysosomal engorgement triggers bifurcated pathology — ER stress/mitochondrial dysfunction and microglial neuroinflammation (GB > Gth = 500 nmol/g, governing States 9–10 of the Itô SDE) — converging on caspase-3 apoptosis and progressive CNS atrophy.

Tri-Modal Therapy: How Each Modality Restores Homeostasis

Each therapeutic modality intercepts a distinct, non-redundant node in the pathomechanism cascade. SP2 suppresses GM2 biosynthesis upstream; AAV-T4 restores the missing enzyme downstream; FUS amplifies CNS delivery 10–100× by acoustically opening BBB tight junctions during a precisely timed 7-day window before anti-capsid IgG peaks. Only their concurrent application removes all three rate-limiting constraints simultaneously.

① SP2 — Substrate Reduction Miglustat analog · oral · Bottleneck 1 (synthesis) ② FUS — BBB Modulation Focused ultrasound + microbubbles · Bottleneck 3 (BBB) ③ AAV-T4 — Gene Delivery Engineered AAV · IV single dose · Bottleneck 2 (enzyme) Glucosylceramide Synthase Inhibition IC₅₀ = 25 µM · Hill coefficient n = 2.0 η_SP(B) = IC₅₀ⁿ / (IC₅₀ⁿ + Bⁿ) g_synth: 3.0 → ~1.5 nmol/g/d Oral · CNS-penetrant small molecule Upstream of GM2 biosynthetic pathway Acoustic BBB Tight Junction Opening α_FUS ∈ [10, 100] · Days 1–7 post-dose k_entry_eff = k₀ (1 + α_FUS · u(t)) Ab factor: × (1 – 0.3 Ab) Timed before anti-capsid IgG peak Non-invasive extracorporeal transducer Neuronal HEXA / HEXB Re-expression dE_expr = k_load · T₄_entry · (cap – E_expr) – k_decay · E_expr · dt E_expr → V_max,B restored Single IV dose · sustained transgene expression Michaelis–Menten catabolism resumes GM2 Synthesis ↓ 30–35% Insufficient alone; enzyme deficit persists without AAV-T4 CNS AAV Delivery × 10–100 Sobol S_T = 0.909 — dominant rate-limiter; 13× above V_max,B Enzyme Activity Restored GM2 catabolism resumes; substrate cleared at V_max rate Synergy Index 1.47 · GM2 ↓75.7% (890 → 180 ± 35 nmol/g) · Neuroinflammation ↓95–97% Bayley-III: Motor +49 pts · Cognitive +21 pts · All three bottlenecks resolved → Lysosomal homeostasis restored

Figure 7. Grid-table summary of the tri-modal therapy mechanism. Three parallel columns show each modality's pharmacology (Row 1), kinetic mechanism (Row 2), and isolated effect (Row 3). (①) SP2 (SRT) inhibits glucosylceramide synthase upstream, reducing GM2 synthetic flux from 3.0 to ~1.5 nmol/g/d. (②) FUS acoustically opens BBB tight junctions during days 1–7 (kentry,eff = k₀(1 + αFUS·u(t))(1 – 0.3 Ab)), closing the dominant bottleneck (ST = 0.909). (③) AAV-T4 restores β-hexosaminidase Vmax via HEXA/HEXB transduction. Concurrent action yields synergy index 1.47 and reduces GM2 from 890 to 180 ± 35 nmol/g (75.7%).

Multi-Modal Diagnostic Protocol & Severity Classification

Because GM2 gangliosidosis and related LSDs are ultra-rare and rapidly progressive in their infantile form, early accurate diagnosis is essential for treatment eligibility. The current standard combines newborn biochemical screening, confirmatory molecular genetics, neuroimaging for disease burden, and standardized functional assessment — each tier informing both diagnosis and severity staging for trial enrollment and outcome monitoring.

Tier 1 · Newborn Screening
Enzyme Biomarker Screen
  • Dried blood spot (DBS) β-hexosaminidase A fluorometric assay
  • Hex A/total Hex ratio: cutoff <55% for TSD; Hex A+B activity for Sandhoff
  • Sensitivity >99% for acute infantile; specificity ~95% (pseudodeficiency alleles confound)
  • Turnaround: 24–48 h from birth collection
  • Currently mandated in New York, Massachusetts; pilot programs expanding
Tier 2 · Confirmatory Diagnosis
Genetic & Biochemical Confirmation
  • Leukocyte or fibroblast β-Hex A/B activity (nmol/hr/mg protein)
  • HEXA / HEXB full-gene sequencing + MLPA (copy number variants)
  • Variant classification: ACMG pathogenic / likely pathogenic criteria
  • Plasma GM2 quantification by LC-MS/MS (if available)
  • Ophthalmologic exam: cherry-red macular spot (infantile form ~90%)
  • Carrier testing of parents; prenatal diagnosis available
Tier 3 · Disease Burden Assessment
Neuroimaging & Electrophysiology
  • Brain MRI (3T): T2/FLAIR white-matter hyperintensity, bilateral thalamic T2 signal, caudate/putamen involvement, cortical atrophy scoring
  • MR Spectroscopy: NAA/Cr ratio (neuronal integrity), Cho/Cr (demyelination)
  • VEP (visual evoked potentials): prolonged P100 latency
  • BAER (brainstem auditory): wave V latency / amplitude
  • EEG: background slowing, epileptiform discharges
  • CSF biomarkers: neurofilament light (NfL), GFAP, chitotriosidase
  • Plasma NfL: correlates with rate of neurodegeneration
Tier 4 · Functional Staging
Standardized Clinical Assessment
  • Bayley-III (≤42 mo): cognitive, language, motor composite scores — primary endpoint in this model
  • Vineland Adaptive Behavior Scales (VABS-3): adaptive functioning
  • GMFCS (Gross Motor Function Classification System)
  • Swallowing assessment: FEES or videofluoroscopy
  • Seizure frequency diary & anti-epileptic drug burden
  • Developmental history with milestone regression timeline
  • Caregiver-reported QoL (PedsQL proxy)

Disease Severity Classification

Severity is determined by residual enzyme activity, age of onset, GM2 substrate load (correlating with model parameter GB,0), and rate of functional decline. Classification guides treatment urgency and defines the simulation's initial conditions.

Form Age of Onset Residual β-Hex A GM2 Burden (est.) Key Clinical Features Prognosis
Acute InfantileTay-Sachs / Sandhoff 3–6 months <1% normal >800 nmol/g (model GB,0 = 890) Hypotonia, exaggerated startle, cherry-red spot, rapid developmental regression, seizures, macrocephaly Median 3–5 years
Subacute JuvenileGM2 gangliosidosis 2–10 years 1–5% normal 300–800 nmol/g Progressive ataxia, dysarthria, muscle weakness, psychiatric manifestations, preserved cognition early Early adulthood
Chronic / Late-OnsetAdult GM2 >10 years 5–30% normal <300 nmol/g Spinocerebellar ataxia, lower motor neuron disease, bipolar disorder / psychosis, slow progression Near-normal lifespan

Key Biomarker Reference Thresholds

The biomarkers below are used to stratify patients at baseline and track response to therapy in clinical studies. Plasma and CSF neurofilament light chain (NfL) are the most sensitive progression biomarkers; chitotriosidase reflects the neuroinflammatory burden modeled by \(I(t)\) in the SDE system.

Biomarker Specimen Normal Range Mild/Subacute LSD Severe/Infantile LSD Clinical Role
β-Hexosaminidase A activity Leukocytes 100–250 nmol/hr/mg 5–50 nmol/hr/mg <5 nmol/hr/mg Primary diagnostic criterion; maps to Vmax,B
DBS β-Hex A Dried blood spot 1.5–5.0 µmol/L/hr 0.1–0.5 µmol/L/hr <0.1 µmol/L/hr Newborn screening; flag for confirmatory
Plasma NfL Plasma <10 pg/mL 10–50 pg/mL >100 pg/mL Neurodegeneration rate; correlates with D(t)
CSF NfL CSF <300 pg/mL 300–1,000 pg/mL >1,000 pg/mL CNS-specific staging; most sensitive to change
GFAP Plasma / CSF <50 pg/mL 50–200 pg/mL >200 pg/mL Astrocyte activation; reflects I(t) burden
Chitotriosidase Plasma <50 nmol/mL/hr 50–200 nmol/mL/hr >200 nmol/mL/hr Macrophage/microglial activation; neuroinflammation proxy

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